diff --git a/packages/CLPBN/clpbn/bp/out.damping.txt b/packages/CLPBN/clpbn/bp/out.damping.txt deleted file mode 100644 index 1955ef29f..000000000 --- a/packages/CLPBN/clpbn/bp/out.damping.txt +++ /dev/null @@ -1,21187 +0,0 @@ -Variable: Burglar -Domain: b1, b2 -Parents: -Childs: Alarm -cpt ----------------- -b1 0.005 -b2 0.995 - -Variable: FreightTruck -Domain: f1, f2 -Parents: -Childs: Alarm -cpt ----------------- -f1 0.03 -f2 0.97 - -Variable: Alarm -Domain: a1, a2 -Parents: Burglar, FreightTruck -Childs: -cpt b1,f1 b1,f2 b2,f1 b2,f2 ----------------------------------------------------- -a1 0.992 0.99 0.2 0.003 -a2 0.008 0.01 0.8 0.997 - -Variable: Burglar -Domain: b1, b2 -Parents: -Childs: Alarm -cpt ----------------- -b1 0.005 -b2 0.995 - -Variable: FreightTruck -Domain: f1, f2 -Parents: -Childs: Alarm, _Jn -cpt ----------------- -f1 0.03 -f2 0.97 - -Variable: Alarm -Domain: a1, a2 -Parents: Burglar, FreightTruck -Childs: _Jn -cpt b1,f1 b1,f2 b2,f1 b2,f2 ----------------------------------------------------- -a1 0.992 0.99 0.2 0.003 -a2 0.008 0.01 0.8 0.997 - -Variable: _Jn -Domain: _jn0, _jn1, _jn2, _jn3 -Parents: FreightTruck, Alarm -Childs: -cpt f1,a1 f1,a2 f2,a1 f2,a2 ----------------------------------------------------- -_jn0 1 0 0 0 -_jn1 0 1 0 0 -_jn2 0 0 1 0 -_jn3 0 0 0 1 - -The graph is not single connected. Iterative belief propagation will be used. - -Initializing solver --> schedule = parallel --> max iters = 150 --> stable threashold = 1e-20 --> query vars = FreightTruck Alarm -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 1 1 0.5 -b2 1 1 0.5 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.5 0.5 -b2 0.5 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 1 1 0.5 -f2 1 1 0.5 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.5 0.5 -f2 0.5 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.5 0.5 -f2 0.5 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 1 1 0.5 -a2 1 1 0.5 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.5 0.5 -a2 0.5 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 1 1 0.25 -_jn1 1 1 0.25 -_jn2 1 1 0.25 -_jn3 1 1 0.25 - - - -******************************************************************************** - Iteration 1 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.5) + (0.99x0.5)]x1 -+ [(0.008x0.5) + (0.01x0.5)]x1 = 1 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.5) + (0.003x0.5)]x1 -+ [(0.8x0.5) + (0.997x0.5)]x1 = 1 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.5) + (0.2x0.5)]x1 -+ [(0.008x0.5) + (0.8x0.5)]x1 = 1 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.5) + (0.003x0.5)]x1 -+ [(0.01x0.5) + (0.997x0.5)]x1 = 1 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.5) + (0x0.5)]x1 -+ [(0x0.5) + (1x0.5)]x1 -+ [(0x0.5) + (0x0.5)]x1 -+ [(0x0.5) + (0x0.5)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.5) + (0x0.5)]x1 -+ [(0x0.5) + (0x0.5)]x1 -+ [(1x0.5) + (0x0.5)]x1 -+ [(0x0.5) + (1x0.5)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.5) + (0x0.5)]x1 -+ [(0x0.5) + (0x0.5)]x1 -+ [(0x0.5) + (1x0.5)]x1 -+ [(0x0.5) + (0x0.5)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.5) + (0x0.5)]x1 -+ [(1x0.5) + (0x0.5)]x1 -+ [(0x0.5) + (0x0.5)]x1 -+ [(0x0.5) + (1x0.5)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 1 = 1 -π_Jn(a2) = π(a2) = 1 = 1 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 1 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 1 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.2525x0.343333) -+ (0.99x0.2525x0.656667) -+ (0.2x0.7475x0.343333) -+ (0.003x0.7475x0.656667) = 0.3029492917 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.2525x0.343333) -+ (0.01x0.2525x0.656667) -+ (0.8x0.7475x0.343333) -+ (0.997x0.7475x0.656667) = 0.6970507083 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 1 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.343333x0.5) -+ (0x0.343333x0.5) -+ (0x0.656667x0.5) -+ (0x0.656667x0.5) = 0.1716666667 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.343333x0.5) -+ (1x0.343333x0.5) -+ (0x0.656667x0.5) -+ (0x0.656667x0.5) = 0.1716666667 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.343333x0.5) -+ (0x0.343333x0.5) -+ (1x0.656667x0.5) -+ (0x0.656667x0.5) = 0.3283333333 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.343333x0.5) -+ (0x0.343333x0.5) -+ (0x0.656667x0.5) -+ (1x0.656667x0.5) = 0.3283333333 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 1 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.2525 0.5 -b2 0.7475 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.3433333333 0.5 -f2 0.6566666667 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.3433333333 0.5 -f2 0.6566666667 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.3029492917 0.5 0.3029492917 -a2 0.6970507083 0.5 0.6970507083 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.5 0.5 -a2 0.5 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.1716666667 1 0.1716666667 -_jn1 0.1716666667 1 0.1716666667 -_jn2 0.3283333333 1 0.3283333333 -_jn3 0.3283333333 1 0.3283333333 - - - -******************************************************************************** - Iteration 2 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.343333) + (0.99x0.656667)]x0.5 -+ [(0.008x0.343333) + (0.01x0.656667)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.343333) + (0.003x0.656667)]x0.5 -+ [(0.8x0.343333) + (0.997x0.656667)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.2525) + (0.2x0.7475)]x0.5 -+ [(0.008x0.2525) + (0.8x0.7475)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.2525) + (0.003x0.7475)]x0.5 -+ [(0.01x0.2525) + (0.997x0.7475)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.5) + (0x0.5)]x1 -+ [(0x0.5) + (1x0.5)]x1 -+ [(0x0.5) + (0x0.5)]x1 -+ [(0x0.5) + (0x0.5)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.5) + (0x0.5)]x1 -+ [(0x0.5) + (0x0.5)]x1 -+ [(1x0.5) + (0x0.5)]x1 -+ [(0x0.5) + (1x0.5)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.343333) + (0x0.656667)]x1 -+ [(0x0.343333) + (0x0.656667)]x1 -+ [(0x0.343333) + (1x0.656667)]x1 -+ [(0x0.343333) + (0x0.656667)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.343333) + (0x0.656667)]x1 -+ [(1x0.343333) + (0x0.656667)]x1 -+ [(0x0.343333) + (0x0.656667)]x1 -+ [(0x0.343333) + (1x0.656667)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.302949 = 0.3029492917 -π_Jn(a2) = π(a2) = 0.697051 = 0.6970507083 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 8.67361738e-19 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.12875x0.238889) -+ (0.99x0.12875x0.761111) -+ (0.2x0.87125x0.238889) -+ (0.003x0.87125x0.761111) = 0.1711397569 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.12875x0.238889) -+ (0.01x0.12875x0.761111) -+ (0.8x0.87125x0.238889) -+ (0.997x0.87125x0.761111) = 0.8288602431 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 0.2636190694 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.238889x0.401475) -+ (0x0.238889x0.598525) -+ (0x0.761111x0.401475) -+ (0x0.761111x0.598525) = 0.09590783206 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.238889x0.401475) -+ (1x0.238889x0.598525) -+ (0x0.761111x0.401475) -+ (0x0.761111x0.598525) = 0.1429810568 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.238889x0.401475) -+ (0x0.238889x0.598525) -+ (1x0.761111x0.401475) -+ (0x0.761111x0.598525) = 0.3055668138 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.238889x0.401475) -+ (0x0.238889x0.598525) -+ (0x0.761111x0.401475) -+ (1x0.761111x0.598525) = 0.4555442973 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 0.254421928 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.12875 0.5 -b2 0.87125 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.2388888889 0.5 -f2 0.7611111111 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.2388888889 0.5 -f2 0.7611111111 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.1711397569 0.5 0.1711397569 -a2 0.8288602431 0.5 0.8288602431 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.4014746458 0.5 -a2 0.5985253542 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.09590783206 1 0.09590783206 -_jn1 0.1429810568 1 0.1429810568 -_jn2 0.3055668138 1 0.3055668138 -_jn3 0.4555442973 1 0.4555442973 - - - -******************************************************************************** - Iteration 3 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.238889) + (0.99x0.761111)]x0.5 -+ [(0.008x0.238889) + (0.01x0.761111)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.238889) + (0.003x0.761111)]x0.5 -+ [(0.8x0.238889) + (0.997x0.761111)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.12875) + (0.2x0.87125)]x0.5 -+ [(0.008x0.12875) + (0.8x0.87125)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.12875) + (0.003x0.87125)]x0.5 -+ [(0.01x0.12875) + (0.997x0.87125)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.401475) + (0x0.598525)]x1 -+ [(0x0.401475) + (1x0.598525)]x1 -+ [(0x0.401475) + (0x0.598525)]x1 -+ [(0x0.401475) + (0x0.598525)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.401475) + (0x0.598525)]x1 -+ [(0x0.401475) + (0x0.598525)]x1 -+ [(1x0.401475) + (0x0.598525)]x1 -+ [(0x0.401475) + (1x0.598525)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.238889) + (0x0.761111)]x1 -+ [(0x0.238889) + (0x0.761111)]x1 -+ [(0x0.238889) + (1x0.761111)]x1 -+ [(0x0.238889) + (0x0.761111)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.238889) + (0x0.761111)]x1 -+ [(1x0.238889) + (0x0.761111)]x1 -+ [(0x0.238889) + (0x0.761111)]x1 -+ [(0x0.238889) + (1x0.761111)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.17114 = 0.1711397569 -π_Jn(a2) = π(a2) = 0.82886 = 0.8288602431 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 8.67361738e-19 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.066875x0.169259) -+ (0.99x0.066875x0.830741) -+ (0.2x0.933125x0.169259) -+ (0.003x0.933125x0.830741) = 0.1001424525 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.066875x0.169259) -+ (0.01x0.066875x0.830741) -+ (0.8x0.933125x0.169259) -+ (0.997x0.933125x0.830741) = 0.8998575475 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 0.1419946088 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.169259x0.286307) -+ (0x0.169259x0.713693) -+ (0x0.830741x0.286307) -+ (0x0.830741x0.713693) = 0.04846014483 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.169259x0.286307) -+ (1x0.169259x0.713693) -+ (0x0.830741x0.286307) -+ (0x0.830741x0.713693) = 0.1207991144 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.169259x0.286307) -+ (0x0.169259x0.713693) -+ (1x0.830741x0.286307) -+ (0x0.830741x0.713693) = 0.2378470566 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.169259x0.286307) -+ (0x0.169259x0.713693) -+ (0x0.830741x0.286307) -+ (1x0.830741x0.713693) = 0.5928936842 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 0.2746987737 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.066875 0.5 -b2 0.933125 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.1692592593 0.5 -f2 0.8307407407 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.1692592593 0.5 -f2 0.8307407407 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.1001424525 0.5 0.1001424525 -a2 0.8998575475 0.5 0.8998575475 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.2863072014 0.5 -a2 0.7136927986 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.04846014483 1 0.04846014483 -_jn1 0.1207991144 1 0.1207991144 -_jn2 0.2378470566 1 0.2378470566 -_jn3 0.5928936842 1 0.5928936842 - - - -******************************************************************************** - Iteration 4 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.169259) + (0.99x0.830741)]x0.5 -+ [(0.008x0.169259) + (0.01x0.830741)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.169259) + (0.003x0.830741)]x0.5 -+ [(0.8x0.169259) + (0.997x0.830741)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.066875) + (0.2x0.933125)]x0.5 -+ [(0.008x0.066875) + (0.8x0.933125)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.066875) + (0.003x0.933125)]x0.5 -+ [(0.01x0.066875) + (0.997x0.933125)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.286307) + (0x0.713693)]x1 -+ [(0x0.286307) + (1x0.713693)]x1 -+ [(0x0.286307) + (0x0.713693)]x1 -+ [(0x0.286307) + (0x0.713693)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.286307) + (0x0.713693)]x1 -+ [(0x0.286307) + (0x0.713693)]x1 -+ [(1x0.286307) + (0x0.713693)]x1 -+ [(0x0.286307) + (1x0.713693)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.169259) + (0x0.830741)]x1 -+ [(0x0.169259) + (0x0.830741)]x1 -+ [(0x0.169259) + (1x0.830741)]x1 -+ [(0x0.169259) + (0x0.830741)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.169259) + (0x0.830741)]x1 -+ [(1x0.169259) + (0x0.830741)]x1 -+ [(0x0.169259) + (0x0.830741)]x1 -+ [(0x0.169259) + (1x0.830741)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.100142 = 0.1001424525 -π_Jn(a2) = π(a2) = 0.899858 = 0.8998575475 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.0359375x0.12284) -+ (0.99x0.0359375x0.87716) -+ (0.2x0.964063x0.12284) -+ (0.003x0.964063x0.87716) = 0.06180885899 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.0359375x0.12284) -+ (0.01x0.0359375x0.87716) -+ (0.8x0.964063x0.12284) -+ (0.997x0.964063x0.87716) = 0.938191141 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 0.07666718711 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.12284x0.193225) -+ (0x0.12284x0.806775) -+ (0x0.87716x0.193225) -+ (0x0.87716x0.806775) = 0.02373564233 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.12284x0.193225) -+ (1x0.12284x0.806775) -+ (0x0.87716x0.193225) -+ (0x0.87716x0.806775) = 0.09910386385 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.12284x0.193225) -+ (0x0.12284x0.806775) -+ (1x0.87716x0.193225) -+ (0x0.87716x0.806775) = 0.1694891846 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.12284x0.193225) -+ (0x0.12284x0.806775) -+ (0x0.87716x0.193225) -+ (1x0.87716x0.806775) = 0.7076713092 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 0.22955525 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.0359375 0.5 -b2 0.9640625 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.1228395062 0.5 -f2 0.8771604938 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.1228395062 0.5 -f2 0.8771604938 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.06180885899 0.5 0.06180885899 -a2 0.938191141 0.5 0.938191141 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.193224827 0.5 -a2 0.806775173 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.02373564233 1 0.02373564233 -_jn1 0.09910386385 1 0.09910386385 -_jn2 0.1694891846 1 0.1694891846 -_jn3 0.7076713092 1 0.7076713092 - - - -******************************************************************************** - Iteration 5 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.12284) + (0.99x0.87716)]x0.5 -+ [(0.008x0.12284) + (0.01x0.87716)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.12284) + (0.003x0.87716)]x0.5 -+ [(0.8x0.12284) + (0.997x0.87716)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.0359375) + (0.2x0.964063)]x0.5 -+ [(0.008x0.0359375) + (0.8x0.964063)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.0359375) + (0.003x0.964063)]x0.5 -+ [(0.01x0.0359375) + (0.997x0.964063)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.193225) + (0x0.806775)]x1 -+ [(0x0.193225) + (1x0.806775)]x1 -+ [(0x0.193225) + (0x0.806775)]x1 -+ [(0x0.193225) + (0x0.806775)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.193225) + (0x0.806775)]x1 -+ [(0x0.193225) + (0x0.806775)]x1 -+ [(1x0.193225) + (0x0.806775)]x1 -+ [(0x0.193225) + (1x0.806775)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.12284) + (0x0.87716)]x1 -+ [(0x0.12284) + (0x0.87716)]x1 -+ [(0x0.12284) + (1x0.87716)]x1 -+ [(0x0.12284) + (0x0.87716)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.12284) + (0x0.87716)]x1 -+ [(1x0.12284) + (0x0.87716)]x1 -+ [(0x0.12284) + (0x0.87716)]x1 -+ [(0x0.12284) + (1x0.87716)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0618089 = 0.06180885899 -π_Jn(a2) = π(a2) = 0.938191 = 0.938191141 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.0204688x0.091893) -+ (0.99x0.0204688x0.908107) -+ (0.2x0.979531x0.091893) -+ (0.003x0.979531x0.908107) = 0.04093879575 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.0204688x0.091893) -+ (0.01x0.0204688x0.908107) -+ (0.8x0.979531x0.091893) -+ (0.997x0.979531x0.908107) = 0.9590612043 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 0.04174012648 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.091893x0.127517) -+ (0x0.091893x0.872483) -+ (0x0.908107x0.127517) -+ (0x0.908107x0.872483) = 0.01171790578 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.091893x0.127517) -+ (1x0.091893x0.872483) -+ (0x0.908107x0.127517) -+ (0x0.908107x0.872483) = 0.08017509834 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.091893x0.127517) -+ (0x0.091893x0.872483) -+ (1x0.908107x0.127517) -+ (0x0.908107x0.872483) = 0.1157989372 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.091893x0.127517) -+ (0x0.091893x0.872483) -+ (0x0.908107x0.127517) -+ (1x0.908107x0.872483) = 0.7923080587 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 0.169273499 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.02046875 0.5 -b2 0.97953125 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.09189300412 0.5 -f2 0.9081069959 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.09189300412 0.5 -f2 0.9081069959 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.04093879575 0.5 0.04093879575 -a2 0.9590612043 0.5 0.9590612043 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.127516843 0.5 -a2 0.872483157 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.01171790578 1 0.01171790578 -_jn1 0.08017509834 1 0.08017509834 -_jn2 0.1157989372 1 0.1157989372 -_jn3 0.7923080587 1 0.7923080587 - - - -******************************************************************************** - Iteration 6 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.091893) + (0.99x0.908107)]x0.5 -+ [(0.008x0.091893) + (0.01x0.908107)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.091893) + (0.003x0.908107)]x0.5 -+ [(0.8x0.091893) + (0.997x0.908107)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.0204688) + (0.2x0.979531)]x0.5 -+ [(0.008x0.0204688) + (0.8x0.979531)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.0204688) + (0.003x0.979531)]x0.5 -+ [(0.01x0.0204688) + (0.997x0.979531)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.127517) + (0x0.872483)]x1 -+ [(0x0.127517) + (1x0.872483)]x1 -+ [(0x0.127517) + (0x0.872483)]x1 -+ [(0x0.127517) + (0x0.872483)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.127517) + (0x0.872483)]x1 -+ [(0x0.127517) + (0x0.872483)]x1 -+ [(1x0.127517) + (0x0.872483)]x1 -+ [(0x0.127517) + (1x0.872483)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.091893) + (0x0.908107)]x1 -+ [(0x0.091893) + (0x0.908107)]x1 -+ [(0x0.091893) + (1x0.908107)]x1 -+ [(0x0.091893) + (0x0.908107)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.091893) + (0x0.908107)]x1 -+ [(1x0.091893) + (0x0.908107)]x1 -+ [(0x0.091893) + (0x0.908107)]x1 -+ [(0x0.091893) + (1x0.908107)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0409388 = 0.04093879575 -π_Jn(a2) = π(a2) = 0.959061 = 0.9590612043 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.0127344x0.071262) -+ (0.99x0.0127344x0.928738) -+ (0.2x0.987266x0.071262) -+ (0.003x0.987266x0.928738) = 0.02943048464 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.0127344x0.071262) -+ (0.01x0.0127344x0.928738) -+ (0.8x0.987266x0.071262) -+ (0.997x0.987266x0.928738) = 0.9705695154 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 0.02301662222 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.071262x0.0842278) -+ (0x0.071262x0.915772) -+ (0x0.928738x0.0842278) -+ (0x0.928738x0.915772) = 0.006002243095 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.071262x0.0842278) -+ (1x0.071262x0.915772) -+ (0x0.928738x0.0842278) -+ (0x0.928738x0.915772) = 0.06525975965 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.071262x0.0842278) -+ (0x0.071262x0.915772) -+ (1x0.928738x0.0842278) -+ (0x0.928738x0.915772) = 0.07822557627 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.071262x0.0842278) -+ (0x0.071262x0.915772) -+ (0x0.928738x0.0842278) -+ (1x0.928738x0.915772) = 0.850512421 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 0.1164087246 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.012734375 0.5 -b2 0.987265625 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.07126200274 0.5 -f2 0.9287379973 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.07126200274 0.5 -f2 0.9287379973 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.02943048464 0.5 0.02943048464 -a2 0.9705695154 0.5 0.9705695154 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.08422781936 0.5 -a2 0.9157721806 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.006002243095 1 0.006002243095 -_jn1 0.06525975965 1 0.06525975965 -_jn2 0.07822557627 1 0.07822557627 -_jn3 0.850512421 1 0.850512421 - - - -******************************************************************************** - Iteration 7 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.071262) + (0.99x0.928738)]x0.5 -+ [(0.008x0.071262) + (0.01x0.928738)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.071262) + (0.003x0.928738)]x0.5 -+ [(0.8x0.071262) + (0.997x0.928738)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.0127344) + (0.2x0.987266)]x0.5 -+ [(0.008x0.0127344) + (0.8x0.987266)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.0127344) + (0.003x0.987266)]x0.5 -+ [(0.01x0.0127344) + (0.997x0.987266)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0842278) + (0x0.915772)]x1 -+ [(0x0.0842278) + (1x0.915772)]x1 -+ [(0x0.0842278) + (0x0.915772)]x1 -+ [(0x0.0842278) + (0x0.915772)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0842278) + (0x0.915772)]x1 -+ [(0x0.0842278) + (0x0.915772)]x1 -+ [(1x0.0842278) + (0x0.915772)]x1 -+ [(0x0.0842278) + (1x0.915772)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.071262) + (0x0.928738)]x1 -+ [(0x0.071262) + (0x0.928738)]x1 -+ [(0x0.071262) + (1x0.928738)]x1 -+ [(0x0.071262) + (0x0.928738)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.071262) + (0x0.928738)]x1 -+ [(1x0.071262) + (0x0.928738)]x1 -+ [(0x0.071262) + (0x0.928738)]x1 -+ [(0x0.071262) + (1x0.928738)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0294305 = 0.02943048464 -π_Jn(a2) = π(a2) = 0.97057 = 0.9705695154 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.00886719x0.057508) -+ (0.99x0.00886719x0.942492) -+ (0.2x0.991133x0.057508) -+ (0.003x0.991133x0.942492) = 0.02298155325 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.00886719x0.057508) -+ (0.01x0.00886719x0.942492) -+ (0.8x0.991133x0.057508) -+ (0.997x0.991133x0.942492) = 0.9770184468 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 0.01289786278 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.057508x0.0568292) -+ (0x0.057508x0.943171) -+ (0x0.942492x0.0568292) -+ (0x0.942492x0.943171) = 0.003268130977 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.057508x0.0568292) -+ (1x0.057508x0.943171) -+ (0x0.942492x0.0568292) -+ (0x0.942492x0.943171) = 0.05423987085 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.057508x0.0568292) -+ (0x0.057508x0.943171) -+ (1x0.942492x0.0568292) -+ (0x0.942492x0.943171) = 0.05356102102 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.057508x0.0568292) -+ (0x0.057508x0.943171) -+ (0x0.942492x0.0568292) -+ (1x0.942492x0.943171) = 0.8889309771 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 0.07683711232 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.0088671875 0.5 -b2 0.9911328125 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.05750800183 0.5 -f2 0.9424919982 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.05750800183 0.5 -f2 0.9424919982 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.02298155325 0.5 0.02298155325 -a2 0.9770184468 0.5 0.9770184468 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.056829152 0.5 -a2 0.943170848 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.003268130977 1 0.003268130977 -_jn1 0.05423987085 1 0.05423987085 -_jn2 0.05356102102 1 0.05356102102 -_jn3 0.8889309771 1 0.8889309771 - - - -******************************************************************************** - Iteration 8 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.057508) + (0.99x0.942492)]x0.5 -+ [(0.008x0.057508) + (0.01x0.942492)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.057508) + (0.003x0.942492)]x0.5 -+ [(0.8x0.057508) + (0.997x0.942492)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.00886719) + (0.2x0.991133)]x0.5 -+ [(0.008x0.00886719) + (0.8x0.991133)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.00886719) + (0.003x0.991133)]x0.5 -+ [(0.01x0.00886719) + (0.997x0.991133)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0568292) + (0x0.943171)]x1 -+ [(0x0.0568292) + (1x0.943171)]x1 -+ [(0x0.0568292) + (0x0.943171)]x1 -+ [(0x0.0568292) + (0x0.943171)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0568292) + (0x0.943171)]x1 -+ [(0x0.0568292) + (0x0.943171)]x1 -+ [(1x0.0568292) + (0x0.943171)]x1 -+ [(0x0.0568292) + (1x0.943171)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.057508) + (0x0.942492)]x1 -+ [(0x0.057508) + (0x0.942492)]x1 -+ [(0x0.057508) + (1x0.942492)]x1 -+ [(0x0.057508) + (0x0.942492)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.057508) + (0x0.942492)]x1 -+ [(1x0.057508) + (0x0.942492)]x1 -+ [(0x0.057508) + (0x0.942492)]x1 -+ [(0x0.057508) + (1x0.942492)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0229816 = 0.02298155325 -π_Jn(a2) = π(a2) = 0.977018 = 0.9770184468 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.00693359x0.0483387) -+ (0.99x0.00693359x0.951661) -+ (0.2x0.993066x0.0483387) -+ (0.003x0.993066x0.951661) = 0.01930081827 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.00693359x0.0483387) -+ (0.01x0.00693359x0.951661) -+ (0.8x0.993066x0.0483387) -+ (0.997x0.993066x0.951661) = 0.9806991817 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 0.007361469952 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.0483387x0.0399054) -+ (0x0.0483387x0.960095) -+ (0x0.951661x0.0399054) -+ (0x0.951661x0.960095) = 0.001928971587 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0483387x0.0399054) -+ (1x0.0483387x0.960095) -+ (0x0.951661x0.0399054) -+ (0x0.951661x0.960095) = 0.0464096963 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0483387x0.0399054) -+ (0x0.0483387x0.960095) -+ (1x0.951661x0.0399054) -+ (0x0.951661x0.960095) = 0.03797638104 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0483387x0.0399054) -+ (0x0.0483387x0.960095) -+ (0x0.951661x0.0399054) -+ (1x0.951661x0.960095) = 0.9136849511 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 0.04950794786 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.00693359375 0.5 -b2 0.9930664063 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.04833866789 0.5 -f2 0.9516613321 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.04833866789 0.5 -f2 0.9516613321 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01930081827 0.5 0.01930081827 -a2 0.9806991817 0.5 0.9806991817 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.03990535262 0.5 -a2 0.9600946474 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.001928971587 1 0.001928971587 -_jn1 0.0464096963 1 0.0464096963 -_jn2 0.03797638104 1 0.03797638104 -_jn3 0.9136849511 1 0.9136849511 - - - -******************************************************************************** - Iteration 9 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.0483387) + (0.99x0.951661)]x0.5 -+ [(0.008x0.0483387) + (0.01x0.951661)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.0483387) + (0.003x0.951661)]x0.5 -+ [(0.8x0.0483387) + (0.997x0.951661)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.00693359) + (0.2x0.993066)]x0.5 -+ [(0.008x0.00693359) + (0.8x0.993066)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.00693359) + (0.003x0.993066)]x0.5 -+ [(0.01x0.00693359) + (0.997x0.993066)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0399054) + (0x0.960095)]x1 -+ [(0x0.0399054) + (1x0.960095)]x1 -+ [(0x0.0399054) + (0x0.960095)]x1 -+ [(0x0.0399054) + (0x0.960095)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0399054) + (0x0.960095)]x1 -+ [(0x0.0399054) + (0x0.960095)]x1 -+ [(1x0.0399054) + (0x0.960095)]x1 -+ [(0x0.0399054) + (1x0.960095)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.0483387) + (0x0.951661)]x1 -+ [(0x0.0483387) + (0x0.951661)]x1 -+ [(0x0.0483387) + (1x0.951661)]x1 -+ [(0x0.0483387) + (0x0.951661)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.0483387) + (0x0.951661)]x1 -+ [(1x0.0483387) + (0x0.951661)]x1 -+ [(0x0.0483387) + (0x0.951661)]x1 -+ [(0x0.0483387) + (1x0.951661)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0193008 = 0.01930081827 -π_Jn(a2) = π(a2) = 0.980699 = 0.9806991817 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.0059668x0.0422258) -+ (0.99x0.0059668x0.957774) -+ (0.2x0.994033x0.0422258) -+ (0.003x0.994033x0.957774) = 0.01715857613 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.0059668x0.0422258) -+ (0.01x0.0059668x0.957774) -+ (0.8x0.994033x0.0422258) -+ (0.997x0.994033x0.957774) = 0.9828414239 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 0.004284484277 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.0422258x0.0296031) -+ (0x0.0422258x0.970397) -+ (0x0.957774x0.0296031) -+ (0x0.957774x0.970397) = 0.001250013332 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0422258x0.0296031) -+ (1x0.0422258x0.970397) -+ (0x0.957774x0.0296031) -+ (0x0.957774x0.970397) = 0.04097576526 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0422258x0.0296031) -+ (0x0.0422258x0.970397) -+ (1x0.957774x0.0296031) -+ (0x0.957774x0.970397) = 0.02835307212 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0422258x0.0296031) -+ (0x0.0422258x0.970397) -+ (0x0.957774x0.0296031) -+ (1x0.957774x0.970397) = 0.9294211493 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 0.03147239643 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005966796875 0.5 -b2 0.9940332031 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.04222577859 0.5 -f2 0.9577742214 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.04222577859 0.5 -f2 0.9577742214 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01715857613 0.5 0.01715857613 -a2 0.9828414239 0.5 0.9828414239 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.02960308545 0.5 -a2 0.9703969146 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.001250013332 1 0.001250013332 -_jn1 0.04097576526 1 0.04097576526 -_jn2 0.02835307212 1 0.02835307212 -_jn3 0.9294211493 1 0.9294211493 - - - -******************************************************************************** - Iteration 10 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.0422258) + (0.99x0.957774)]x0.5 -+ [(0.008x0.0422258) + (0.01x0.957774)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.0422258) + (0.003x0.957774)]x0.5 -+ [(0.8x0.0422258) + (0.997x0.957774)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.0059668) + (0.2x0.994033)]x0.5 -+ [(0.008x0.0059668) + (0.8x0.994033)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.0059668) + (0.003x0.994033)]x0.5 -+ [(0.01x0.0059668) + (0.997x0.994033)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0296031) + (0x0.970397)]x1 -+ [(0x0.0296031) + (1x0.970397)]x1 -+ [(0x0.0296031) + (0x0.970397)]x1 -+ [(0x0.0296031) + (0x0.970397)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0296031) + (0x0.970397)]x1 -+ [(0x0.0296031) + (0x0.970397)]x1 -+ [(1x0.0296031) + (0x0.970397)]x1 -+ [(0x0.0296031) + (1x0.970397)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.0422258) + (0x0.957774)]x1 -+ [(0x0.0422258) + (0x0.957774)]x1 -+ [(0x0.0422258) + (1x0.957774)]x1 -+ [(0x0.0422258) + (0x0.957774)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.0422258) + (0x0.957774)]x1 -+ [(1x0.0422258) + (0x0.957774)]x1 -+ [(0x0.0422258) + (0x0.957774)]x1 -+ [(0x0.0422258) + (1x0.957774)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0171586 = 0.01715857613 -π_Jn(a2) = π(a2) = 0.982841 = 0.9828414239 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.0054834x0.0381505) -+ (0.99x0.0054834x0.961849) -+ (0.2x0.994517x0.0381505) -+ (0.003x0.994517x0.961849) = 0.01588697359 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.0054834x0.0381505) -+ (0.01x0.0054834x0.961849) -+ (0.8x0.994517x0.0381505) -+ (0.997x0.994517x0.961849) = 0.9841130264 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 0.002543205093 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.0381505x0.0233808) -+ (0x0.0381505x0.976619) -+ (0x0.961849x0.0233808) -+ (0x0.961849x0.976619) = 0.0008919908307 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0381505x0.0233808) -+ (1x0.0381505x0.976619) -+ (0x0.961849x0.0233808) -+ (0x0.961849x0.976619) = 0.03725852823 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0381505x0.0233808) -+ (0x0.0381505x0.976619) -+ (1x0.961849x0.0233808) -+ (0x0.961849x0.976619) = 0.02248883996 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0381505x0.0233808) -+ (0x0.0381505x0.976619) -+ (0x0.961849x0.0233808) -+ (1x0.961849x0.976619) = 0.939360641 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 0.01987898337 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005483398438 0.5 -b2 0.9945166016 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03815051906 0.5 -f2 0.9618494809 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03815051906 0.5 -f2 0.9618494809 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01588697359 0.5 0.01588697359 -a2 0.9841130264 0.5 0.9841130264 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.02338083079 0.5 -a2 0.9766191692 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0008919908307 1 0.0008919908307 -_jn1 0.03725852823 1 0.03725852823 -_jn2 0.02248883996 1 0.02248883996 -_jn3 0.939360641 1 0.939360641 - - - -******************************************************************************** - Iteration 11 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.0381505) + (0.99x0.961849)]x0.5 -+ [(0.008x0.0381505) + (0.01x0.961849)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.0381505) + (0.003x0.961849)]x0.5 -+ [(0.8x0.0381505) + (0.997x0.961849)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.0054834) + (0.2x0.994517)]x0.5 -+ [(0.008x0.0054834) + (0.8x0.994517)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.0054834) + (0.003x0.994517)]x0.5 -+ [(0.01x0.0054834) + (0.997x0.994517)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0233808) + (0x0.976619)]x1 -+ [(0x0.0233808) + (1x0.976619)]x1 -+ [(0x0.0233808) + (0x0.976619)]x1 -+ [(0x0.0233808) + (0x0.976619)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0233808) + (0x0.976619)]x1 -+ [(0x0.0233808) + (0x0.976619)]x1 -+ [(1x0.0233808) + (0x0.976619)]x1 -+ [(0x0.0233808) + (1x0.976619)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.0381505) + (0x0.961849)]x1 -+ [(0x0.0381505) + (0x0.961849)]x1 -+ [(0x0.0381505) + (1x0.961849)]x1 -+ [(0x0.0381505) + (0x0.961849)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.0381505) + (0x0.961849)]x1 -+ [(1x0.0381505) + (0x0.961849)]x1 -+ [(0x0.0381505) + (0x0.961849)]x1 -+ [(0x0.0381505) + (1x0.961849)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.015887 = 0.01588697359 -π_Jn(a2) = π(a2) = 0.984113 = 0.9841130264 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.0052417x0.0354337) -+ (0.99x0.0052417x0.964566) -+ (0.2x0.994758x0.0354337) -+ (0.003x0.994758x0.964566) = 0.01511777409 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.0052417x0.0354337) -+ (0.01x0.0052417x0.964566) -+ (0.8x0.994758x0.0354337) -+ (0.997x0.994758x0.964566) = 0.9848822259 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 0.00153839899 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.0354337x0.0196339) -+ (0x0.0354337x0.980366) -+ (0x0.964566x0.0196339) -+ (0x0.964566x0.980366) = 0.000695701395 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0354337x0.0196339) -+ (1x0.0354337x0.980366) -+ (0x0.964566x0.0196339) -+ (0x0.964566x0.980366) = 0.03473797798 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0354337x0.0196339) -+ (0x0.0354337x0.980366) -+ (1x0.964566x0.0196339) -+ (0x0.964566x0.980366) = 0.01893820079 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0354337x0.0196339) -+ (0x0.0354337x0.980366) -+ (0x0.964566x0.0196339) -+ (1x0.964566x0.980366) = 0.9456281198 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 0.01253495771 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005241699219 0.5 -b2 0.9947583008 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03543367937 0.5 -f2 0.9645663206 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03543367937 0.5 -f2 0.9645663206 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01511777409 0.5 0.01511777409 -a2 0.9848822259 0.5 0.9848822259 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01963390219 0.5 -a2 0.9803660978 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.000695701395 1 0.000695701395 -_jn1 0.03473797798 1 0.03473797798 -_jn2 0.01893820079 1 0.01893820079 -_jn3 0.9456281198 1 0.9456281198 - - - -******************************************************************************** - Iteration 12 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.0354337) + (0.99x0.964566)]x0.5 -+ [(0.008x0.0354337) + (0.01x0.964566)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.0354337) + (0.003x0.964566)]x0.5 -+ [(0.8x0.0354337) + (0.997x0.964566)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.0052417) + (0.2x0.994758)]x0.5 -+ [(0.008x0.0052417) + (0.8x0.994758)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.0052417) + (0.003x0.994758)]x0.5 -+ [(0.01x0.0052417) + (0.997x0.994758)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0196339) + (0x0.980366)]x1 -+ [(0x0.0196339) + (1x0.980366)]x1 -+ [(0x0.0196339) + (0x0.980366)]x1 -+ [(0x0.0196339) + (0x0.980366)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0196339) + (0x0.980366)]x1 -+ [(0x0.0196339) + (0x0.980366)]x1 -+ [(1x0.0196339) + (0x0.980366)]x1 -+ [(0x0.0196339) + (1x0.980366)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.0354337) + (0x0.964566)]x1 -+ [(0x0.0354337) + (0x0.964566)]x1 -+ [(0x0.0354337) + (1x0.964566)]x1 -+ [(0x0.0354337) + (0x0.964566)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.0354337) + (0x0.964566)]x1 -+ [(1x0.0354337) + (0x0.964566)]x1 -+ [(0x0.0354337) + (0x0.964566)]x1 -+ [(0x0.0354337) + (1x0.964566)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0151178 = 0.01511777409 -π_Jn(a2) = π(a2) = 0.984882 = 0.9848822259 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.00512085x0.0336225) -+ (0.99x0.00512085x0.966378) -+ (0.2x0.994879x0.0336225) -+ (0.003x0.994879x0.966378) = 0.01464432756 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.00512085x0.0336225) -+ (0.01x0.00512085x0.966378) -+ (0.8x0.994879x0.0336225) -+ (0.997x0.994879x0.966378) = 0.9853556724 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 0.0009468930591 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.0336225x0.0173758) -+ (0x0.0336225x0.982624) -+ (0x0.966378x0.0173758) -+ (0x0.966378x0.982624) = 0.0005842182997 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0336225x0.0173758) -+ (1x0.0336225x0.982624) -+ (0x0.966378x0.0173758) -+ (0x0.966378x0.982624) = 0.03303823462 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0336225x0.0173758) -+ (0x0.0336225x0.982624) -+ (1x0.966378x0.0173758) -+ (0x0.966378x0.982624) = 0.01679161984 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0336225x0.0173758) -+ (0x0.0336225x0.982624) -+ (0x0.966378x0.0173758) -+ (1x0.966378x0.982624) = 0.9495859272 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 0.007915614822 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005120849609 0.5 -b2 0.9948791504 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03362245292 0.5 -f2 0.9663775471 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03362245292 0.5 -f2 0.9663775471 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01464432756 0.5 0.01464432756 -a2 0.9853556724 0.5 0.9853556724 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01737583814 0.5 -a2 0.9826241619 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0005842182997 1 0.0005842182997 -_jn1 0.03303823462 1 0.03303823462 -_jn2 0.01679161984 1 0.01679161984 -_jn3 0.9495859272 1 0.9495859272 - - - -******************************************************************************** - Iteration 13 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.0336225) + (0.99x0.966378)]x0.5 -+ [(0.008x0.0336225) + (0.01x0.966378)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.0336225) + (0.003x0.966378)]x0.5 -+ [(0.8x0.0336225) + (0.997x0.966378)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.00512085) + (0.2x0.994879)]x0.5 -+ [(0.008x0.00512085) + (0.8x0.994879)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.00512085) + (0.003x0.994879)]x0.5 -+ [(0.01x0.00512085) + (0.997x0.994879)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0173758) + (0x0.982624)]x1 -+ [(0x0.0173758) + (1x0.982624)]x1 -+ [(0x0.0173758) + (0x0.982624)]x1 -+ [(0x0.0173758) + (0x0.982624)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0173758) + (0x0.982624)]x1 -+ [(0x0.0173758) + (0x0.982624)]x1 -+ [(1x0.0173758) + (0x0.982624)]x1 -+ [(0x0.0173758) + (1x0.982624)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.0336225) + (0x0.966378)]x1 -+ [(0x0.0336225) + (0x0.966378)]x1 -+ [(0x0.0336225) + (1x0.966378)]x1 -+ [(0x0.0336225) + (0x0.966378)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.0336225) + (0x0.966378)]x1 -+ [(1x0.0336225) + (0x0.966378)]x1 -+ [(0x0.0336225) + (0x0.966378)]x1 -+ [(0x0.0336225) + (1x0.966378)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0146443 = 0.01464432756 -π_Jn(a2) = π(a2) = 0.985356 = 0.9853556724 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.00506042x0.032415) -+ (0.99x0.00506042x0.967585) -+ (0.2x0.99494x0.032415) -+ (0.003x0.99494x0.967585) = 0.01434840156 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.00506042x0.032415) -+ (0.01x0.00506042x0.967585) -+ (0.8x0.99494x0.032415) -+ (0.997x0.99494x0.967585) = 0.9856515984 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 0.0005918519954 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.032415x0.0160101) -+ (0x0.032415x0.98399) -+ (0x0.967585x0.0160101) -+ (0x0.967585x0.98399) = 0.0005189663331 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.032415x0.0160101) -+ (1x0.032415x0.98399) -+ (0x0.967585x0.0160101) -+ (0x0.967585x0.98399) = 0.03189600228 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.032415x0.0160101) -+ (0x0.032415x0.98399) -+ (1x0.967585x0.0160101) -+ (0x0.967585x0.98399) = 0.01549111652 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.032415x0.0160101) -+ (0x0.032415x0.98399) -+ (0x0.967585x0.0160101) -+ (1x0.967585x0.98399) = 0.9520939149 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 0.005015975255 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005060424805 0.5 -b2 0.9949395752 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03241496861 0.5 -f2 0.9675850314 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03241496861 0.5 -f2 0.9675850314 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01434840156 0.5 0.01434840156 -a2 0.9856515984 0.5 0.9856515984 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01601008285 0.5 -a2 0.9839899171 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0005189663331 1 0.0005189663331 -_jn1 0.03189600228 1 0.03189600228 -_jn2 0.01549111652 1 0.01549111652 -_jn3 0.9520939149 1 0.9520939149 - - - -******************************************************************************** - Iteration 14 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.032415) + (0.99x0.967585)]x0.5 -+ [(0.008x0.032415) + (0.01x0.967585)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.032415) + (0.003x0.967585)]x0.5 -+ [(0.8x0.032415) + (0.997x0.967585)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.00506042) + (0.2x0.99494)]x0.5 -+ [(0.008x0.00506042) + (0.8x0.99494)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.00506042) + (0.003x0.99494)]x0.5 -+ [(0.01x0.00506042) + (0.997x0.99494)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0160101) + (0x0.98399)]x1 -+ [(0x0.0160101) + (1x0.98399)]x1 -+ [(0x0.0160101) + (0x0.98399)]x1 -+ [(0x0.0160101) + (0x0.98399)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0160101) + (0x0.98399)]x1 -+ [(0x0.0160101) + (0x0.98399)]x1 -+ [(1x0.0160101) + (0x0.98399)]x1 -+ [(0x0.0160101) + (1x0.98399)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.032415) + (0x0.967585)]x1 -+ [(0x0.032415) + (0x0.967585)]x1 -+ [(0x0.032415) + (1x0.967585)]x1 -+ [(0x0.032415) + (0x0.967585)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.032415) + (0x0.967585)]x1 -+ [(1x0.032415) + (0x0.967585)]x1 -+ [(0x0.032415) + (0x0.967585)]x1 -+ [(0x0.032415) + (1x0.967585)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0143484 = 0.01434840156 -π_Jn(a2) = π(a2) = 0.985652 = 0.9856515984 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.00503021x0.03161) -+ (0.99x0.00503021x0.96839) -+ (0.2x0.99497x0.03161) -+ (0.003x0.99497x0.96839) = 0.01416097956 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.00503021x0.03161) -+ (0.01x0.00503021x0.96839) -+ (0.8x0.99497x0.03161) -+ (0.997x0.99497x0.96839) = 0.9858390204 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 0.0003748440048 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.03161x0.0151792) -+ (0x0.03161x0.984821) -+ (0x0.96839x0.0151792) -+ (0x0.96839x0.984821) = 0.0004798155285 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03161x0.0151792) -+ (1x0.03161x0.984821) -+ (0x0.96839x0.0151792) -+ (0x0.96839x0.984821) = 0.03113016355 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03161x0.0151792) -+ (0x0.03161x0.984821) -+ (1x0.96839x0.0151792) -+ (0x0.96839x0.984821) = 0.01469942668 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03161x0.0151792) -+ (0x0.03161x0.984821) -+ (0x0.96839x0.0151792) -+ (1x0.96839x0.984821) = 0.9536905942 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 0.003193358751 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005030212402 0.5 -b2 0.9949697876 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03160997907 0.5 -f2 0.9683900209 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03160997907 0.5 -f2 0.9683900209 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01416097956 0.5 0.01416097956 -a2 0.9858390204 0.5 0.9858390204 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01517924221 0.5 -a2 0.9848207578 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004798155285 1 0.0004798155285 -_jn1 0.03113016355 1 0.03113016355 -_jn2 0.01469942668 1 0.01469942668 -_jn3 0.9536905942 1 0.9536905942 - - - -******************************************************************************** - Iteration 15 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.03161) + (0.99x0.96839)]x0.5 -+ [(0.008x0.03161) + (0.01x0.96839)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.03161) + (0.003x0.96839)]x0.5 -+ [(0.8x0.03161) + (0.997x0.96839)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.00503021) + (0.2x0.99497)]x0.5 -+ [(0.008x0.00503021) + (0.8x0.99497)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.00503021) + (0.003x0.99497)]x0.5 -+ [(0.01x0.00503021) + (0.997x0.99497)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0151792) + (0x0.984821)]x1 -+ [(0x0.0151792) + (1x0.984821)]x1 -+ [(0x0.0151792) + (0x0.984821)]x1 -+ [(0x0.0151792) + (0x0.984821)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0151792) + (0x0.984821)]x1 -+ [(0x0.0151792) + (0x0.984821)]x1 -+ [(1x0.0151792) + (0x0.984821)]x1 -+ [(0x0.0151792) + (1x0.984821)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.03161) + (0x0.96839)]x1 -+ [(0x0.03161) + (0x0.96839)]x1 -+ [(0x0.03161) + (1x0.96839)]x1 -+ [(0x0.03161) + (0x0.96839)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.03161) + (0x0.96839)]x1 -+ [(1x0.03161) + (0x0.96839)]x1 -+ [(0x0.03161) + (0x0.96839)]x1 -+ [(0x0.03161) + (1x0.96839)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.014161 = 0.01416097956 -π_Jn(a2) = π(a2) = 0.985839 = 0.9858390204 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.00501511x0.0310733) -+ (0.99x0.00501511x0.968927) -+ (0.2x0.994985x0.0310733) -+ (0.003x0.994985x0.968927) = 0.01404096572 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.00501511x0.0310733) -+ (0.01x0.00501511x0.968927) -+ (0.8x0.994985x0.0310733) -+ (0.997x0.994985x0.968927) = 0.9859590343 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 0.0002400276838 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.0310733x0.0146701) -+ (0x0.0310733x0.98533) -+ (0x0.968927x0.0146701) -+ (0x0.968927x0.98533) = 0.0004558490409 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0310733x0.0146701) -+ (1x0.0310733x0.98533) -+ (0x0.968927x0.0146701) -+ (0x0.968927x0.98533) = 0.03061747034 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0310733x0.0146701) -+ (0x0.0310733x0.98533) -+ (1x0.968927x0.0146701) -+ (0x0.968927x0.98533) = 0.01421426184 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0310733x0.0146701) -+ (0x0.0310733x0.98533) -+ (0x0.968927x0.0146701) -+ (1x0.968927x0.98533) = 0.9547124188 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 0.002043649053 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005015106201 0.5 -b2 0.9949848938 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03107331938 0.5 -f2 0.9689266806 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03107331938 0.5 -f2 0.9689266806 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01404096572 0.5 0.01404096572 -a2 0.9859590343 0.5 0.9859590343 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01467011088 0.5 -a2 0.9853298891 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004558490409 1 0.0004558490409 -_jn1 0.03061747034 1 0.03061747034 -_jn2 0.01421426184 1 0.01421426184 -_jn3 0.9547124188 1 0.9547124188 - - - -******************************************************************************** - Iteration 16 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.0310733) + (0.99x0.968927)]x0.5 -+ [(0.008x0.0310733) + (0.01x0.968927)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.0310733) + (0.003x0.968927)]x0.5 -+ [(0.8x0.0310733) + (0.997x0.968927)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.00501511) + (0.2x0.994985)]x0.5 -+ [(0.008x0.00501511) + (0.8x0.994985)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.00501511) + (0.003x0.994985)]x0.5 -+ [(0.01x0.00501511) + (0.997x0.994985)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0146701) + (0x0.98533)]x1 -+ [(0x0.0146701) + (1x0.98533)]x1 -+ [(0x0.0146701) + (0x0.98533)]x1 -+ [(0x0.0146701) + (0x0.98533)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0146701) + (0x0.98533)]x1 -+ [(0x0.0146701) + (0x0.98533)]x1 -+ [(1x0.0146701) + (0x0.98533)]x1 -+ [(0x0.0146701) + (1x0.98533)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.0310733) + (0x0.968927)]x1 -+ [(0x0.0310733) + (0x0.968927)]x1 -+ [(0x0.0310733) + (1x0.968927)]x1 -+ [(0x0.0310733) + (0x0.968927)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.0310733) + (0x0.968927)]x1 -+ [(1x0.0310733) + (0x0.968927)]x1 -+ [(0x0.0310733) + (0x0.968927)]x1 -+ [(0x0.0310733) + (1x0.968927)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.014041 = 0.01404096572 -π_Jn(a2) = π(a2) = 0.985959 = 0.9859590343 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.00500755x0.0307155) -+ (0.99x0.00500755x0.969284) -+ (0.2x0.994992x0.0307155) -+ (0.003x0.994992x0.969284) = 0.01396342463 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.00500755x0.0307155) -+ (0.01x0.00500755x0.969284) -+ (0.8x0.994992x0.0307155) -+ (0.997x0.994992x0.969284) = 0.9860365754 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 0.0001550821883 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.0307155x0.0143555) -+ (0x0.0307155x0.985644) -+ (0x0.969284x0.0143555) -+ (0x0.969284x0.985644) = 0.0004409382007 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0307155x0.0143555) -+ (1x0.0307155x0.985644) -+ (0x0.969284x0.0143555) -+ (0x0.969284x0.985644) = 0.03027460805 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0307155x0.0143555) -+ (0x0.0307155x0.985644) -+ (1x0.969284x0.0143555) -+ (0x0.969284x0.985644) = 0.0139146001 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0307155x0.0143555) -+ (0x0.0307155x0.985644) -+ (0x0.969284x0.0143555) -+ (1x0.969284x0.985644) = 0.9553698536 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 0.001314869739 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005007553101 0.5 -b2 0.9949924469 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03071554625 0.5 -f2 0.9692844537 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03071554625 0.5 -f2 0.9692844537 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01396342463 0.5 0.01396342463 -a2 0.9860365754 0.5 0.9860365754 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.0143555383 0.5 -a2 0.9856444617 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004409382007 1 0.0004409382007 -_jn1 0.03027460805 1 0.03027460805 -_jn2 0.0139146001 1 0.0139146001 -_jn3 0.9553698536 1 0.9553698536 - - - -******************************************************************************** - Iteration 17 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.0307155) + (0.99x0.969284)]x0.5 -+ [(0.008x0.0307155) + (0.01x0.969284)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.0307155) + (0.003x0.969284)]x0.5 -+ [(0.8x0.0307155) + (0.997x0.969284)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.00500755) + (0.2x0.994992)]x0.5 -+ [(0.008x0.00500755) + (0.8x0.994992)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.00500755) + (0.003x0.994992)]x0.5 -+ [(0.01x0.00500755) + (0.997x0.994992)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0143555) + (0x0.985644)]x1 -+ [(0x0.0143555) + (1x0.985644)]x1 -+ [(0x0.0143555) + (0x0.985644)]x1 -+ [(0x0.0143555) + (0x0.985644)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0143555) + (0x0.985644)]x1 -+ [(0x0.0143555) + (0x0.985644)]x1 -+ [(1x0.0143555) + (0x0.985644)]x1 -+ [(0x0.0143555) + (1x0.985644)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.0307155) + (0x0.969284)]x1 -+ [(0x0.0307155) + (0x0.969284)]x1 -+ [(0x0.0307155) + (1x0.969284)]x1 -+ [(0x0.0307155) + (0x0.969284)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.0307155) + (0x0.969284)]x1 -+ [(1x0.0307155) + (0x0.969284)]x1 -+ [(0x0.0307155) + (0x0.969284)]x1 -+ [(0x0.0307155) + (1x0.969284)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0139634 = 0.01396342463 -π_Jn(a2) = π(a2) = 0.986037 = 0.9860365754 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.00500378x0.030477) -+ (0.99x0.00500378x0.969523) -+ (0.2x0.994996x0.030477) -+ (0.003x0.994996x0.969523) = 0.01391296498 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.00500378x0.030477) -+ (0.01x0.00500378x0.969523) -+ (0.8x0.994996x0.030477) -+ (0.997x0.994996x0.969523) = 0.986087035 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 0.0001009192892 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.030477x0.0141595) -+ (0x0.030477x0.985841) -+ (0x0.969523x0.0141595) -+ (0x0.969523x0.985841) = 0.0004315389532 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.030477x0.0141595) -+ (1x0.030477x0.985841) -+ (0x0.969523x0.0141595) -+ (0x0.969523x0.985841) = 0.03004549188 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.030477x0.0141595) -+ (0x0.030477x0.985841) -+ (1x0.969523x0.0141595) -+ (0x0.969523x0.985841) = 0.01372794251 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.030477x0.0141595) -+ (0x0.030477x0.985841) -+ (0x0.969523x0.0141595) -+ (1x0.969523x0.985841) = 0.9557950267 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 0.0008503460181 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.00500377655 0.5 -b2 0.9949962234 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03047703084 0.5 -f2 0.9695229692 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03047703084 0.5 -f2 0.9695229692 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01391296498 0.5 0.01391296498 -a2 0.986087035 0.5 0.986087035 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01415948146 0.5 -a2 0.9858405185 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004315389532 1 0.0004315389532 -_jn1 0.03004549188 1 0.03004549188 -_jn2 0.01372794251 1 0.01372794251 -_jn3 0.9557950267 1 0.9557950267 - - - -******************************************************************************** - Iteration 18 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.030477) + (0.99x0.969523)]x0.5 -+ [(0.008x0.030477) + (0.01x0.969523)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.030477) + (0.003x0.969523)]x0.5 -+ [(0.8x0.030477) + (0.997x0.969523)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.00500378) + (0.2x0.994996)]x0.5 -+ [(0.008x0.00500378) + (0.8x0.994996)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.00500378) + (0.003x0.994996)]x0.5 -+ [(0.01x0.00500378) + (0.997x0.994996)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0141595) + (0x0.985841)]x1 -+ [(0x0.0141595) + (1x0.985841)]x1 -+ [(0x0.0141595) + (0x0.985841)]x1 -+ [(0x0.0141595) + (0x0.985841)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0141595) + (0x0.985841)]x1 -+ [(0x0.0141595) + (0x0.985841)]x1 -+ [(1x0.0141595) + (0x0.985841)]x1 -+ [(0x0.0141595) + (1x0.985841)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.030477) + (0x0.969523)]x1 -+ [(0x0.030477) + (0x0.969523)]x1 -+ [(0x0.030477) + (1x0.969523)]x1 -+ [(0x0.030477) + (0x0.969523)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.030477) + (0x0.969523)]x1 -+ [(1x0.030477) + (0x0.969523)]x1 -+ [(0x0.030477) + (0x0.969523)]x1 -+ [(0x0.030477) + (1x0.969523)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.013913 = 0.01391296498 -π_Jn(a2) = π(a2) = 0.986087 = 0.986087035 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.00500189x0.030318) -+ (0.99x0.00500189x0.969682) -+ (0.2x0.994998x0.030318) -+ (0.003x0.994998x0.969682) = 0.01387994254 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.00500189x0.030318) -+ (0.01x0.00500189x0.969682) -+ (0.8x0.994998x0.030318) -+ (0.997x0.994998x0.969682) = 0.9861200575 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 6.604487376e-05 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.030318x0.0140362) -+ (0x0.030318x0.985964) -+ (0x0.969682x0.0140362) -+ (0x0.969682x0.985964) = 0.0004255505042 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.030318x0.0140362) -+ (1x0.030318x0.985964) -+ (0x0.969682x0.0140362) -+ (0x0.969682x0.985964) = 0.02989247005 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.030318x0.0140362) -+ (0x0.030318x0.985964) -+ (1x0.969682x0.0140362) -+ (0x0.969682x0.985964) = 0.01361067272 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.030318x0.0140362) -+ (0x0.030318x0.985964) -+ (0x0.969682x0.0140362) -+ (1x0.969682x0.985964) = 0.9560713067 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 0.0005525601426 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005001888275 0.5 -b2 0.9949981117 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03031802056 0.5 -f2 0.9696819794 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03031802056 0.5 -f2 0.9696819794 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01387994254 0.5 0.01387994254 -a2 0.9861200575 0.5 0.9861200575 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01403622322 0.5 -a2 0.9859637768 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004255505042 1 0.0004255505042 -_jn1 0.02989247005 1 0.02989247005 -_jn2 0.01361067272 1 0.01361067272 -_jn3 0.9560713067 1 0.9560713067 - - - -******************************************************************************** - Iteration 19 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.030318) + (0.99x0.969682)]x0.5 -+ [(0.008x0.030318) + (0.01x0.969682)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.030318) + (0.003x0.969682)]x0.5 -+ [(0.8x0.030318) + (0.997x0.969682)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.00500189) + (0.2x0.994998)]x0.5 -+ [(0.008x0.00500189) + (0.8x0.994998)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.00500189) + (0.003x0.994998)]x0.5 -+ [(0.01x0.00500189) + (0.997x0.994998)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0140362) + (0x0.985964)]x1 -+ [(0x0.0140362) + (1x0.985964)]x1 -+ [(0x0.0140362) + (0x0.985964)]x1 -+ [(0x0.0140362) + (0x0.985964)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0140362) + (0x0.985964)]x1 -+ [(0x0.0140362) + (0x0.985964)]x1 -+ [(1x0.0140362) + (0x0.985964)]x1 -+ [(0x0.0140362) + (1x0.985964)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.030318) + (0x0.969682)]x1 -+ [(0x0.030318) + (0x0.969682)]x1 -+ [(0x0.030318) + (1x0.969682)]x1 -+ [(0x0.030318) + (0x0.969682)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.030318) + (0x0.969682)]x1 -+ [(1x0.030318) + (0x0.969682)]x1 -+ [(0x0.030318) + (0x0.969682)]x1 -+ [(0x0.030318) + (1x0.969682)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138799 = 0.01387994254 -π_Jn(a2) = π(a2) = 0.98612 = 0.9861200575 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.00500094x0.030212) -+ (0.99x0.00500094x0.969788) -+ (0.2x0.994999x0.030212) -+ (0.003x0.994999x0.969788) = 0.01385823629 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.00500094x0.030212) -+ (0.01x0.00500094x0.969788) -+ (0.8x0.994999x0.030212) -+ (0.997x0.994999x0.969788) = 0.9861417637 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 4.341251158e-05 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.030212x0.0139581) -+ (0x0.030212x0.986042) -+ (0x0.969788x0.0139581) -+ (0x0.969788x0.986042) = 0.0004217017914 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.030212x0.0139581) -+ (1x0.030212x0.986042) -+ (0x0.969788x0.0139581) -+ (0x0.969788x0.986042) = 0.02979031191 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.030212x0.0139581) -+ (0x0.030212x0.986042) -+ (1x0.969788x0.0139581) -+ (0x0.969788x0.986042) = 0.01353638109 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.030212x0.0139581) -+ (0x0.030212x0.986042) -+ (0x0.969788x0.0139581) -+ (1x0.969788x0.986042) = 0.9562516052 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 0.0003605969578 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005000944138 0.5 -b2 0.9949990559 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03021201371 0.5 -f2 0.9697879863 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03021201371 0.5 -f2 0.9697879863 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01385823629 0.5 0.01385823629 -a2 0.9861417637 0.5 0.9861417637 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01395808288 0.5 -a2 0.9860419171 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004217017914 1 0.0004217017914 -_jn1 0.02979031191 1 0.02979031191 -_jn2 0.01353638109 1 0.01353638109 -_jn3 0.9562516052 1 0.9562516052 - - - -******************************************************************************** - Iteration 20 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.030212) + (0.99x0.969788)]x0.5 -+ [(0.008x0.030212) + (0.01x0.969788)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.030212) + (0.003x0.969788)]x0.5 -+ [(0.8x0.030212) + (0.997x0.969788)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.00500094) + (0.2x0.994999)]x0.5 -+ [(0.008x0.00500094) + (0.8x0.994999)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.00500094) + (0.003x0.994999)]x0.5 -+ [(0.01x0.00500094) + (0.997x0.994999)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0139581) + (0x0.986042)]x1 -+ [(0x0.0139581) + (1x0.986042)]x1 -+ [(0x0.0139581) + (0x0.986042)]x1 -+ [(0x0.0139581) + (0x0.986042)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0139581) + (0x0.986042)]x1 -+ [(0x0.0139581) + (0x0.986042)]x1 -+ [(1x0.0139581) + (0x0.986042)]x1 -+ [(0x0.0139581) + (1x0.986042)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.030212) + (0x0.969788)]x1 -+ [(0x0.030212) + (0x0.969788)]x1 -+ [(0x0.030212) + (1x0.969788)]x1 -+ [(0x0.030212) + (0x0.969788)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.030212) + (0x0.969788)]x1 -+ [(1x0.030212) + (0x0.969788)]x1 -+ [(0x0.030212) + (0x0.969788)]x1 -+ [(0x0.030212) + (1x0.969788)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138582 = 0.01385823629 -π_Jn(a2) = π(a2) = 0.986142 = 0.9861417637 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.00500047x0.0301413) -+ (0.99x0.00500047x0.969859) -+ (0.2x0.995x0.0301413) -+ (0.003x0.995x0.969859) = 0.01384391981 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.00500047x0.0301413) -+ (0.01x0.00500047x0.969859) -+ (0.8x0.995x0.0301413) -+ (0.997x0.995x0.969859) = 0.9861560802 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 2.863294624e-05 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.0301413x0.0139082) -+ (0x0.0301413x0.986092) -+ (0x0.969859x0.0139082) -+ (0x0.969859x0.986092) = 0.0004192106012 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0301413x0.0139082) -+ (1x0.0301413x0.986092) -+ (0x0.969859x0.0139082) -+ (0x0.969859x0.986092) = 0.02972213187 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0301413x0.0139082) -+ (0x0.0301413x0.986092) -+ (1x0.969859x0.0139082) -+ (0x0.969859x0.986092) = 0.01348894898 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0301413x0.0139082) -+ (0x0.0301413x0.986092) -+ (0x0.969859x0.0139082) -+ (1x0.969859x0.986092) = 0.9563697085 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 0.0002362066847 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005000472069 0.5 -b2 0.9949995279 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03014134247 0.5 -f2 0.9698586575 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03014134247 0.5 -f2 0.9698586575 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01384391981 0.5 0.01384391981 -a2 0.9861560802 0.5 0.9861560802 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01390815959 0.5 -a2 0.9860918404 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004192106012 1 0.0004192106012 -_jn1 0.02972213187 1 0.02972213187 -_jn2 0.01348894898 1 0.01348894898 -_jn3 0.9563697085 1 0.9563697085 - - - -******************************************************************************** - Iteration 21 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.0301413) + (0.99x0.969859)]x0.5 -+ [(0.008x0.0301413) + (0.01x0.969859)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.0301413) + (0.003x0.969859)]x0.5 -+ [(0.8x0.0301413) + (0.997x0.969859)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.00500047) + (0.2x0.995)]x0.5 -+ [(0.008x0.00500047) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.00500047) + (0.003x0.995)]x0.5 -+ [(0.01x0.00500047) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0139082) + (0x0.986092)]x1 -+ [(0x0.0139082) + (1x0.986092)]x1 -+ [(0x0.0139082) + (0x0.986092)]x1 -+ [(0x0.0139082) + (0x0.986092)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0139082) + (0x0.986092)]x1 -+ [(0x0.0139082) + (0x0.986092)]x1 -+ [(1x0.0139082) + (0x0.986092)]x1 -+ [(0x0.0139082) + (1x0.986092)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.0301413) + (0x0.969859)]x1 -+ [(0x0.0301413) + (0x0.969859)]x1 -+ [(0x0.0301413) + (1x0.969859)]x1 -+ [(0x0.0301413) + (0x0.969859)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.0301413) + (0x0.969859)]x1 -+ [(1x0.0301413) + (0x0.969859)]x1 -+ [(0x0.0301413) + (0x0.969859)]x1 -+ [(0x0.0301413) + (1x0.969859)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138439 = 0.01384391981 -π_Jn(a2) = π(a2) = 0.986156 = 0.9861560802 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.00500024x0.0300942) -+ (0.99x0.00500024x0.969906) -+ (0.2x0.995x0.0300942) -+ (0.003x0.995x0.969906) = 0.01383445269 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.00500024x0.0300942) -+ (0.01x0.00500024x0.969906) -+ (0.8x0.995x0.0300942) -+ (0.997x0.995x0.969906) = 0.9861655473 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 1.893425808e-05 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.0300942x0.013876) -+ (0x0.0300942x0.986124) -+ (0x0.969906x0.013876) -+ (0x0.969906x0.986124) = 0.0004175887068 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0300942x0.013876) -+ (1x0.0300942x0.986124) -+ (0x0.969906x0.013876) -+ (0x0.969906x0.986124) = 0.02967663961 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0300942x0.013876) -+ (0x0.0300942x0.986124) -+ (1x0.969906x0.013876) -+ (0x0.969906x0.986124) = 0.01345845099 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0300942x0.013876) -+ (0x0.0300942x0.986124) -+ (0x0.969906x0.013876) -+ (1x0.969906x0.986124) = 0.9564473207 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 0.0001552242953 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005000236034 0.5 -b2 0.994999764 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03009422831 0.5 -f2 0.9699057717 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03009422831 0.5 -f2 0.9699057717 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01383445269 0.5 0.01383445269 -a2 0.9861655473 0.5 0.9861655473 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.0138760397 0.5 -a2 0.9861239603 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004175887068 1 0.0004175887068 -_jn1 0.02967663961 1 0.02967663961 -_jn2 0.01345845099 1 0.01345845099 -_jn3 0.9564473207 1 0.9564473207 - - - -******************************************************************************** - Iteration 22 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.0300942) + (0.99x0.969906)]x0.5 -+ [(0.008x0.0300942) + (0.01x0.969906)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.0300942) + (0.003x0.969906)]x0.5 -+ [(0.8x0.0300942) + (0.997x0.969906)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.00500024) + (0.2x0.995)]x0.5 -+ [(0.008x0.00500024) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.00500024) + (0.003x0.995)]x0.5 -+ [(0.01x0.00500024) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.013876) + (0x0.986124)]x1 -+ [(0x0.013876) + (1x0.986124)]x1 -+ [(0x0.013876) + (0x0.986124)]x1 -+ [(0x0.013876) + (0x0.986124)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.013876) + (0x0.986124)]x1 -+ [(0x0.013876) + (0x0.986124)]x1 -+ [(1x0.013876) + (0x0.986124)]x1 -+ [(0x0.013876) + (1x0.986124)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.0300942) + (0x0.969906)]x1 -+ [(0x0.0300942) + (0x0.969906)]x1 -+ [(0x0.0300942) + (1x0.969906)]x1 -+ [(0x0.0300942) + (0x0.969906)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.0300942) + (0x0.969906)]x1 -+ [(1x0.0300942) + (0x0.969906)]x1 -+ [(0x0.0300942) + (0x0.969906)]x1 -+ [(0x0.0300942) + (1x0.969906)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138345 = 0.01383445269 -π_Jn(a2) = π(a2) = 0.986166 = 0.9861655473 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.00500012x0.0300628) -+ (0.99x0.00500012x0.969937) -+ (0.2x0.995x0.0300628) -+ (0.003x0.995x0.969937) = 0.01382817986 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.00500012x0.0300628) -+ (0.01x0.00500012x0.969937) -+ (0.8x0.995x0.0300628) -+ (0.997x0.995x0.969937) = 0.9861718201 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 1.254564945e-05 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.0300628x0.0138552) -+ (0x0.0300628x0.986145) -+ (0x0.969937x0.0138552) -+ (0x0.969937x0.986145) = 0.0004165277568 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0300628x0.0138552) -+ (1x0.0300628x0.986145) -+ (0x0.969937x0.0138552) -+ (0x0.969937x0.986145) = 0.02964629112 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0300628x0.0138552) -+ (0x0.0300628x0.986145) -+ (1x0.969937x0.0138552) -+ (0x0.969937x0.986145) = 0.01343871844 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0300628x0.0138552) -+ (0x0.0300628x0.986145) -+ (0x0.969937x0.0138552) -+ (1x0.969937x0.986145) = 0.9564984627 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 0.0001022839899 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005000118017 0.5 -b2 0.994999882 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03006281888 0.5 -f2 0.9699371811 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03006281888 0.5 -f2 0.9699371811 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01382817986 0.5 0.01382817986 -a2 0.9861718201 0.5 0.9861718201 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01385524619 0.5 -a2 0.9861447538 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004165277568 1 0.0004165277568 -_jn1 0.02964629112 1 0.02964629112 -_jn2 0.01343871844 1 0.01343871844 -_jn3 0.9564984627 1 0.9564984627 - - - -******************************************************************************** - Iteration 23 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.0300628) + (0.99x0.969937)]x0.5 -+ [(0.008x0.0300628) + (0.01x0.969937)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.0300628) + (0.003x0.969937)]x0.5 -+ [(0.8x0.0300628) + (0.997x0.969937)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.00500012) + (0.2x0.995)]x0.5 -+ [(0.008x0.00500012) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.00500012) + (0.003x0.995)]x0.5 -+ [(0.01x0.00500012) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138552) + (0x0.986145)]x1 -+ [(0x0.0138552) + (1x0.986145)]x1 -+ [(0x0.0138552) + (0x0.986145)]x1 -+ [(0x0.0138552) + (0x0.986145)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138552) + (0x0.986145)]x1 -+ [(0x0.0138552) + (0x0.986145)]x1 -+ [(1x0.0138552) + (0x0.986145)]x1 -+ [(0x0.0138552) + (1x0.986145)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.0300628) + (0x0.969937)]x1 -+ [(0x0.0300628) + (0x0.969937)]x1 -+ [(0x0.0300628) + (1x0.969937)]x1 -+ [(0x0.0300628) + (0x0.969937)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.0300628) + (0x0.969937)]x1 -+ [(1x0.0300628) + (0x0.969937)]x1 -+ [(0x0.0300628) + (0x0.969937)]x1 -+ [(0x0.0300628) + (1x0.969937)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138282 = 0.01382817986 -π_Jn(a2) = π(a2) = 0.986172 = 0.9861718201 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.00500006x0.0300419) -+ (0.99x0.00500006x0.969958) -+ (0.2x0.995x0.0300419) -+ (0.003x0.995x0.969958) = 0.01382401728 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.00500006x0.0300419) -+ (0.01x0.00500006x0.969958) -+ (0.8x0.995x0.0300419) -+ (0.997x0.995x0.969958) = 0.9861759827 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 8.325170706e-06 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.0300419x0.0138417) -+ (0x0.0300419x0.986158) -+ (0x0.969958x0.0138417) -+ (0x0.969958x0.986158) = 0.0004158310714 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0300419x0.0138417) -+ (1x0.0300419x0.986158) -+ (0x0.969958x0.0138417) -+ (0x0.969958x0.986158) = 0.02962604818 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0300419x0.0138417) -+ (0x0.0300419x0.986158) -+ (1x0.969958x0.0138417) -+ (0x0.969958x0.986158) = 0.01342588196 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0300419x0.0138417) -+ (0x0.0300419x0.986158) -+ (0x0.969958x0.0138417) -+ (1x0.969958x0.986158) = 0.9565322388 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 6.75522115e-05 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005000059009 0.5 -b2 0.994999941 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03004187925 0.5 -f2 0.9699581207 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03004187925 0.5 -f2 0.9699581207 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01382401728 0.5 0.01382401728 -a2 0.9861759827 0.5 0.9861759827 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01384171303 0.5 -a2 0.986158287 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004158310714 1 0.0004158310714 -_jn1 0.02962604818 1 0.02962604818 -_jn2 0.01342588196 1 0.01342588196 -_jn3 0.9565322388 1 0.9565322388 - - - -******************************************************************************** - Iteration 24 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.0300419) + (0.99x0.969958)]x0.5 -+ [(0.008x0.0300419) + (0.01x0.969958)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.0300419) + (0.003x0.969958)]x0.5 -+ [(0.8x0.0300419) + (0.997x0.969958)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.00500006) + (0.2x0.995)]x0.5 -+ [(0.008x0.00500006) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.00500006) + (0.003x0.995)]x0.5 -+ [(0.01x0.00500006) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138417) + (0x0.986158)]x1 -+ [(0x0.0138417) + (1x0.986158)]x1 -+ [(0x0.0138417) + (0x0.986158)]x1 -+ [(0x0.0138417) + (0x0.986158)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138417) + (0x0.986158)]x1 -+ [(0x0.0138417) + (0x0.986158)]x1 -+ [(1x0.0138417) + (0x0.986158)]x1 -+ [(0x0.0138417) + (1x0.986158)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.0300419) + (0x0.969958)]x1 -+ [(0x0.0300419) + (0x0.969958)]x1 -+ [(0x0.0300419) + (1x0.969958)]x1 -+ [(0x0.0300419) + (0x0.969958)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.0300419) + (0x0.969958)]x1 -+ [(1x0.0300419) + (0x0.969958)]x1 -+ [(0x0.0300419) + (0x0.969958)]x1 -+ [(0x0.0300419) + (1x0.969958)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.013824 = 0.01382401728 -π_Jn(a2) = π(a2) = 0.986176 = 0.9861759827 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.00500003x0.0300279) -+ (0.99x0.00500003x0.969972) -+ (0.2x0.995x0.0300279) -+ (0.003x0.995x0.969972) = 0.01382125187 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.00500003x0.0300279) -+ (0.01x0.00500003x0.969972) -+ (0.8x0.995x0.0300279) -+ (0.997x0.995x0.969972) = 0.9861787481 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 5.530815684e-06 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.0300279x0.0138329) -+ (0x0.0300279x0.986167) -+ (0x0.969972x0.0138329) -+ (0x0.969972x0.986167) = 0.0004153721612 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0300279x0.0138329) -+ (1x0.0300279x0.986167) -+ (0x0.969972x0.0138329) -+ (0x0.969972x0.986167) = 0.02961254734 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0300279x0.0138329) -+ (0x0.0300279x0.986167) -+ (1x0.969972x0.0138329) -+ (0x0.969972x0.986167) = 0.01341749299 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0300279x0.0138329) -+ (0x0.0300279x0.986167) -+ (0x0.969972x0.0138329) -+ (1x0.969972x0.986167) = 0.9565545875 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 4.469743126e-05 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005000029504 0.5 -b2 0.9949999705 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.0300279195 0.5 -f2 0.9699720805 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.0300279195 0.5 -f2 0.9699720805 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01382125187 0.5 0.01382125187 -a2 0.9861787481 0.5 0.9861787481 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01383286515 0.5 -a2 0.9861671348 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004153721612 1 0.0004153721612 -_jn1 0.02961254734 1 0.02961254734 -_jn2 0.01341749299 1 0.01341749299 -_jn3 0.9565545875 1 0.9565545875 - - - -******************************************************************************** - Iteration 25 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.0300279) + (0.99x0.969972)]x0.5 -+ [(0.008x0.0300279) + (0.01x0.969972)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.0300279) + (0.003x0.969972)]x0.5 -+ [(0.8x0.0300279) + (0.997x0.969972)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.00500003) + (0.2x0.995)]x0.5 -+ [(0.008x0.00500003) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.00500003) + (0.003x0.995)]x0.5 -+ [(0.01x0.00500003) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138329) + (0x0.986167)]x1 -+ [(0x0.0138329) + (1x0.986167)]x1 -+ [(0x0.0138329) + (0x0.986167)]x1 -+ [(0x0.0138329) + (0x0.986167)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138329) + (0x0.986167)]x1 -+ [(0x0.0138329) + (0x0.986167)]x1 -+ [(1x0.0138329) + (0x0.986167)]x1 -+ [(0x0.0138329) + (1x0.986167)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.0300279) + (0x0.969972)]x1 -+ [(0x0.0300279) + (0x0.969972)]x1 -+ [(0x0.0300279) + (1x0.969972)]x1 -+ [(0x0.0300279) + (0x0.969972)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.0300279) + (0x0.969972)]x1 -+ [(1x0.0300279) + (0x0.969972)]x1 -+ [(0x0.0300279) + (0x0.969972)]x1 -+ [(0x0.0300279) + (1x0.969972)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138213 = 0.01382125187 -π_Jn(a2) = π(a2) = 0.986179 = 0.9861787481 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.00500001x0.0300186) -+ (0.99x0.00500001x0.969981) -+ (0.2x0.995x0.0300186) -+ (0.003x0.995x0.969981) = 0.01381941309 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.00500001x0.0300186) -+ (0.01x0.00500001x0.969981) -+ (0.8x0.995x0.0300186) -+ (0.997x0.995x0.969981) = 0.9861805869 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 3.677561289e-06 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.0300186x0.0138271) -+ (0x0.0300186x0.986173) -+ (0x0.969981x0.0138271) -+ (0x0.969981x0.986173) = 0.0004150691183 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0300186x0.0138271) -+ (1x0.0300186x0.986173) -+ (0x0.969981x0.0138271) -+ (0x0.969981x0.986173) = 0.02960354388 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0300186x0.0138271) -+ (0x0.0300186x0.986173) -+ (1x0.969981x0.0138271) -+ (0x0.969981x0.986173) = 0.01341198939 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0300186x0.0138271) -+ (0x0.0300186x0.986173) -+ (0x0.969981x0.0138271) -+ (1x0.969981x0.986173) = 0.9565693976 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 2.962019789e-05 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005000014752 0.5 -b2 0.9949999852 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.030018613 0.5 -f2 0.969981387 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.030018613 0.5 -f2 0.969981387 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381941309 0.5 0.01381941309 -a2 0.9861805869 0.5 0.9861805869 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01382705851 0.5 -a2 0.9861729415 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004150691183 1 0.0004150691183 -_jn1 0.02960354388 1 0.02960354388 -_jn2 0.01341198939 1 0.01341198939 -_jn3 0.9565693976 1 0.9565693976 - - - -******************************************************************************** - Iteration 26 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.0300186) + (0.99x0.969981)]x0.5 -+ [(0.008x0.0300186) + (0.01x0.969981)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.0300186) + (0.003x0.969981)]x0.5 -+ [(0.8x0.0300186) + (0.997x0.969981)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.00500001) + (0.2x0.995)]x0.5 -+ [(0.008x0.00500001) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.00500001) + (0.003x0.995)]x0.5 -+ [(0.01x0.00500001) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138271) + (0x0.986173)]x1 -+ [(0x0.0138271) + (1x0.986173)]x1 -+ [(0x0.0138271) + (0x0.986173)]x1 -+ [(0x0.0138271) + (0x0.986173)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138271) + (0x0.986173)]x1 -+ [(0x0.0138271) + (0x0.986173)]x1 -+ [(1x0.0138271) + (0x0.986173)]x1 -+ [(0x0.0138271) + (1x0.986173)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.0300186) + (0x0.969981)]x1 -+ [(0x0.0300186) + (0x0.969981)]x1 -+ [(0x0.0300186) + (1x0.969981)]x1 -+ [(0x0.0300186) + (0x0.969981)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.0300186) + (0x0.969981)]x1 -+ [(1x0.0300186) + (0x0.969981)]x1 -+ [(0x0.0300186) + (0x0.969981)]x1 -+ [(0x0.0300186) + (1x0.969981)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138194 = 0.01381941309 -π_Jn(a2) = π(a2) = 0.986181 = 0.9861805869 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.00500001x0.0300124) -+ (0.99x0.00500001x0.969988) -+ (0.2x0.995x0.0300124) -+ (0.003x0.995x0.969988) = 0.01381818965 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.00500001x0.0300124) -+ (0.01x0.00500001x0.969988) -+ (0.8x0.995x0.0300124) -+ (0.997x0.995x0.969988) = 0.9861818104 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 2.446882907e-06 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.0300124x0.0138232) -+ (0x0.0300124x0.986177) -+ (0x0.969988x0.0138232) -+ (0x0.969988x0.986177) = 0.0004148686019 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0300124x0.0138232) -+ (1x0.0300124x0.986177) -+ (0x0.969988x0.0138232) -+ (0x0.969988x0.986177) = 0.02959754006 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0300124x0.0138232) -+ (0x0.0300124x0.986177) -+ (1x0.969988x0.0138232) -+ (0x0.969988x0.986177) = 0.0134083672 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0300124x0.0138232) -+ (0x0.0300124x0.986177) -+ (0x0.969988x0.0138232) -+ (1x0.969988x0.986177) = 0.9565792241 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 1.965305627e-05 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005000007376 0.5 -b2 0.9949999926 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03001240867 0.5 -f2 0.9699875913 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03001240867 0.5 -f2 0.9699875913 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381818965 0.5 0.01381818965 -a2 0.9861818104 0.5 0.9861818104 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.0138232358 0.5 -a2 0.9861767642 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004148686019 1 0.0004148686019 -_jn1 0.02959754006 1 0.02959754006 -_jn2 0.0134083672 1 0.0134083672 -_jn3 0.9565792241 1 0.9565792241 - - - -******************************************************************************** - Iteration 27 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.0300124) + (0.99x0.969988)]x0.5 -+ [(0.008x0.0300124) + (0.01x0.969988)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.0300124) + (0.003x0.969988)]x0.5 -+ [(0.8x0.0300124) + (0.997x0.969988)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.00500001) + (0.2x0.995)]x0.5 -+ [(0.008x0.00500001) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.00500001) + (0.003x0.995)]x0.5 -+ [(0.01x0.00500001) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138232) + (0x0.986177)]x1 -+ [(0x0.0138232) + (1x0.986177)]x1 -+ [(0x0.0138232) + (0x0.986177)]x1 -+ [(0x0.0138232) + (0x0.986177)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138232) + (0x0.986177)]x1 -+ [(0x0.0138232) + (0x0.986177)]x1 -+ [(1x0.0138232) + (0x0.986177)]x1 -+ [(0x0.0138232) + (1x0.986177)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.0300124) + (0x0.969988)]x1 -+ [(0x0.0300124) + (0x0.969988)]x1 -+ [(0x0.0300124) + (1x0.969988)]x1 -+ [(0x0.0300124) + (0x0.969988)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.0300124) + (0x0.969988)]x1 -+ [(1x0.0300124) + (0x0.969988)]x1 -+ [(0x0.0300124) + (0x0.969988)]x1 -+ [(0x0.0300124) + (1x0.969988)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138182 = 0.01381818965 -π_Jn(a2) = π(a2) = 0.986182 = 0.9861818104 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.0300083) -+ (0.99x0.005x0.969992) -+ (0.2x0.995x0.0300083) -+ (0.003x0.995x0.969992) = 0.01381737522 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.0300083) -+ (0.01x0.005x0.969992) -+ (0.8x0.995x0.0300083) -+ (0.997x0.995x0.969992) = 0.9861826248 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 1.62884295e-06 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.0300083x0.0138207) -+ (0x0.0300083x0.986179) -+ (0x0.969992x0.0138207) -+ (0x0.969992x0.986179) = 0.0004147357127 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0300083x0.0138207) -+ (1x0.0300083x0.986179) -+ (0x0.969992x0.0138207) -+ (0x0.969992x0.986179) = 0.02959353673 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0300083x0.0138207) -+ (0x0.0300083x0.986179) -+ (1x0.969992x0.0138207) -+ (0x0.969992x0.986179) = 0.01340597701 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0300083x0.0138207) -+ (0x0.0300083x0.986179) -+ (0x0.969992x0.0138207) -+ (1x0.969992x0.986179) = 0.9565857505 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 1.30528189e-05 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005000003688 0.5 -b2 0.9949999963 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03000827244 0.5 -f2 0.9699917276 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03000827244 0.5 -f2 0.9699917276 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381737522 0.5 0.01381737522 -a2 0.9861826248 0.5 0.9861826248 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01382071272 0.5 -a2 0.9861792873 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004147357127 1 0.0004147357127 -_jn1 0.02959353673 1 0.02959353673 -_jn2 0.01340597701 1 0.01340597701 -_jn3 0.9565857505 1 0.9565857505 - - - -******************************************************************************** - Iteration 28 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.0300083) + (0.99x0.969992)]x0.5 -+ [(0.008x0.0300083) + (0.01x0.969992)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.0300083) + (0.003x0.969992)]x0.5 -+ [(0.8x0.0300083) + (0.997x0.969992)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138207) + (0x0.986179)]x1 -+ [(0x0.0138207) + (1x0.986179)]x1 -+ [(0x0.0138207) + (0x0.986179)]x1 -+ [(0x0.0138207) + (0x0.986179)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138207) + (0x0.986179)]x1 -+ [(0x0.0138207) + (0x0.986179)]x1 -+ [(1x0.0138207) + (0x0.986179)]x1 -+ [(0x0.0138207) + (1x0.986179)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.0300083) + (0x0.969992)]x1 -+ [(0x0.0300083) + (0x0.969992)]x1 -+ [(0x0.0300083) + (1x0.969992)]x1 -+ [(0x0.0300083) + (0x0.969992)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.0300083) + (0x0.969992)]x1 -+ [(1x0.0300083) + (0x0.969992)]x1 -+ [(0x0.0300083) + (0x0.969992)]x1 -+ [(0x0.0300083) + (1x0.969992)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138174 = 0.01381737522 -π_Jn(a2) = π(a2) = 0.986183 = 0.9861826248 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.0300055) -+ (0.99x0.005x0.969994) -+ (0.2x0.995x0.0300055) -+ (0.003x0.995x0.969994) = 0.01381683288 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.0300055) -+ (0.01x0.005x0.969994) -+ (0.8x0.995x0.0300055) -+ (0.997x0.995x0.969994) = 0.9861831671 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 1.084689135e-06 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.0300055x0.013819) -+ (0x0.0300055x0.986181) -+ (0x0.969994x0.013819) -+ (0x0.969994x0.986181) = 0.0004146475307 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0300055x0.013819) -+ (1x0.0300055x0.986181) -+ (0x0.969994x0.013819) -+ (0x0.969994x0.986181) = 0.02959086743 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0300055x0.013819) -+ (0x0.0300055x0.986181) -+ (1x0.969994x0.013819) -+ (0x0.969994x0.986181) = 0.01340439644 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0300055x0.013819) -+ (0x0.0300055x0.986181) -+ (0x0.969994x0.013819) -+ (1x0.969994x0.986181) = 0.9565900886 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 8.676096756e-06 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005000001844 0.5 -b2 0.9949999982 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03000551496 0.5 -f2 0.969994485 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03000551496 0.5 -f2 0.969994485 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381683288 0.5 0.01381683288 -a2 0.9861831671 0.5 0.9861831671 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01381904397 0.5 -a2 0.986180956 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004146475307 1 0.0004146475307 -_jn1 0.02959086743 1 0.02959086743 -_jn2 0.01340439644 1 0.01340439644 -_jn3 0.9565900886 1 0.9565900886 - - - -******************************************************************************** - Iteration 29 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.0300055) + (0.99x0.969994)]x0.5 -+ [(0.008x0.0300055) + (0.01x0.969994)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.0300055) + (0.003x0.969994)]x0.5 -+ [(0.8x0.0300055) + (0.997x0.969994)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.013819) + (0x0.986181)]x1 -+ [(0x0.013819) + (1x0.986181)]x1 -+ [(0x0.013819) + (0x0.986181)]x1 -+ [(0x0.013819) + (0x0.986181)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.013819) + (0x0.986181)]x1 -+ [(0x0.013819) + (0x0.986181)]x1 -+ [(1x0.013819) + (0x0.986181)]x1 -+ [(0x0.013819) + (1x0.986181)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.0300055) + (0x0.969994)]x1 -+ [(0x0.0300055) + (0x0.969994)]x1 -+ [(0x0.0300055) + (1x0.969994)]x1 -+ [(0x0.0300055) + (0x0.969994)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.0300055) + (0x0.969994)]x1 -+ [(1x0.0300055) + (0x0.969994)]x1 -+ [(0x0.0300055) + (0x0.969994)]x1 -+ [(0x0.0300055) + (1x0.969994)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138168 = 0.01381683288 -π_Jn(a2) = π(a2) = 0.986183 = 0.9861831671 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.0300037) -+ (0.99x0.005x0.969996) -+ (0.2x0.995x0.0300037) -+ (0.003x0.995x0.969996) = 0.01381647162 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.0300037) -+ (0.01x0.005x0.969996) -+ (0.8x0.995x0.0300037) -+ (0.997x0.995x0.969996) = 0.9861835284 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 7.225230066e-07 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.0300037x0.0138179) -+ (0x0.0300037x0.986182) -+ (0x0.969996x0.0138179) -+ (0x0.969996x0.986182) = 0.0004145889564 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0300037x0.0138179) -+ (1x0.0300037x0.986182) -+ (0x0.969996x0.0138179) -+ (0x0.969996x0.986182) = 0.02958908769 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0300037x0.0138179) -+ (0x0.0300037x0.986182) -+ (1x0.969996x0.0138179) -+ (0x0.969996x0.986182) = 0.01340334947 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0300037x0.0138179) -+ (0x0.0300037x0.986182) -+ (0x0.969996x0.0138179) -+ (1x0.969996x0.986182) = 0.9565929739 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 5.770586867e-06 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005000000922 0.5 -b2 0.9949999991 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03000367664 0.5 -f2 0.9699963234 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03000367664 0.5 -f2 0.9699963234 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381647162 0.5 0.01381647162 -a2 0.9861835284 0.5 0.9861835284 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01381793843 0.5 -a2 0.9861820616 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004145889564 1 0.0004145889564 -_jn1 0.02958908769 1 0.02958908769 -_jn2 0.01340334947 1 0.01340334947 -_jn3 0.9565929739 1 0.9565929739 - - - -******************************************************************************** - Iteration 30 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.0300037) + (0.99x0.969996)]x0.5 -+ [(0.008x0.0300037) + (0.01x0.969996)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.0300037) + (0.003x0.969996)]x0.5 -+ [(0.8x0.0300037) + (0.997x0.969996)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138179) + (0x0.986182)]x1 -+ [(0x0.0138179) + (1x0.986182)]x1 -+ [(0x0.0138179) + (0x0.986182)]x1 -+ [(0x0.0138179) + (0x0.986182)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138179) + (0x0.986182)]x1 -+ [(0x0.0138179) + (0x0.986182)]x1 -+ [(1x0.0138179) + (0x0.986182)]x1 -+ [(0x0.0138179) + (1x0.986182)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.0300037) + (0x0.969996)]x1 -+ [(0x0.0300037) + (0x0.969996)]x1 -+ [(0x0.0300037) + (1x0.969996)]x1 -+ [(0x0.0300037) + (0x0.969996)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.0300037) + (0x0.969996)]x1 -+ [(1x0.0300037) + (0x0.969996)]x1 -+ [(0x0.0300037) + (0x0.969996)]x1 -+ [(0x0.0300037) + (1x0.969996)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138165 = 0.01381647162 -π_Jn(a2) = π(a2) = 0.986184 = 0.9861835284 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.0300025) -+ (0.99x0.005x0.969998) -+ (0.2x0.995x0.0300025) -+ (0.003x0.995x0.969998) = 0.01381623093 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.0300025) -+ (0.01x0.005x0.969998) -+ (0.8x0.995x0.0300025) -+ (0.997x0.995x0.969998) = 0.9861837691 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 4.813804621e-07 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.0300025x0.0138172) -+ (0x0.0300025x0.986183) -+ (0x0.969998x0.0138172) -+ (0x0.969998x0.986183) = 0.000414550018 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0300025x0.0138172) -+ (1x0.0300025x0.986183) -+ (0x0.969998x0.0138172) -+ (0x0.969998x0.986183) = 0.02958790108 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0300025x0.0138172) -+ (0x0.0300025x0.986183) -+ (1x0.969998x0.0138172) -+ (0x0.969998x0.986183) = 0.013402655 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0300025x0.0138172) -+ (0x0.0300025x0.986183) -+ (0x0.969998x0.0138172) -+ (1x0.969998x0.986183) = 0.9565948939 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 3.840025993e-06 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005000000461 0.5 -b2 0.9949999995 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03000245109 0.5 -f2 0.9699975489 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03000245109 0.5 -f2 0.9699975489 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381623093 0.5 0.01381623093 -a2 0.9861837691 0.5 0.9861837691 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01381720502 0.5 -a2 0.986182795 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.000414550018 1 0.000414550018 -_jn1 0.02958790108 1 0.02958790108 -_jn2 0.013402655 1 0.013402655 -_jn3 0.9565948939 1 0.9565948939 - - - -******************************************************************************** - Iteration 31 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.0300025) + (0.99x0.969998)]x0.5 -+ [(0.008x0.0300025) + (0.01x0.969998)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.0300025) + (0.003x0.969998)]x0.5 -+ [(0.8x0.0300025) + (0.997x0.969998)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138172) + (0x0.986183)]x1 -+ [(0x0.0138172) + (1x0.986183)]x1 -+ [(0x0.0138172) + (0x0.986183)]x1 -+ [(0x0.0138172) + (0x0.986183)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138172) + (0x0.986183)]x1 -+ [(0x0.0138172) + (0x0.986183)]x1 -+ [(1x0.0138172) + (0x0.986183)]x1 -+ [(0x0.0138172) + (1x0.986183)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.0300025) + (0x0.969998)]x1 -+ [(0x0.0300025) + (0x0.969998)]x1 -+ [(0x0.0300025) + (1x0.969998)]x1 -+ [(0x0.0300025) + (0x0.969998)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.0300025) + (0x0.969998)]x1 -+ [(1x0.0300025) + (0x0.969998)]x1 -+ [(0x0.0300025) + (0x0.969998)]x1 -+ [(0x0.0300025) + (1x0.969998)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138162 = 0.01381623093 -π_Jn(a2) = π(a2) = 0.986184 = 0.9861837691 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.0300016) -+ (0.99x0.005x0.969998) -+ (0.2x0.995x0.0300016) -+ (0.003x0.995x0.969998) = 0.01381607054 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.0300016) -+ (0.01x0.005x0.969998) -+ (0.8x0.995x0.0300016) -+ (0.997x0.995x0.969998) = 0.9861839295 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 3.207695366e-07 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.0300016x0.0138167) -+ (0x0.0300016x0.986183) -+ (0x0.969998x0.0138167) -+ (0x0.969998x0.986183) = 0.0004145241166 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0300016x0.0138167) -+ (1x0.0300016x0.986183) -+ (0x0.969998x0.0138167) -+ (0x0.969998x0.986183) = 0.02958710995 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0300016x0.0138167) -+ (0x0.0300016x0.986183) -+ (1x0.969998x0.0138167) -+ (0x0.969998x0.986183) = 0.01340219386 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0300016x0.0138167) -+ (0x0.0300016x0.986183) -+ (0x0.969998x0.0138167) -+ (1x0.969998x0.986183) = 0.9565961721 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 2.556354858e-06 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005000000231 0.5 -b2 0.9949999998 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03000163406 0.5 -f2 0.9699983659 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03000163406 0.5 -f2 0.9699983659 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381607054 0.5 0.01381607054 -a2 0.9861839295 0.5 0.9861839295 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01381671798 0.5 -a2 0.986183282 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004145241166 1 0.0004145241166 -_jn1 0.02958710995 1 0.02958710995 -_jn2 0.01340219386 1 0.01340219386 -_jn3 0.9565961721 1 0.9565961721 - - - -******************************************************************************** - Iteration 32 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.0300016) + (0.99x0.969998)]x0.5 -+ [(0.008x0.0300016) + (0.01x0.969998)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.0300016) + (0.003x0.969998)]x0.5 -+ [(0.8x0.0300016) + (0.997x0.969998)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138167) + (0x0.986183)]x1 -+ [(0x0.0138167) + (1x0.986183)]x1 -+ [(0x0.0138167) + (0x0.986183)]x1 -+ [(0x0.0138167) + (0x0.986183)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138167) + (0x0.986183)]x1 -+ [(0x0.0138167) + (0x0.986183)]x1 -+ [(1x0.0138167) + (0x0.986183)]x1 -+ [(0x0.0138167) + (1x0.986183)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.0300016) + (0x0.969998)]x1 -+ [(0x0.0300016) + (0x0.969998)]x1 -+ [(0x0.0300016) + (1x0.969998)]x1 -+ [(0x0.0300016) + (0x0.969998)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.0300016) + (0x0.969998)]x1 -+ [(1x0.0300016) + (0x0.969998)]x1 -+ [(0x0.0300016) + (0x0.969998)]x1 -+ [(0x0.0300016) + (1x0.969998)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138161 = 0.01381607054 -π_Jn(a2) = π(a2) = 0.986184 = 0.9861839295 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.0300011) -+ (0.99x0.005x0.969999) -+ (0.2x0.995x0.0300011) -+ (0.003x0.995x0.969999) = 0.01381596366 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.0300011) -+ (0.01x0.005x0.969999) -+ (0.8x0.995x0.0300011) -+ (0.997x0.995x0.969999) = 0.9861840363 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 2.137709722e-07 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.0300011x0.0138164) -+ (0x0.0300011x0.986184) -+ (0x0.969999x0.0138164) -+ (0x0.969999x0.986184) = 0.000414506879 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0300011x0.0138164) -+ (1x0.0300011x0.986184) -+ (0x0.969999x0.0138164) -+ (0x0.969999x0.986184) = 0.0295865825 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0300011x0.0138164) -+ (0x0.0300011x0.986184) -+ (1x0.969999x0.0138164) -+ (0x0.969999x0.986184) = 0.01340188738 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0300011x0.0138164) -+ (0x0.0300011x0.986184) -+ (0x0.969999x0.0138164) -+ (1x0.969999x0.986184) = 0.9565970232 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 1.702332097e-06 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005000000115 0.5 -b2 0.9949999999 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03000108938 0.5 -f2 0.9699989106 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03000108938 0.5 -f2 0.9699989106 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381596366 0.5 0.01381596366 -a2 0.9861840363 0.5 0.9861840363 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01381639426 0.5 -a2 0.9861836057 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.000414506879 1 0.000414506879 -_jn1 0.0295865825 1 0.0295865825 -_jn2 0.01340188738 1 0.01340188738 -_jn3 0.9565970232 1 0.9565970232 - - - -******************************************************************************** - Iteration 33 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.0300011) + (0.99x0.969999)]x0.5 -+ [(0.008x0.0300011) + (0.01x0.969999)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.0300011) + (0.003x0.969999)]x0.5 -+ [(0.8x0.0300011) + (0.997x0.969999)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138164) + (0x0.986184)]x1 -+ [(0x0.0138164) + (1x0.986184)]x1 -+ [(0x0.0138164) + (0x0.986184)]x1 -+ [(0x0.0138164) + (0x0.986184)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138164) + (0x0.986184)]x1 -+ [(0x0.0138164) + (0x0.986184)]x1 -+ [(1x0.0138164) + (0x0.986184)]x1 -+ [(0x0.0138164) + (1x0.986184)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.0300011) + (0x0.969999)]x1 -+ [(0x0.0300011) + (0x0.969999)]x1 -+ [(0x0.0300011) + (1x0.969999)]x1 -+ [(0x0.0300011) + (0x0.969999)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.0300011) + (0x0.969999)]x1 -+ [(1x0.0300011) + (0x0.969999)]x1 -+ [(0x0.0300011) + (0x0.969999)]x1 -+ [(0x0.0300011) + (1x0.969999)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.013816 = 0.01381596366 -π_Jn(a2) = π(a2) = 0.986184 = 0.9861840363 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.0300007) -+ (0.99x0.005x0.969999) -+ (0.2x0.995x0.0300007) -+ (0.003x0.995x0.969999) = 0.01381589242 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.0300007) -+ (0.01x0.005x0.969999) -+ (0.8x0.995x0.0300007) -+ (0.997x0.995x0.969999) = 0.9861841076 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 1.424762886e-07 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.0300007x0.0138162) -+ (0x0.0300007x0.986184) -+ (0x0.969999x0.0138162) -+ (0x0.969999x0.986184) = 0.0004144954028 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0300007x0.0138162) -+ (1x0.0300007x0.986184) -+ (0x0.969999x0.0138162) -+ (0x0.969999x0.986184) = 0.02958623085 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0300007x0.0138162) -+ (0x0.0300007x0.986184) -+ (1x0.969999x0.0138162) -+ (0x0.969999x0.986184) = 0.01340168356 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0300007x0.0138162) -+ (0x0.0300007x0.986184) -+ (0x0.969999x0.0138162) -+ (1x0.969999x0.986184) = 0.9565975902 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 1.133899215e-06 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005000000058 0.5 -b2 0.9949999999 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03000072625 0.5 -f2 0.9699992737 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03000072625 0.5 -f2 0.9699992737 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381589242 0.5 0.01381589242 -a2 0.9861841076 0.5 0.9861841076 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01381617896 0.5 -a2 0.986183821 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004144954028 1 0.0004144954028 -_jn1 0.02958623085 1 0.02958623085 -_jn2 0.01340168356 1 0.01340168356 -_jn3 0.9565975902 1 0.9565975902 - - - -******************************************************************************** - Iteration 34 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.0300007) + (0.99x0.969999)]x0.5 -+ [(0.008x0.0300007) + (0.01x0.969999)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.0300007) + (0.003x0.969999)]x0.5 -+ [(0.8x0.0300007) + (0.997x0.969999)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138162) + (0x0.986184)]x1 -+ [(0x0.0138162) + (1x0.986184)]x1 -+ [(0x0.0138162) + (0x0.986184)]x1 -+ [(0x0.0138162) + (0x0.986184)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138162) + (0x0.986184)]x1 -+ [(0x0.0138162) + (0x0.986184)]x1 -+ [(1x0.0138162) + (0x0.986184)]x1 -+ [(0x0.0138162) + (1x0.986184)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.0300007) + (0x0.969999)]x1 -+ [(0x0.0300007) + (0x0.969999)]x1 -+ [(0x0.0300007) + (1x0.969999)]x1 -+ [(0x0.0300007) + (0x0.969999)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.0300007) + (0x0.969999)]x1 -+ [(1x0.0300007) + (0x0.969999)]x1 -+ [(0x0.0300007) + (0x0.969999)]x1 -+ [(0x0.0300007) + (1x0.969999)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138159 = 0.01381589242 -π_Jn(a2) = π(a2) = 0.986184 = 0.9861841076 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 8.67361738e-19 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.0300005) -+ (0.99x0.005x0.97) -+ (0.2x0.995x0.0300005) -+ (0.003x0.995x0.97) = 0.01381584494 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.0300005) -+ (0.01x0.005x0.97) -+ (0.8x0.995x0.0300005) -+ (0.997x0.995x0.97) = 0.9861841551 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 9.496534587e-08 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.0300005x0.013816) -+ (0x0.0300005x0.986184) -+ (0x0.97x0.013816) -+ (0x0.97x0.986184) = 0.0004144877599 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0300005x0.013816) -+ (1x0.0300005x0.986184) -+ (0x0.97x0.013816) -+ (0x0.97x0.986184) = 0.02958599641 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0300005x0.013816) -+ (0x0.0300005x0.986184) -+ (1x0.97x0.013816) -+ (0x0.97x0.986184) = 0.01340154793 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0300005x0.013816) -+ (0x0.0300005x0.986184) -+ (0x0.97x0.013816) -+ (1x0.97x0.986184) = 0.9565979679 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 7.554200814e-07 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005000000029 0.5 -b2 0.995 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03000048417 0.5 -f2 0.9699995158 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03000048417 0.5 -f2 0.9699995158 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381584494 0.5 0.01381584494 -a2 0.9861841551 0.5 0.9861841551 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01381603569 0.5 -a2 0.9861839643 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004144877599 1 0.0004144877599 -_jn1 0.02958599641 1 0.02958599641 -_jn2 0.01340154793 1 0.01340154793 -_jn3 0.9565979679 1 0.9565979679 - - - -******************************************************************************** - Iteration 35 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.0300005) + (0.99x0.97)]x0.5 -+ [(0.008x0.0300005) + (0.01x0.97)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.0300005) + (0.003x0.97)]x0.5 -+ [(0.8x0.0300005) + (0.997x0.97)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.013816) + (0x0.986184)]x1 -+ [(0x0.013816) + (1x0.986184)]x1 -+ [(0x0.013816) + (0x0.986184)]x1 -+ [(0x0.013816) + (0x0.986184)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.013816) + (0x0.986184)]x1 -+ [(0x0.013816) + (0x0.986184)]x1 -+ [(1x0.013816) + (0x0.986184)]x1 -+ [(0x0.013816) + (1x0.986184)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.0300005) + (0x0.97)]x1 -+ [(0x0.0300005) + (0x0.97)]x1 -+ [(0x0.0300005) + (1x0.97)]x1 -+ [(0x0.0300005) + (0x0.97)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.0300005) + (0x0.97)]x1 -+ [(1x0.0300005) + (0x0.97)]x1 -+ [(0x0.0300005) + (0x0.97)]x1 -+ [(0x0.0300005) + (1x0.97)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138158 = 0.01381584494 -π_Jn(a2) = π(a2) = 0.986184 = 0.9861841551 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 8.67361738e-19 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.0300003) -+ (0.99x0.005x0.97) -+ (0.2x0.995x0.0300003) -+ (0.003x0.995x0.97) = 0.01381581329 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.0300003) -+ (0.01x0.005x0.97) -+ (0.8x0.995x0.0300003) -+ (0.997x0.995x0.97) = 0.9861841867 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 6.330080745e-08 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.0300003x0.0138159) -+ (0x0.0300003x0.986184) -+ (0x0.97x0.0138159) -+ (0x0.97x0.986184) = 0.0004144826689 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0300003x0.0138159) -+ (1x0.0300003x0.986184) -+ (0x0.97x0.0138159) -+ (0x0.97x0.986184) = 0.02958584011 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0300003x0.0138159) -+ (0x0.0300003x0.986184) -+ (1x0.97x0.0138159) -+ (0x0.97x0.986184) = 0.01340145764 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0300003x0.0138159) -+ (0x0.0300003x0.986184) -+ (0x0.97x0.0138159) -+ (1x0.97x0.986184) = 0.9565982196 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 5.033478731e-07 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005000000014 0.5 -b2 0.995 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03000032278 0.5 -f2 0.9699996772 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03000032278 0.5 -f2 0.9699996772 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381581329 0.5 0.01381581329 -a2 0.9861841867 0.5 0.9861841867 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01381594031 0.5 -a2 0.9861840597 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004144826689 1 0.0004144826689 -_jn1 0.02958584011 1 0.02958584011 -_jn2 0.01340145764 1 0.01340145764 -_jn3 0.9565982196 1 0.9565982196 - - - -******************************************************************************** - Iteration 36 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.0300003) + (0.99x0.97)]x0.5 -+ [(0.008x0.0300003) + (0.01x0.97)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.0300003) + (0.003x0.97)]x0.5 -+ [(0.8x0.0300003) + (0.997x0.97)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138159) + (0x0.986184)]x1 -+ [(0x0.0138159) + (1x0.986184)]x1 -+ [(0x0.0138159) + (0x0.986184)]x1 -+ [(0x0.0138159) + (0x0.986184)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138159) + (0x0.986184)]x1 -+ [(0x0.0138159) + (0x0.986184)]x1 -+ [(1x0.0138159) + (0x0.986184)]x1 -+ [(0x0.0138159) + (1x0.986184)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.0300003) + (0x0.97)]x1 -+ [(0x0.0300003) + (0x0.97)]x1 -+ [(0x0.0300003) + (1x0.97)]x1 -+ [(0x0.0300003) + (0x0.97)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.0300003) + (0x0.97)]x1 -+ [(1x0.0300003) + (0x0.97)]x1 -+ [(0x0.0300003) + (0x0.97)]x1 -+ [(0x0.0300003) + (1x0.97)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138158 = 0.01381581329 -π_Jn(a2) = π(a2) = 0.986184 = 0.9861841867 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.0300002) -+ (0.99x0.005x0.97) -+ (0.2x0.995x0.0300002) -+ (0.003x0.995x0.97) = 0.01381579219 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.0300002) -+ (0.01x0.005x0.97) -+ (0.8x0.995x0.0300002) -+ (0.997x0.995x0.97) = 0.9861842078 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 4.219582663e-08 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.0300002x0.0138159) -+ (0x0.0300002x0.986184) -+ (0x0.97x0.0138159) -+ (0x0.97x0.986184) = 0.000414479277 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0300002x0.0138159) -+ (1x0.0300002x0.986184) -+ (0x0.97x0.0138159) -+ (0x0.97x0.986184) = 0.02958573591 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0300002x0.0138159) -+ (0x0.0300002x0.986184) -+ (1x0.97x0.0138159) -+ (0x0.97x0.986184) = 0.01340139752 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0300002x0.0138159) -+ (0x0.0300002x0.986184) -+ (0x0.97x0.0138159) -+ (1x0.97x0.986184) = 0.9565983873 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 3.354279168e-07 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005000000007 0.5 -b2 0.995 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03000021519 0.5 -f2 0.9699997848 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03000021519 0.5 -f2 0.9699997848 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381579219 0.5 0.01381579219 -a2 0.9861842078 0.5 0.9861842078 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.0138158768 0.5 -a2 0.9861841232 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.000414479277 1 0.000414479277 -_jn1 0.02958573591 1 0.02958573591 -_jn2 0.01340139752 1 0.01340139752 -_jn3 0.9565983873 1 0.9565983873 - - - -******************************************************************************** - Iteration 37 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.0300002) + (0.99x0.97)]x0.5 -+ [(0.008x0.0300002) + (0.01x0.97)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.0300002) + (0.003x0.97)]x0.5 -+ [(0.8x0.0300002) + (0.997x0.97)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138159) + (0x0.986184)]x1 -+ [(0x0.0138159) + (1x0.986184)]x1 -+ [(0x0.0138159) + (0x0.986184)]x1 -+ [(0x0.0138159) + (0x0.986184)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138159) + (0x0.986184)]x1 -+ [(0x0.0138159) + (0x0.986184)]x1 -+ [(1x0.0138159) + (0x0.986184)]x1 -+ [(0x0.0138159) + (1x0.986184)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.0300002) + (0x0.97)]x1 -+ [(0x0.0300002) + (0x0.97)]x1 -+ [(0x0.0300002) + (1x0.97)]x1 -+ [(0x0.0300002) + (0x0.97)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.0300002) + (0x0.97)]x1 -+ [(1x0.0300002) + (0x0.97)]x1 -+ [(0x0.0300002) + (0x0.97)]x1 -+ [(0x0.0300002) + (1x0.97)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138158 = 0.01381579219 -π_Jn(a2) = π(a2) = 0.986184 = 0.9861842078 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.0300001) -+ (0.99x0.005x0.97) -+ (0.2x0.995x0.0300001) -+ (0.003x0.995x0.97) = 0.01381577812 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.0300001) -+ (0.01x0.005x0.97) -+ (0.8x0.995x0.0300001) -+ (0.997x0.995x0.97) = 0.9861842219 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 2.812819542e-08 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.0300001x0.0138158) -+ (0x0.0300001x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0004144770168 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0300001x0.0138158) -+ (1x0.0300001x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.02958566644 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0300001x0.0138158) -+ (0x0.0300001x0.986184) -+ (1x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.01340135748 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0300001x0.0138158) -+ (0x0.0300001x0.986184) -+ (0x0.97x0.0138158) -+ (1x0.97x0.986184) = 0.9565984991 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 2.235476582e-07 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005000000004 0.5 -b2 0.995 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03000014346 0.5 -f2 0.9699998565 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03000014346 0.5 -f2 0.9699998565 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381577812 0.5 0.01381577812 -a2 0.9861842219 0.5 0.9861842219 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01381583449 0.5 -a2 0.9861841655 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004144770168 1 0.0004144770168 -_jn1 0.02958566644 1 0.02958566644 -_jn2 0.01340135748 1 0.01340135748 -_jn3 0.9565984991 1 0.9565984991 - - - -******************************************************************************** - Iteration 38 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.0300001) + (0.99x0.97)]x0.5 -+ [(0.008x0.0300001) + (0.01x0.97)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.0300001) + (0.003x0.97)]x0.5 -+ [(0.8x0.0300001) + (0.997x0.97)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.0300001) + (0x0.97)]x1 -+ [(0x0.0300001) + (0x0.97)]x1 -+ [(0x0.0300001) + (1x0.97)]x1 -+ [(0x0.0300001) + (0x0.97)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.0300001) + (0x0.97)]x1 -+ [(1x0.0300001) + (0x0.97)]x1 -+ [(0x0.0300001) + (0x0.97)]x1 -+ [(0x0.0300001) + (1x0.97)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138158 = 0.01381577812 -π_Jn(a2) = π(a2) = 0.986184 = 0.9861842219 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.0300001) -+ (0.99x0.005x0.97) -+ (0.2x0.995x0.0300001) -+ (0.003x0.995x0.97) = 0.01381576875 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.0300001) -+ (0.01x0.005x0.97) -+ (0.8x0.995x0.0300001) -+ (0.997x0.995x0.97) = 0.9861842313 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 1.875095211e-08 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.0300001x0.0138158) -+ (0x0.0300001x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0004144755106 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0300001x0.0138158) -+ (1x0.0300001x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.02958562013 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0300001x0.0138158) -+ (0x0.0300001x0.986184) -+ (1x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0134013308 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0300001x0.0138158) -+ (0x0.0300001x0.986184) -+ (0x0.97x0.0138158) -+ (1x0.97x0.986184) = 0.9565985736 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 1.489951524e-07 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005000000002 0.5 -b2 0.995 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03000009564 0.5 -f2 0.9699999044 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03000009564 0.5 -f2 0.9699999044 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381576875 0.5 0.01381576875 -a2 0.9861842313 0.5 0.9861842313 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01381580631 0.5 -a2 0.9861841937 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004144755106 1 0.0004144755106 -_jn1 0.02958562013 1 0.02958562013 -_jn2 0.0134013308 1 0.0134013308 -_jn3 0.9565985736 1 0.9565985736 - - - -******************************************************************************** - Iteration 39 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.0300001) + (0.99x0.97)]x0.5 -+ [(0.008x0.0300001) + (0.01x0.97)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.0300001) + (0.003x0.97)]x0.5 -+ [(0.8x0.0300001) + (0.997x0.97)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.0300001) + (0x0.97)]x1 -+ [(0x0.0300001) + (0x0.97)]x1 -+ [(0x0.0300001) + (1x0.97)]x1 -+ [(0x0.0300001) + (0x0.97)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.0300001) + (0x0.97)]x1 -+ [(1x0.0300001) + (0x0.97)]x1 -+ [(0x0.0300001) + (0x0.97)]x1 -+ [(0x0.0300001) + (1x0.97)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138158 = 0.01381576875 -π_Jn(a2) = π(a2) = 0.986184 = 0.9861842313 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.0300001) -+ (0.99x0.005x0.97) -+ (0.2x0.995x0.0300001) -+ (0.003x0.995x0.97) = 0.0138157625 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.0300001) -+ (0.01x0.005x0.97) -+ (0.8x0.995x0.0300001) -+ (0.997x0.995x0.97) = 0.9861842375 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 1.250004601e-08 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.0300001x0.0138158) -+ (0x0.0300001x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0004144745068 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0300001x0.0138158) -+ (1x0.0300001x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.02958558925 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0300001x0.0138158) -+ (0x0.0300001x0.986184) -+ (1x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.01340131302 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.0300001x0.0138158) -+ (0x0.0300001x0.986184) -+ (0x0.97x0.0138158) -+ (1x0.97x0.986184) = 0.9565986232 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 9.931121969e-08 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005000000001 0.5 -b2 0.995 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03000006376 0.5 -f2 0.9699999362 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03000006376 0.5 -f2 0.9699999362 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.0138157625 0.5 0.0138157625 -a2 0.9861842375 0.5 0.9861842375 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01381578753 0.5 -a2 0.9861842125 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004144745068 1 0.0004144745068 -_jn1 0.02958558925 1 0.02958558925 -_jn2 0.01340131302 1 0.01340131302 -_jn3 0.9565986232 1 0.9565986232 - - - -******************************************************************************** - Iteration 40 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.0300001) + (0.99x0.97)]x0.5 -+ [(0.008x0.0300001) + (0.01x0.97)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.0300001) + (0.003x0.97)]x0.5 -+ [(0.8x0.0300001) + (0.997x0.97)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.0300001) + (0x0.97)]x1 -+ [(0x0.0300001) + (0x0.97)]x1 -+ [(0x0.0300001) + (1x0.97)]x1 -+ [(0x0.0300001) + (0x0.97)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.0300001) + (0x0.97)]x1 -+ [(1x0.0300001) + (0x0.97)]x1 -+ [(0x0.0300001) + (0x0.97)]x1 -+ [(0x0.0300001) + (1x0.97)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138158 = 0.0138157625 -π_Jn(a2) = π(a2) = 0.986184 = 0.9861842375 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.03) -+ (0.99x0.005x0.97) -+ (0.2x0.995x0.03) -+ (0.003x0.995x0.97) = 0.01381575833 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.03) -+ (0.01x0.005x0.97) -+ (0.8x0.995x0.03) -+ (0.997x0.995x0.97) = 0.9861842417 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 8.333069516e-09 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0004144738377 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (1x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.02958556867 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (1x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.01340130118 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (1x0.97x0.986184) = 0.9565986563 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 6.61977534e-08 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005 0.5 -b2 0.995 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03000004251 0.5 -f2 0.9699999575 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03000004251 0.5 -f2 0.9699999575 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381575833 0.5 0.01381575833 -a2 0.9861842417 0.5 0.9861842417 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01381577501 0.5 -a2 0.986184225 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004144738377 1 0.0004144738377 -_jn1 0.02958556867 1 0.02958556867 -_jn2 0.01340130118 1 0.01340130118 -_jn3 0.9565986563 1 0.9565986563 - - - -******************************************************************************** - Iteration 41 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.03) + (0.99x0.97)]x0.5 -+ [(0.008x0.03) + (0.01x0.97)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.03) + (0.003x0.97)]x0.5 -+ [(0.8x0.03) + (0.997x0.97)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.03) + (0x0.97)]x1 -+ [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138158 = 0.01381575833 -π_Jn(a2) = π(a2) = 0.986184 = 0.9861842417 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.03) -+ (0.99x0.005x0.97) -+ (0.2x0.995x0.03) -+ (0.003x0.995x0.97) = 0.01381575556 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.03) -+ (0.01x0.005x0.97) -+ (0.8x0.995x0.03) -+ (0.997x0.995x0.97) = 0.9861842444 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 5.555232455e-09 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0004144733917 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (1x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.02958555495 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (1x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.01340129328 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (1x0.97x0.986184) = 0.9565986784 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 4.412682933e-08 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005 0.5 -b2 0.995 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03000002834 0.5 -f2 0.9699999717 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03000002834 0.5 -f2 0.9699999717 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381575556 0.5 0.01381575556 -a2 0.9861842444 0.5 0.9861842444 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01381576667 0.5 -a2 0.9861842333 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004144733917 1 0.0004144733917 -_jn1 0.02958555495 1 0.02958555495 -_jn2 0.01340129328 1 0.01340129328 -_jn3 0.9565986784 1 0.9565986784 - - - -******************************************************************************** - Iteration 42 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.03) + (0.99x0.97)]x0.5 -+ [(0.008x0.03) + (0.01x0.97)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.03) + (0.003x0.97)]x0.5 -+ [(0.8x0.03) + (0.997x0.97)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.03) + (0x0.97)]x1 -+ [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138158 = 0.01381575556 -π_Jn(a2) = π(a2) = 0.986184 = 0.9861842444 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.03) -+ (0.99x0.005x0.97) -+ (0.2x0.995x0.03) -+ (0.003x0.995x0.97) = 0.0138157537 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.03) -+ (0.01x0.005x0.97) -+ (0.8x0.995x0.03) -+ (0.997x0.995x0.97) = 0.9861842463 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 3.703414561e-09 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0004144730944 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (1x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0295855458 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (1x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.01340128802 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (1x0.97x0.986184) = 0.9565986931 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 2.941531181e-08 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005 0.5 -b2 0.995 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03000001889 0.5 -f2 0.9699999811 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03000001889 0.5 -f2 0.9699999811 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.0138157537 0.5 0.0138157537 -a2 0.9861842463 0.5 0.9861842463 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01381576111 0.5 -a2 0.9861842389 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004144730944 1 0.0004144730944 -_jn1 0.0295855458 1 0.0295855458 -_jn2 0.01340128802 1 0.01340128802 -_jn3 0.9565986931 1 0.9565986931 - - - -******************************************************************************** - Iteration 43 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.03) + (0.99x0.97)]x0.5 -+ [(0.008x0.03) + (0.01x0.97)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.03) + (0.003x0.97)]x0.5 -+ [(0.8x0.03) + (0.997x0.97)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.03) + (0x0.97)]x1 -+ [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138158 = 0.0138157537 -π_Jn(a2) = π(a2) = 0.986184 = 0.9861842463 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.03) -+ (0.99x0.005x0.97) -+ (0.2x0.995x0.03) -+ (0.003x0.995x0.97) = 0.01381575247 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.03) -+ (0.01x0.005x0.97) -+ (0.8x0.995x0.03) -+ (0.997x0.995x0.97) = 0.9861842475 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 2.46890635e-09 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0004144728963 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (1x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0295855397 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (1x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.01340128451 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (1x0.97x0.986184) = 0.9565987029 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 1.960888467e-08 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005 0.5 -b2 0.995 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03000001259 0.5 -f2 0.9699999874 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03000001259 0.5 -f2 0.9699999874 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381575247 0.5 0.01381575247 -a2 0.9861842475 0.5 0.9861842475 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01381575741 0.5 -a2 0.9861842426 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004144728963 1 0.0004144728963 -_jn1 0.0295855397 1 0.0295855397 -_jn2 0.01340128451 1 0.01340128451 -_jn3 0.9565987029 1 0.9565987029 - - - -******************************************************************************** - Iteration 44 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.03) + (0.99x0.97)]x0.5 -+ [(0.008x0.03) + (0.01x0.97)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.03) + (0.003x0.97)]x0.5 -+ [(0.8x0.03) + (0.997x0.97)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.03) + (0x0.97)]x1 -+ [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138158 = 0.01381575247 -π_Jn(a2) = π(a2) = 0.986184 = 0.9861842475 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.03) -+ (0.99x0.005x0.97) -+ (0.2x0.995x0.03) -+ (0.003x0.995x0.97) = 0.01381575165 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.03) -+ (0.01x0.005x0.97) -+ (0.8x0.995x0.03) -+ (0.997x0.995x0.97) = 0.9861842484 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 1.645919151e-09 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0004144727642 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (1x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.02958553563 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (1x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.01340128217 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (1x0.97x0.986184) = 0.9565987094 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 1.307191058e-08 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005 0.5 -b2 0.995 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.0300000084 0.5 -f2 0.9699999916 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.0300000084 0.5 -f2 0.9699999916 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381575165 0.5 0.01381575165 -a2 0.9861842484 0.5 0.9861842484 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01381575494 0.5 -a2 0.9861842451 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004144727642 1 0.0004144727642 -_jn1 0.02958553563 1 0.02958553563 -_jn2 0.01340128217 1 0.01340128217 -_jn3 0.9565987094 1 0.9565987094 - - - -******************************************************************************** - Iteration 45 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.03) + (0.99x0.97)]x0.5 -+ [(0.008x0.03) + (0.01x0.97)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.03) + (0.003x0.97)]x0.5 -+ [(0.8x0.03) + (0.997x0.97)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.03) + (0x0.97)]x1 -+ [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138158 = 0.01381575165 -π_Jn(a2) = π(a2) = 0.986184 = 0.9861842484 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.03) -+ (0.99x0.005x0.97) -+ (0.2x0.995x0.03) -+ (0.003x0.995x0.97) = 0.0138157511 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.03) -+ (0.01x0.005x0.97) -+ (0.8x0.995x0.03) -+ (0.997x0.995x0.97) = 0.9861842489 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 1.097270131e-09 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0004144726761 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (1x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.02958553292 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (1x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.01340128062 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (1x0.97x0.986184) = 0.9565987138 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 8.714258307e-09 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005 0.5 -b2 0.995 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.0300000056 0.5 -f2 0.9699999944 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.0300000056 0.5 -f2 0.9699999944 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.0138157511 0.5 0.0138157511 -a2 0.9861842489 0.5 0.9861842489 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01381575329 0.5 -a2 0.9861842467 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004144726761 1 0.0004144726761 -_jn1 0.02958553292 1 0.02958553292 -_jn2 0.01340128062 1 0.01340128062 -_jn3 0.9565987138 1 0.9565987138 - - - -******************************************************************************** - Iteration 46 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.03) + (0.99x0.97)]x0.5 -+ [(0.008x0.03) + (0.01x0.97)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.03) + (0.003x0.97)]x0.5 -+ [(0.8x0.03) + (0.997x0.97)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.03) + (0x0.97)]x1 -+ [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138158 = 0.0138157511 -π_Jn(a2) = π(a2) = 0.986184 = 0.9861842489 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.03) -+ (0.99x0.005x0.97) -+ (0.2x0.995x0.03) -+ (0.003x0.995x0.97) = 0.01381575073 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.03) -+ (0.01x0.005x0.97) -+ (0.8x0.995x0.03) -+ (0.997x0.995x0.97) = 0.9861842493 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 7.315088656e-10 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0004144726174 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (1x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.02958553111 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (1x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.01340127958 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (1x0.97x0.986184) = 0.9565987167 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 5.809326921e-09 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005 0.5 -b2 0.995 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03000000373 0.5 -f2 0.9699999963 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03000000373 0.5 -f2 0.9699999963 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381575073 0.5 0.01381575073 -a2 0.9861842493 0.5 0.9861842493 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01381575219 0.5 -a2 0.9861842478 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004144726174 1 0.0004144726174 -_jn1 0.02958553111 1 0.02958553111 -_jn2 0.01340127958 1 0.01340127958 -_jn3 0.9565987167 1 0.9565987167 - - - -******************************************************************************** - Iteration 47 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.03) + (0.99x0.97)]x0.5 -+ [(0.008x0.03) + (0.01x0.97)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.03) + (0.003x0.97)]x0.5 -+ [(0.8x0.03) + (0.997x0.97)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.03) + (0x0.97)]x1 -+ [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138158 = 0.01381575073 -π_Jn(a2) = π(a2) = 0.986184 = 0.9861842493 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.03) -+ (0.99x0.005x0.97) -+ (0.2x0.995x0.03) -+ (0.003x0.995x0.97) = 0.01381575049 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.03) -+ (0.01x0.005x0.97) -+ (0.8x0.995x0.03) -+ (0.997x0.995x0.97) = 0.9861842495 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 4.876703156e-10 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0004144725783 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (1x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.02958552991 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (1x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.01340127888 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (1x0.97x0.986184) = 0.9565987186 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 3.872792849e-09 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005 0.5 -b2 0.995 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03000000249 0.5 -f2 0.9699999975 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03000000249 0.5 -f2 0.9699999975 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381575049 0.5 0.01381575049 -a2 0.9861842495 0.5 0.9861842495 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01381575146 0.5 -a2 0.9861842485 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004144725783 1 0.0004144725783 -_jn1 0.02958552991 1 0.02958552991 -_jn2 0.01340127888 1 0.01340127888 -_jn3 0.9565987186 1 0.9565987186 - - - -******************************************************************************** - Iteration 48 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.03) + (0.99x0.97)]x0.5 -+ [(0.008x0.03) + (0.01x0.97)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.03) + (0.003x0.97)]x0.5 -+ [(0.8x0.03) + (0.997x0.97)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.03) + (0x0.97)]x1 -+ [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138158 = 0.01381575049 -π_Jn(a2) = π(a2) = 0.986184 = 0.9861842495 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.03) -+ (0.99x0.005x0.97) -+ (0.2x0.995x0.03) -+ (0.003x0.995x0.97) = 0.01381575033 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.03) -+ (0.01x0.005x0.97) -+ (0.8x0.995x0.03) -+ (0.997x0.995x0.97) = 0.9861842497 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 3.25112378e-10 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0004144725522 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (1x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.02958552911 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (1x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.01340127842 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (1x0.97x0.986184) = 0.9565987199 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 2.58181512e-09 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005 0.5 -b2 0.995 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03000000166 0.5 -f2 0.9699999983 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03000000166 0.5 -f2 0.9699999983 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381575033 0.5 0.01381575033 -a2 0.9861842497 0.5 0.9861842497 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01381575098 0.5 -a2 0.986184249 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004144725522 1 0.0004144725522 -_jn1 0.02958552911 1 0.02958552911 -_jn2 0.01340127842 1 0.01340127842 -_jn3 0.9565987199 1 0.9565987199 - - - -******************************************************************************** - Iteration 49 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.03) + (0.99x0.97)]x0.5 -+ [(0.008x0.03) + (0.01x0.97)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.03) + (0.003x0.97)]x0.5 -+ [(0.8x0.03) + (0.997x0.97)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.03) + (0x0.97)]x1 -+ [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138158 = 0.01381575033 -π_Jn(a2) = π(a2) = 0.986184 = 0.9861842497 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.03) -+ (0.99x0.005x0.97) -+ (0.2x0.995x0.03) -+ (0.003x0.995x0.97) = 0.01381575022 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.03) -+ (0.01x0.005x0.97) -+ (0.8x0.995x0.03) -+ (0.997x0.995x0.97) = 0.9861842498 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 2.167409273e-10 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0004144725348 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (1x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.02958552857 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (1x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.01340127812 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (1x0.97x0.986184) = 0.9565987208 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 1.721185934e-09 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005 0.5 -b2 0.995 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03000000111 0.5 -f2 0.9699999989 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03000000111 0.5 -f2 0.9699999989 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381575022 0.5 0.01381575022 -a2 0.9861842498 0.5 0.9861842498 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01381575065 0.5 -a2 0.9861842493 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004144725348 1 0.0004144725348 -_jn1 0.02958552857 1 0.02958552857 -_jn2 0.01340127812 1 0.01340127812 -_jn3 0.9565987208 1 0.9565987208 - - - -******************************************************************************** - Iteration 50 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.03) + (0.99x0.97)]x0.5 -+ [(0.008x0.03) + (0.01x0.97)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.03) + (0.003x0.97)]x0.5 -+ [(0.8x0.03) + (0.997x0.97)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.03) + (0x0.97)]x1 -+ [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138158 = 0.01381575022 -π_Jn(a2) = π(a2) = 0.986184 = 0.9861842498 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 8.67361738e-19 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.03) -+ (0.99x0.005x0.97) -+ (0.2x0.995x0.03) -+ (0.003x0.995x0.97) = 0.01381575014 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.03) -+ (0.01x0.005x0.97) -+ (0.8x0.995x0.03) -+ (0.997x0.995x0.97) = 0.9861842499 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 1.444937295e-10 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0004144725232 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (1x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.02958552821 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (1x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.01340127791 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (1x0.97x0.986184) = 0.9565987214 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 1.147445038e-09 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005 0.5 -b2 0.995 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03000000074 0.5 -f2 0.9699999993 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03000000074 0.5 -f2 0.9699999993 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381575014 0.5 0.01381575014 -a2 0.9861842499 0.5 0.9861842499 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01381575043 0.5 -a2 0.9861842496 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004144725232 1 0.0004144725232 -_jn1 0.02958552821 1 0.02958552821 -_jn2 0.01340127791 1 0.01340127791 -_jn3 0.9565987214 1 0.9565987214 - - - -******************************************************************************** - Iteration 51 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.03) + (0.99x0.97)]x0.5 -+ [(0.008x0.03) + (0.01x0.97)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.03) + (0.003x0.97)]x0.5 -+ [(0.8x0.03) + (0.997x0.97)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.03) + (0x0.97)]x1 -+ [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138158 = 0.01381575014 -π_Jn(a2) = π(a2) = 0.986184 = 0.9861842499 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 8.67361738e-19 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.03) -+ (0.99x0.005x0.97) -+ (0.2x0.995x0.03) -+ (0.003x0.995x0.97) = 0.0138157501 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.03) -+ (0.01x0.005x0.97) -+ (0.8x0.995x0.03) -+ (0.997x0.995x0.97) = 0.9861842499 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 9.632908707e-11 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0004144725155 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (1x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.02958552798 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (1x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.01340127777 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (1x0.97x0.986184) = 0.9565987217 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 7.649571397e-10 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005 0.5 -b2 0.995 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03000000049 0.5 -f2 0.9699999995 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03000000049 0.5 -f2 0.9699999995 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.0138157501 0.5 0.0138157501 -a2 0.9861842499 0.5 0.9861842499 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01381575029 0.5 -a2 0.9861842497 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004144725155 1 0.0004144725155 -_jn1 0.02958552798 1 0.02958552798 -_jn2 0.01340127777 1 0.01340127777 -_jn3 0.9565987217 1 0.9565987217 - - - -******************************************************************************** - Iteration 52 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.03) + (0.99x0.97)]x0.5 -+ [(0.008x0.03) + (0.01x0.97)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.03) + (0.003x0.97)]x0.5 -+ [(0.8x0.03) + (0.997x0.97)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.03) + (0x0.97)]x1 -+ [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138158 = 0.0138157501 -π_Jn(a2) = π(a2) = 0.986184 = 0.9861842499 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 8.67361738e-19 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.03) -+ (0.99x0.005x0.97) -+ (0.2x0.995x0.03) -+ (0.003x0.995x0.97) = 0.01381575006 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.03) -+ (0.01x0.005x0.97) -+ (0.8x0.995x0.03) -+ (0.997x0.995x0.97) = 0.9861842499 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 6.421927573e-11 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0004144725103 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (1x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.02958552782 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (1x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.01340127768 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (1x0.97x0.986184) = 0.956598722 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 5.099682295e-10 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005 0.5 -b2 0.995 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03000000033 0.5 -f2 0.9699999997 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03000000033 0.5 -f2 0.9699999997 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381575006 0.5 0.01381575006 -a2 0.9861842499 0.5 0.9861842499 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01381575019 0.5 -a2 0.9861842498 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004144725103 1 0.0004144725103 -_jn1 0.02958552782 1 0.02958552782 -_jn2 0.01340127768 1 0.01340127768 -_jn3 0.956598722 1 0.956598722 - - - -******************************************************************************** - Iteration 53 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.03) + (0.99x0.97)]x0.5 -+ [(0.008x0.03) + (0.01x0.97)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.03) + (0.003x0.97)]x0.5 -+ [(0.8x0.03) + (0.997x0.97)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.03) + (0x0.97)]x1 -+ [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138158 = 0.01381575006 -π_Jn(a2) = π(a2) = 0.986184 = 0.9861842499 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 8.67361738e-19 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.03) -+ (0.99x0.005x0.97) -+ (0.2x0.995x0.03) -+ (0.003x0.995x0.97) = 0.01381575004 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.03) -+ (0.01x0.005x0.97) -+ (0.8x0.995x0.03) -+ (0.997x0.995x0.97) = 0.98618425 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 4.281283314e-11 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0004144725069 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (1x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.02958552771 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (1x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.01340127762 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (1x0.97x0.986184) = 0.9565987222 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 3.399771473e-10 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005 0.5 -b2 0.995 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03000000022 0.5 -f2 0.9699999998 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03000000022 0.5 -f2 0.9699999998 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381575004 0.5 0.01381575004 -a2 0.98618425 0.5 0.98618425 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01381575013 0.5 -a2 0.9861842499 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004144725069 1 0.0004144725069 -_jn1 0.02958552771 1 0.02958552771 -_jn2 0.01340127762 1 0.01340127762 -_jn3 0.9565987222 1 0.9565987222 - - - -******************************************************************************** - Iteration 54 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.03) + (0.99x0.97)]x0.5 -+ [(0.008x0.03) + (0.01x0.97)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.03) + (0.003x0.97)]x0.5 -+ [(0.8x0.03) + (0.997x0.97)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.03) + (0x0.97)]x1 -+ [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138158 = 0.01381575004 -π_Jn(a2) = π(a2) = 0.986184 = 0.98618425 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.03) -+ (0.99x0.005x0.97) -+ (0.2x0.995x0.03) -+ (0.003x0.995x0.97) = 0.01381575003 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.03) -+ (0.01x0.005x0.97) -+ (0.8x0.995x0.03) -+ (0.997x0.995x0.97) = 0.98618425 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 2.854173495e-11 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0004144725046 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (1x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.02958552764 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (1x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.01340127758 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (1x0.97x0.986184) = 0.9565987223 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 2.26650527e-10 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005 0.5 -b2 0.995 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03000000015 0.5 -f2 0.9699999999 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03000000015 0.5 -f2 0.9699999999 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381575003 0.5 0.01381575003 -a2 0.98618425 0.5 0.98618425 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01381575009 0.5 -a2 0.9861842499 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004144725046 1 0.0004144725046 -_jn1 0.02958552764 1 0.02958552764 -_jn2 0.01340127758 1 0.01340127758 -_jn3 0.9565987223 1 0.9565987223 - - - -******************************************************************************** - Iteration 55 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.03) + (0.99x0.97)]x0.5 -+ [(0.008x0.03) + (0.01x0.97)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.03) + (0.003x0.97)]x0.5 -+ [(0.8x0.03) + (0.997x0.97)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.03) + (0x0.97)]x1 -+ [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138158 = 0.01381575003 -π_Jn(a2) = π(a2) = 0.986184 = 0.98618425 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.03) -+ (0.99x0.005x0.97) -+ (0.2x0.995x0.03) -+ (0.003x0.995x0.97) = 0.01381575002 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.03) -+ (0.01x0.005x0.97) -+ (0.8x0.995x0.03) -+ (0.997x0.995x0.97) = 0.98618425 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 1.90280014e-11 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0004144725031 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (1x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.02958552759 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (1x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.01340127755 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (1x0.97x0.986184) = 0.9565987223 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 1.510999967e-10 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005 0.5 -b2 0.995 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.0300000001 0.5 -f2 0.9699999999 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.0300000001 0.5 -f2 0.9699999999 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381575002 0.5 0.01381575002 -a2 0.98618425 0.5 0.98618425 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01381575006 0.5 -a2 0.9861842499 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004144725031 1 0.0004144725031 -_jn1 0.02958552759 1 0.02958552759 -_jn2 0.01340127755 1 0.01340127755 -_jn3 0.9565987223 1 0.9565987223 - - - -******************************************************************************** - Iteration 56 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.03) + (0.99x0.97)]x0.5 -+ [(0.008x0.03) + (0.01x0.97)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.03) + (0.003x0.97)]x0.5 -+ [(0.8x0.03) + (0.997x0.97)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.03) + (0x0.97)]x1 -+ [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138158 = 0.01381575002 -π_Jn(a2) = π(a2) = 0.986184 = 0.98618425 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.03) -+ (0.99x0.005x0.97) -+ (0.2x0.995x0.03) -+ (0.003x0.995x0.97) = 0.01381575001 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.03) -+ (0.01x0.005x0.97) -+ (0.8x0.995x0.03) -+ (0.997x0.995x0.97) = 0.98618425 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 1.268522093e-11 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.000414472502 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (1x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.02958552756 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (1x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.01340127754 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (1x0.97x0.986184) = 0.9565987224 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 1.007329311e-10 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005 0.5 -b2 0.995 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03000000006 0.5 -f2 0.9699999999 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03000000006 0.5 -f2 0.9699999999 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381575001 0.5 0.01381575001 -a2 0.98618425 0.5 0.98618425 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01381575004 0.5 -a2 0.98618425 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.000414472502 1 0.000414472502 -_jn1 0.02958552756 1 0.02958552756 -_jn2 0.01340127754 1 0.01340127754 -_jn3 0.9565987224 1 0.9565987224 - - - -******************************************************************************** - Iteration 57 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.03) + (0.99x0.97)]x0.5 -+ [(0.008x0.03) + (0.01x0.97)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.03) + (0.003x0.97)]x0.5 -+ [(0.8x0.03) + (0.997x0.97)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.03) + (0x0.97)]x1 -+ [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138158 = 0.01381575001 -π_Jn(a2) = π(a2) = 0.986184 = 0.98618425 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.03) -+ (0.99x0.005x0.97) -+ (0.2x0.995x0.03) -+ (0.003x0.995x0.97) = 0.01381575001 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.03) -+ (0.01x0.005x0.97) -+ (0.8x0.995x0.03) -+ (0.997x0.995x0.97) = 0.98618425 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 8.456813375e-12 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0004144725014 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (1x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.02958552754 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (1x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.01340127752 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (1x0.97x0.986184) = 0.9565987224 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 6.715544169e-11 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005 0.5 -b2 0.995 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03000000004 0.5 -f2 0.97 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03000000004 0.5 -f2 0.97 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381575001 0.5 0.01381575001 -a2 0.98618425 0.5 0.98618425 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01381575003 0.5 -a2 0.98618425 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004144725014 1 0.0004144725014 -_jn1 0.02958552754 1 0.02958552754 -_jn2 0.01340127752 1 0.01340127752 -_jn3 0.9565987224 1 0.9565987224 - - - -******************************************************************************** - Iteration 58 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.03) + (0.99x0.97)]x0.5 -+ [(0.008x0.03) + (0.01x0.97)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.03) + (0.003x0.97)]x0.5 -+ [(0.8x0.03) + (0.997x0.97)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.03) + (0x0.97)]x1 -+ [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138158 = 0.01381575001 -π_Jn(a2) = π(a2) = 0.986184 = 0.98618425 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.03) -+ (0.99x0.005x0.97) -+ (0.2x0.995x0.03) -+ (0.003x0.995x0.97) = 0.01381575001 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.03) -+ (0.01x0.005x0.97) -+ (0.8x0.995x0.03) -+ (0.997x0.995x0.97) = 0.98618425 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 5.637913747e-12 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0004144725009 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (1x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.02958552753 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (1x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.01340127752 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (1x0.97x0.986184) = 0.9565987225 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 4.477005312e-11 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005 0.5 -b2 0.995 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03000000003 0.5 -f2 0.97 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03000000003 0.5 -f2 0.97 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381575001 0.5 0.01381575001 -a2 0.98618425 0.5 0.98618425 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01381575002 0.5 -a2 0.98618425 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004144725009 1 0.0004144725009 -_jn1 0.02958552753 1 0.02958552753 -_jn2 0.01340127752 1 0.01340127752 -_jn3 0.9565987225 1 0.9565987225 - - - -******************************************************************************** - Iteration 59 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.03) + (0.99x0.97)]x0.5 -+ [(0.008x0.03) + (0.01x0.97)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.03) + (0.003x0.97)]x0.5 -+ [(0.8x0.03) + (0.997x0.97)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.03) + (0x0.97)]x1 -+ [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138158 = 0.01381575001 -π_Jn(a2) = π(a2) = 0.986184 = 0.98618425 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.03) -+ (0.99x0.005x0.97) -+ (0.2x0.995x0.03) -+ (0.003x0.995x0.97) = 0.01381575 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.03) -+ (0.01x0.005x0.97) -+ (0.8x0.995x0.03) -+ (0.997x0.995x0.97) = 0.98618425 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 3.75856811e-12 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0004144725006 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (1x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.02958552752 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (1x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.01340127751 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (1x0.97x0.986184) = 0.9565987225 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 2.984675652e-11 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005 0.5 -b2 0.995 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03000000002 0.5 -f2 0.97 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03000000002 0.5 -f2 0.97 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381575 0.5 0.01381575 -a2 0.98618425 0.5 0.98618425 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01381575001 0.5 -a2 0.98618425 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004144725006 1 0.0004144725006 -_jn1 0.02958552752 1 0.02958552752 -_jn2 0.01340127751 1 0.01340127751 -_jn3 0.9565987225 1 0.9565987225 - - - -******************************************************************************** - Iteration 60 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.03) + (0.99x0.97)]x0.5 -+ [(0.008x0.03) + (0.01x0.97)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.03) + (0.003x0.97)]x0.5 -+ [(0.8x0.03) + (0.997x0.97)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.03) + (0x0.97)]x1 -+ [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138158 = 0.01381575 -π_Jn(a2) = π(a2) = 0.986184 = 0.98618425 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.03) -+ (0.99x0.005x0.97) -+ (0.2x0.995x0.03) -+ (0.003x0.995x0.97) = 0.01381575 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.03) -+ (0.01x0.005x0.97) -+ (0.8x0.995x0.03) -+ (0.997x0.995x0.97) = 0.98618425 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 2.50575255e-12 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0004144725004 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (1x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.02958552751 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (1x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.01340127751 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (1x0.97x0.986184) = 0.9565987225 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 1.98978317e-11 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005 0.5 -b2 0.995 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03000000001 0.5 -f2 0.97 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03000000001 0.5 -f2 0.97 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381575 0.5 0.01381575 -a2 0.98618425 0.5 0.98618425 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01381575001 0.5 -a2 0.98618425 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004144725004 1 0.0004144725004 -_jn1 0.02958552751 1 0.02958552751 -_jn2 0.01340127751 1 0.01340127751 -_jn3 0.9565987225 1 0.9565987225 - - - -******************************************************************************** - Iteration 61 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.03) + (0.99x0.97)]x0.5 -+ [(0.008x0.03) + (0.01x0.97)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.03) + (0.003x0.97)]x0.5 -+ [(0.8x0.03) + (0.997x0.97)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.03) + (0x0.97)]x1 -+ [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138158 = 0.01381575 -π_Jn(a2) = π(a2) = 0.986184 = 0.98618425 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.03) -+ (0.99x0.005x0.97) -+ (0.2x0.995x0.03) -+ (0.003x0.995x0.97) = 0.01381575 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.03) -+ (0.01x0.005x0.97) -+ (0.8x0.995x0.03) -+ (0.997x0.995x0.97) = 0.98618425 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 1.67046238e-12 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0004144725003 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (1x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.02958552751 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (1x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0134012775 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (1x0.97x0.986184) = 0.9565987225 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 1.326518344e-11 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005 0.5 -b2 0.995 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03000000001 0.5 -f2 0.97 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03000000001 0.5 -f2 0.97 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381575 0.5 0.01381575 -a2 0.98618425 0.5 0.98618425 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01381575001 0.5 -a2 0.98618425 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004144725003 1 0.0004144725003 -_jn1 0.02958552751 1 0.02958552751 -_jn2 0.0134012775 1 0.0134012775 -_jn3 0.9565987225 1 0.9565987225 - - - -******************************************************************************** - Iteration 62 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.03) + (0.99x0.97)]x0.5 -+ [(0.008x0.03) + (0.01x0.97)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.03) + (0.003x0.97)]x0.5 -+ [(0.8x0.03) + (0.997x0.97)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.03) + (0x0.97)]x1 -+ [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138158 = 0.01381575 -π_Jn(a2) = π(a2) = 0.986184 = 0.98618425 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.03) -+ (0.99x0.005x0.97) -+ (0.2x0.995x0.03) -+ (0.003x0.995x0.97) = 0.01381575 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.03) -+ (0.01x0.005x0.97) -+ (0.8x0.995x0.03) -+ (0.997x0.995x0.97) = 0.98618425 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 1.113716758e-12 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0004144725002 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (1x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.02958552751 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (1x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0134012775 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (1x0.97x0.986184) = 0.9565987225 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 8.843527364e-12 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005 0.5 -b2 0.995 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03000000001 0.5 -f2 0.97 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03000000001 0.5 -f2 0.97 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381575 0.5 0.01381575 -a2 0.98618425 0.5 0.98618425 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01381575 0.5 -a2 0.98618425 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004144725002 1 0.0004144725002 -_jn1 0.02958552751 1 0.02958552751 -_jn2 0.0134012775 1 0.0134012775 -_jn3 0.9565987225 1 0.9565987225 - - - -******************************************************************************** - Iteration 63 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.03) + (0.99x0.97)]x0.5 -+ [(0.008x0.03) + (0.01x0.97)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.03) + (0.003x0.97)]x0.5 -+ [(0.8x0.03) + (0.997x0.97)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.03) + (0x0.97)]x1 -+ [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138158 = 0.01381575 -π_Jn(a2) = π(a2) = 0.986184 = 0.98618425 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.03) -+ (0.99x0.005x0.97) -+ (0.2x0.995x0.03) -+ (0.003x0.995x0.97) = 0.01381575 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.03) -+ (0.01x0.005x0.97) -+ (0.8x0.995x0.03) -+ (0.997x0.995x0.97) = 0.98618425 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 7.423679727e-13 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0004144725001 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (1x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0295855275 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (1x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0134012775 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (1x0.97x0.986184) = 0.9565987225 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 5.89547443e-12 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005 0.5 -b2 0.995 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381575 0.5 0.01381575 -a2 0.98618425 0.5 0.98618425 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01381575 0.5 -a2 0.98618425 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004144725001 1 0.0004144725001 -_jn1 0.0295855275 1 0.0295855275 -_jn2 0.0134012775 1 0.0134012775 -_jn3 0.9565987225 1 0.9565987225 - - - -******************************************************************************** - Iteration 64 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.03) + (0.99x0.97)]x0.5 -+ [(0.008x0.03) + (0.01x0.97)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.03) + (0.003x0.97)]x0.5 -+ [(0.8x0.03) + (0.997x0.97)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.03) + (0x0.97)]x1 -+ [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138158 = 0.01381575 -π_Jn(a2) = π(a2) = 0.986184 = 0.98618425 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.03) -+ (0.99x0.005x0.97) -+ (0.2x0.995x0.03) -+ (0.003x0.995x0.97) = 0.01381575 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.03) -+ (0.01x0.005x0.97) -+ (0.8x0.995x0.03) -+ (0.997x0.995x0.97) = 0.98618425 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 4.949495674e-13 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0004144725001 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (1x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0295855275 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (1x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0134012775 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (1x0.97x0.986184) = 0.9565987225 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 3.930521381e-12 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005 0.5 -b2 0.995 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381575 0.5 0.01381575 -a2 0.98618425 0.5 0.98618425 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01381575 0.5 -a2 0.98618425 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004144725001 1 0.0004144725001 -_jn1 0.0295855275 1 0.0295855275 -_jn2 0.0134012775 1 0.0134012775 -_jn3 0.9565987225 1 0.9565987225 - - - -******************************************************************************** - Iteration 65 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.03) + (0.99x0.97)]x0.5 -+ [(0.008x0.03) + (0.01x0.97)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.03) + (0.003x0.97)]x0.5 -+ [(0.8x0.03) + (0.997x0.97)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.03) + (0x0.97)]x1 -+ [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138158 = 0.01381575 -π_Jn(a2) = π(a2) = 0.986184 = 0.98618425 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.03) -+ (0.99x0.005x0.97) -+ (0.2x0.995x0.03) -+ (0.003x0.995x0.97) = 0.01381575 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.03) -+ (0.01x0.005x0.97) -+ (0.8x0.995x0.03) -+ (0.997x0.995x0.97) = 0.98618425 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 3.299634871e-13 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0004144725001 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (1x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0295855275 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (1x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0134012775 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (1x0.97x0.986184) = 0.9565987225 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 2.620320573e-12 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005 0.5 -b2 0.995 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381575 0.5 0.01381575 -a2 0.98618425 0.5 0.98618425 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01381575 0.5 -a2 0.98618425 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004144725001 1 0.0004144725001 -_jn1 0.0295855275 1 0.0295855275 -_jn2 0.0134012775 1 0.0134012775 -_jn3 0.9565987225 1 0.9565987225 - - - -******************************************************************************** - Iteration 66 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.03) + (0.99x0.97)]x0.5 -+ [(0.008x0.03) + (0.01x0.97)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.03) + (0.003x0.97)]x0.5 -+ [(0.8x0.03) + (0.997x0.97)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.03) + (0x0.97)]x1 -+ [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138158 = 0.01381575 -π_Jn(a2) = π(a2) = 0.986184 = 0.98618425 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.03) -+ (0.99x0.005x0.97) -+ (0.2x0.995x0.03) -+ (0.003x0.995x0.97) = 0.01381575 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.03) -+ (0.01x0.005x0.97) -+ (0.8x0.995x0.03) -+ (0.997x0.995x0.97) = 0.98618425 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 2.200132437e-13 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0004144725 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (1x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0295855275 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (1x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0134012775 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (1x0.97x0.986184) = 0.9565987225 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 1.746729985e-12 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005 0.5 -b2 0.995 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381575 0.5 0.01381575 -a2 0.98618425 0.5 0.98618425 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01381575 0.5 -a2 0.98618425 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004144725 1 0.0004144725 -_jn1 0.0295855275 1 0.0295855275 -_jn2 0.0134012775 1 0.0134012775 -_jn3 0.9565987225 1 0.9565987225 - - - -******************************************************************************** - Iteration 67 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.03) + (0.99x0.97)]x0.5 -+ [(0.008x0.03) + (0.01x0.97)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.03) + (0.003x0.97)]x0.5 -+ [(0.8x0.03) + (0.997x0.97)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.03) + (0x0.97)]x1 -+ [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138158 = 0.01381575 -π_Jn(a2) = π(a2) = 0.986184 = 0.98618425 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.03) -+ (0.99x0.005x0.97) -+ (0.2x0.995x0.03) -+ (0.003x0.995x0.97) = 0.01381575 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.03) -+ (0.01x0.005x0.97) -+ (0.8x0.995x0.03) -+ (0.997x0.995x0.97) = 0.98618425 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 1.466032157e-13 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0004144725 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (1x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0295855275 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (1x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0134012775 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (1x0.97x0.986184) = 0.9565987225 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 1.164591806e-12 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005 0.5 -b2 0.995 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381575 0.5 0.01381575 -a2 0.98618425 0.5 0.98618425 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01381575 0.5 -a2 0.98618425 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004144725 1 0.0004144725 -_jn1 0.0295855275 1 0.0295855275 -_jn2 0.0134012775 1 0.0134012775 -_jn3 0.9565987225 1 0.9565987225 - - - -******************************************************************************** - Iteration 68 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.03) + (0.99x0.97)]x0.5 -+ [(0.008x0.03) + (0.01x0.97)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.03) + (0.003x0.97)]x0.5 -+ [(0.8x0.03) + (0.997x0.97)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.03) + (0x0.97)]x1 -+ [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138158 = 0.01381575 -π_Jn(a2) = π(a2) = 0.986184 = 0.98618425 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.03) -+ (0.99x0.005x0.97) -+ (0.2x0.995x0.03) -+ (0.003x0.995x0.97) = 0.01381575 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.03) -+ (0.01x0.005x0.97) -+ (0.8x0.995x0.03) -+ (0.997x0.995x0.97) = 0.98618425 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 9.784360822e-14 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0004144725 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (1x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0295855275 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (1x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0134012775 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (1x0.97x0.986184) = 0.9565987225 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 7.76429756e-13 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005 0.5 -b2 0.995 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381575 0.5 0.01381575 -a2 0.98618425 0.5 0.98618425 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01381575 0.5 -a2 0.98618425 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004144725 1 0.0004144725 -_jn1 0.0295855275 1 0.0295855275 -_jn2 0.0134012775 1 0.0134012775 -_jn3 0.9565987225 1 0.9565987225 - - - -******************************************************************************** - Iteration 69 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.03) + (0.99x0.97)]x0.5 -+ [(0.008x0.03) + (0.01x0.97)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.03) + (0.003x0.97)]x0.5 -+ [(0.8x0.03) + (0.997x0.97)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.03) + (0x0.97)]x1 -+ [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138158 = 0.01381575 -π_Jn(a2) = π(a2) = 0.986184 = 0.98618425 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 8.67361738e-19 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.03) -+ (0.99x0.005x0.97) -+ (0.2x0.995x0.03) -+ (0.003x0.995x0.97) = 0.01381575 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.03) -+ (0.01x0.005x0.97) -+ (0.8x0.995x0.03) -+ (0.997x0.995x0.97) = 0.98618425 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 6.512151929e-14 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0004144725 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (1x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0295855275 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (1x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0134012775 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (1x0.97x0.986184) = 0.9565987225 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 5.175910698e-13 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005 0.5 -b2 0.995 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381575 0.5 0.01381575 -a2 0.98618425 0.5 0.98618425 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01381575 0.5 -a2 0.98618425 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004144725 1 0.0004144725 -_jn1 0.0295855275 1 0.0295855275 -_jn2 0.0134012775 1 0.0134012775 -_jn3 0.9565987225 1 0.9565987225 - - - -******************************************************************************** - Iteration 70 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.03) + (0.99x0.97)]x0.5 -+ [(0.008x0.03) + (0.01x0.97)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.03) + (0.003x0.97)]x0.5 -+ [(0.8x0.03) + (0.997x0.97)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.03) + (0x0.97)]x1 -+ [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138158 = 0.01381575 -π_Jn(a2) = π(a2) = 0.986184 = 0.98618425 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.03) -+ (0.99x0.005x0.97) -+ (0.2x0.995x0.03) -+ (0.003x0.995x0.97) = 0.01381575 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.03) -+ (0.01x0.005x0.97) -+ (0.8x0.995x0.03) -+ (0.997x0.995x0.97) = 0.98618425 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 4.34860481e-14 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0004144725 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (1x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0295855275 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (1x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0134012775 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (1x0.97x0.986184) = 0.9565987225 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 3.450537382e-13 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005 0.5 -b2 0.995 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381575 0.5 0.01381575 -a2 0.98618425 0.5 0.98618425 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01381575 0.5 -a2 0.98618425 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004144725 1 0.0004144725 -_jn1 0.0295855275 1 0.0295855275 -_jn2 0.0134012775 1 0.0134012775 -_jn3 0.9565987225 1 0.9565987225 - - - -******************************************************************************** - Iteration 71 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.03) + (0.99x0.97)]x0.5 -+ [(0.008x0.03) + (0.01x0.97)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.03) + (0.003x0.97)]x0.5 -+ [(0.8x0.03) + (0.997x0.97)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.03) + (0x0.97)]x1 -+ [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138158 = 0.01381575 -π_Jn(a2) = π(a2) = 0.986184 = 0.98618425 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.03) -+ (0.99x0.005x0.97) -+ (0.2x0.995x0.03) -+ (0.003x0.995x0.97) = 0.01381575 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.03) -+ (0.01x0.005x0.97) -+ (0.8x0.995x0.03) -+ (0.997x0.995x0.97) = 0.98618425 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 2.891784034e-14 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0004144725 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (1x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0295855275 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (1x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0134012775 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (1x0.97x0.986184) = 0.9565987225 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 2.300415717e-13 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005 0.5 -b2 0.995 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381575 0.5 0.01381575 -a2 0.98618425 0.5 0.98618425 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01381575 0.5 -a2 0.98618425 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004144725 1 0.0004144725 -_jn1 0.0295855275 1 0.0295855275 -_jn2 0.0134012775 1 0.0134012775 -_jn3 0.9565987225 1 0.9565987225 - - - -******************************************************************************** - Iteration 72 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.03) + (0.99x0.97)]x0.5 -+ [(0.008x0.03) + (0.01x0.97)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.03) + (0.003x0.97)]x0.5 -+ [(0.8x0.03) + (0.997x0.97)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.03) + (0x0.97)]x1 -+ [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138158 = 0.01381575 -π_Jn(a2) = π(a2) = 0.986184 = 0.98618425 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 8.67361738e-19 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.03) -+ (0.99x0.005x0.97) -+ (0.2x0.995x0.03) -+ (0.003x0.995x0.97) = 0.01381575 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.03) -+ (0.01x0.005x0.97) -+ (0.8x0.995x0.03) -+ (0.997x0.995x0.97) = 0.98618425 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 1.931441118e-14 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0004144725 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (1x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0295855275 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (1x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0134012775 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (1x0.97x0.986184) = 0.9565987225 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 1.533916765e-13 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005 0.5 -b2 0.995 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381575 0.5 0.01381575 -a2 0.98618425 0.5 0.98618425 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01381575 0.5 -a2 0.98618425 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004144725 1 0.0004144725 -_jn1 0.0295855275 1 0.0295855275 -_jn2 0.0134012775 1 0.0134012775 -_jn3 0.9565987225 1 0.9565987225 - - - -******************************************************************************** - Iteration 73 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.03) + (0.99x0.97)]x0.5 -+ [(0.008x0.03) + (0.01x0.97)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.03) + (0.003x0.97)]x0.5 -+ [(0.8x0.03) + (0.997x0.97)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.03) + (0x0.97)]x1 -+ [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138158 = 0.01381575 -π_Jn(a2) = π(a2) = 0.986184 = 0.98618425 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.03) -+ (0.99x0.005x0.97) -+ (0.2x0.995x0.03) -+ (0.003x0.995x0.97) = 0.01381575 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.03) -+ (0.01x0.005x0.97) -+ (0.8x0.995x0.03) -+ (0.997x0.995x0.97) = 0.98618425 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 1.287511764e-14 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0004144725 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (1x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0295855275 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (1x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0134012775 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (1x0.97x0.986184) = 0.9565987225 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 1.021882774e-13 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005 0.5 -b2 0.995 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381575 0.5 0.01381575 -a2 0.98618425 0.5 0.98618425 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01381575 0.5 -a2 0.98618425 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004144725 1 0.0004144725 -_jn1 0.0295855275 1 0.0295855275 -_jn2 0.0134012775 1 0.0134012775 -_jn3 0.9565987225 1 0.9565987225 - - - -******************************************************************************** - Iteration 74 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.03) + (0.99x0.97)]x0.5 -+ [(0.008x0.03) + (0.01x0.97)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.03) + (0.003x0.97)]x0.5 -+ [(0.8x0.03) + (0.997x0.97)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.03) + (0x0.97)]x1 -+ [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138158 = 0.01381575 -π_Jn(a2) = π(a2) = 0.986184 = 0.98618425 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.03) -+ (0.99x0.005x0.97) -+ (0.2x0.995x0.03) -+ (0.003x0.995x0.97) = 0.01381575 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.03) -+ (0.01x0.005x0.97) -+ (0.8x0.995x0.03) -+ (0.997x0.995x0.97) = 0.98618425 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 8.621575676e-15 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0004144725 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (1x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0295855275 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (1x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0134012775 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (1x0.97x0.986184) = 0.9565987225 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 6.816595899e-14 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005 0.5 -b2 0.995 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381575 0.5 0.01381575 -a2 0.98618425 0.5 0.98618425 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01381575 0.5 -a2 0.98618425 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004144725 1 0.0004144725 -_jn1 0.0295855275 1 0.0295855275 -_jn2 0.0134012775 1 0.0134012775 -_jn3 0.9565987225 1 0.9565987225 - - - -******************************************************************************** - Iteration 75 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.03) + (0.99x0.97)]x0.5 -+ [(0.008x0.03) + (0.01x0.97)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.03) + (0.003x0.97)]x0.5 -+ [(0.8x0.03) + (0.997x0.97)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.03) + (0x0.97)]x1 -+ [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138158 = 0.01381575 -π_Jn(a2) = π(a2) = 0.986184 = 0.98618425 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.03) -+ (0.99x0.005x0.97) -+ (0.2x0.995x0.03) -+ (0.003x0.995x0.97) = 0.01381575 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.03) -+ (0.01x0.005x0.97) -+ (0.8x0.995x0.03) -+ (0.997x0.995x0.97) = 0.98618425 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 5.748873599e-15 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0004144725 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (1x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0295855275 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (1x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0134012775 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (1x0.97x0.986184) = 0.9565987225 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 4.547870327e-14 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005 0.5 -b2 0.995 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381575 0.5 0.01381575 -a2 0.98618425 0.5 0.98618425 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01381575 0.5 -a2 0.98618425 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004144725 1 0.0004144725 -_jn1 0.0295855275 1 0.0295855275 -_jn2 0.0134012775 1 0.0134012775 -_jn3 0.9565987225 1 0.9565987225 - - - -******************************************************************************** - Iteration 76 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.03) + (0.99x0.97)]x0.5 -+ [(0.008x0.03) + (0.01x0.97)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.03) + (0.003x0.97)]x0.5 -+ [(0.8x0.03) + (0.997x0.97)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.03) + (0x0.97)]x1 -+ [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138158 = 0.01381575 -π_Jn(a2) = π(a2) = 0.986184 = 0.98618425 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.03) -+ (0.99x0.005x0.97) -+ (0.2x0.995x0.03) -+ (0.003x0.995x0.97) = 0.01381575 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.03) -+ (0.01x0.005x0.97) -+ (0.8x0.995x0.03) -+ (0.997x0.995x0.97) = 0.98618425 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 3.797309689e-15 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0004144725 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (1x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0295855275 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (1x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0134012775 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (1x0.97x0.986184) = 0.9565987225 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 3.024924061e-14 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005 0.5 -b2 0.995 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381575 0.5 0.01381575 -a2 0.98618425 0.5 0.98618425 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01381575 0.5 -a2 0.98618425 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004144725 1 0.0004144725 -_jn1 0.0295855275 1 0.0295855275 -_jn2 0.0134012775 1 0.0134012775 -_jn3 0.9565987225 1 0.9565987225 - - - -******************************************************************************** - Iteration 77 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.03) + (0.99x0.97)]x0.5 -+ [(0.008x0.03) + (0.01x0.97)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.03) + (0.003x0.97)]x0.5 -+ [(0.8x0.03) + (0.997x0.97)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.03) + (0x0.97)]x1 -+ [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138158 = 0.01381575 -π_Jn(a2) = π(a2) = 0.986184 = 0.98618425 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.03) -+ (0.99x0.005x0.97) -+ (0.2x0.995x0.03) -+ (0.003x0.995x0.97) = 0.01381575 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.03) -+ (0.01x0.005x0.97) -+ (0.8x0.995x0.03) -+ (0.997x0.995x0.97) = 0.98618425 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 2.492797635e-15 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0004144725 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (1x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0295855275 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (1x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0134012775 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (1x0.97x0.986184) = 0.9565987225 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 2.019500019e-14 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005 0.5 -b2 0.995 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381575 0.5 0.01381575 -a2 0.98618425 0.5 0.98618425 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01381575 0.5 -a2 0.98618425 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004144725 1 0.0004144725 -_jn1 0.0295855275 1 0.0295855275 -_jn2 0.0134012775 1 0.0134012775 -_jn3 0.9565987225 1 0.9565987225 - - - -******************************************************************************** - Iteration 78 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.03) + (0.99x0.97)]x0.5 -+ [(0.008x0.03) + (0.01x0.97)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.03) + (0.003x0.97)]x0.5 -+ [(0.8x0.03) + (0.997x0.97)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.03) + (0x0.97)]x1 -+ [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138158 = 0.01381575 -π_Jn(a2) = π(a2) = 0.986184 = 0.98618425 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.03) -+ (0.99x0.005x0.97) -+ (0.2x0.995x0.03) -+ (0.003x0.995x0.97) = 0.01381575 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.03) -+ (0.01x0.005x0.97) -+ (0.8x0.995x0.03) -+ (0.997x0.995x0.97) = 0.98618425 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 1.734723476e-15 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0004144725 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (1x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0295855275 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (1x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0134012775 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (1x0.97x0.986184) = 0.9565987225 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 1.350200333e-14 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005 0.5 -b2 0.995 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381575 0.5 0.01381575 -a2 0.98618425 0.5 0.98618425 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01381575 0.5 -a2 0.98618425 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004144725 1 0.0004144725 -_jn1 0.0295855275 1 0.0295855275 -_jn2 0.0134012775 1 0.0134012775 -_jn3 0.9565987225 1 0.9565987225 - - - -******************************************************************************** - Iteration 79 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.03) + (0.99x0.97)]x0.5 -+ [(0.008x0.03) + (0.01x0.97)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.03) + (0.003x0.97)]x0.5 -+ [(0.8x0.03) + (0.997x0.97)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.03) + (0x0.97)]x1 -+ [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138158 = 0.01381575 -π_Jn(a2) = π(a2) = 0.986184 = 0.98618425 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.03) -+ (0.99x0.005x0.97) -+ (0.2x0.995x0.03) -+ (0.003x0.995x0.97) = 0.01381575 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.03) -+ (0.01x0.005x0.97) -+ (0.8x0.995x0.03) -+ (0.997x0.995x0.97) = 0.98618425 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 1.011343786e-15 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0004144725 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (1x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0295855275 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (1x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0134012775 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (1x0.97x0.986184) = 0.9565987225 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 9.038451411e-15 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005 0.5 -b2 0.995 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381575 0.5 0.01381575 -a2 0.98618425 0.5 0.98618425 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01381575 0.5 -a2 0.98618425 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004144725 1 0.0004144725 -_jn1 0.0295855275 1 0.0295855275 -_jn2 0.0134012775 1 0.0134012775 -_jn3 0.9565987225 1 0.9565987225 - - - -******************************************************************************** - Iteration 80 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.03) + (0.99x0.97)]x0.5 -+ [(0.008x0.03) + (0.01x0.97)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.03) + (0.003x0.97)]x0.5 -+ [(0.8x0.03) + (0.997x0.97)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.03) + (0x0.97)]x1 -+ [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138158 = 0.01381575 -π_Jn(a2) = π(a2) = 0.986184 = 0.98618425 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.03) -+ (0.99x0.005x0.97) -+ (0.2x0.995x0.03) -+ (0.003x0.995x0.97) = 0.01381575 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.03) -+ (0.01x0.005x0.97) -+ (0.8x0.995x0.03) -+ (0.997x0.995x0.97) = 0.98618425 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 8.170547572e-16 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0004144725 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (1x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0295855275 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (1x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0134012775 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (1x0.97x0.986184) = 0.9565987225 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 5.989729112e-15 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005 0.5 -b2 0.995 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381575 0.5 0.01381575 -a2 0.98618425 0.5 0.98618425 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01381575 0.5 -a2 0.98618425 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004144725 1 0.0004144725 -_jn1 0.0295855275 1 0.0295855275 -_jn2 0.0134012775 1 0.0134012775 -_jn3 0.9565987225 1 0.9565987225 - - - -******************************************************************************** - Iteration 81 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.03) + (0.99x0.97)]x0.5 -+ [(0.008x0.03) + (0.01x0.97)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.03) + (0.003x0.97)]x0.5 -+ [(0.8x0.03) + (0.997x0.97)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.03) + (0x0.97)]x1 -+ [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138158 = 0.01381575 -π_Jn(a2) = π(a2) = 0.986184 = 0.98618425 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.03) -+ (0.99x0.005x0.97) -+ (0.2x0.995x0.03) -+ (0.003x0.995x0.97) = 0.01381575 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.03) -+ (0.01x0.005x0.97) -+ (0.8x0.995x0.03) -+ (0.997x0.995x0.97) = 0.98618425 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 5.846018114e-16 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0004144725 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (1x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0295855275 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (1x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0134012775 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (1x0.97x0.986184) = 0.9565987225 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 3.880955887e-15 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005 0.5 -b2 0.995 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381575 0.5 0.01381575 -a2 0.98618425 0.5 0.98618425 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01381575 0.5 -a2 0.98618425 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004144725 1 0.0004144725 -_jn1 0.0295855275 1 0.0295855275 -_jn2 0.0134012775 1 0.0134012775 -_jn3 0.9565987225 1 0.9565987225 - - - -******************************************************************************** - Iteration 82 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.03) + (0.99x0.97)]x0.5 -+ [(0.008x0.03) + (0.01x0.97)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.03) + (0.003x0.97)]x0.5 -+ [(0.8x0.03) + (0.997x0.97)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.03) + (0x0.97)]x1 -+ [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138158 = 0.01381575 -π_Jn(a2) = π(a2) = 0.986184 = 0.98618425 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.03) -+ (0.99x0.005x0.97) -+ (0.2x0.995x0.03) -+ (0.003x0.995x0.97) = 0.01381575 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.03) -+ (0.01x0.005x0.97) -+ (0.8x0.995x0.03) -+ (0.997x0.995x0.97) = 0.98618425 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 2.775557562e-16 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0004144725 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (1x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0295855275 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (1x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0134012775 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (1x0.97x0.986184) = 0.9565987225 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 2.665402621e-15 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005 0.5 -b2 0.995 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381575 0.5 0.01381575 -a2 0.98618425 0.5 0.98618425 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01381575 0.5 -a2 0.98618425 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004144725 1 0.0004144725 -_jn1 0.0295855275 1 0.0295855275 -_jn2 0.0134012775 1 0.0134012775 -_jn3 0.9565987225 1 0.9565987225 - - - -******************************************************************************** - Iteration 83 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.03) + (0.99x0.97)]x0.5 -+ [(0.008x0.03) + (0.01x0.97)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.03) + (0.003x0.97)]x0.5 -+ [(0.8x0.03) + (0.997x0.97)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.03) + (0x0.97)]x1 -+ [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138158 = 0.01381575 -π_Jn(a2) = π(a2) = 0.986184 = 0.98618425 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.03) -+ (0.99x0.005x0.97) -+ (0.2x0.995x0.03) -+ (0.003x0.995x0.97) = 0.01381575 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.03) -+ (0.01x0.005x0.97) -+ (0.8x0.995x0.03) -+ (0.997x0.995x0.97) = 0.98618425 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 2.237793284e-16 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0004144725 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (1x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0295855275 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (1x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0134012775 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (1x0.97x0.986184) = 0.9565987225 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 1.776953151e-15 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005 0.5 -b2 0.995 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381575 0.5 0.01381575 -a2 0.98618425 0.5 0.98618425 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01381575 0.5 -a2 0.98618425 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004144725 1 0.0004144725 -_jn1 0.0295855275 1 0.0295855275 -_jn2 0.0134012775 1 0.0134012775 -_jn3 0.9565987225 1 0.9565987225 - - - -******************************************************************************** - Iteration 84 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.03) + (0.99x0.97)]x0.5 -+ [(0.008x0.03) + (0.01x0.97)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.03) + (0.003x0.97)]x0.5 -+ [(0.8x0.03) + (0.997x0.97)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.03) + (0x0.97)]x1 -+ [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138158 = 0.01381575 -π_Jn(a2) = π(a2) = 0.986184 = 0.98618425 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.03) -+ (0.99x0.005x0.97) -+ (0.2x0.995x0.03) -+ (0.003x0.995x0.97) = 0.01381575 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.03) -+ (0.01x0.005x0.97) -+ (0.8x0.995x0.03) -+ (0.997x0.995x0.97) = 0.98618425 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 1.856154119e-16 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0004144725 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (1x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0295855275 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (1x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0134012775 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (1x0.97x0.986184) = 0.9565987225 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 1.250464576e-15 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005 0.5 -b2 0.995 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381575 0.5 0.01381575 -a2 0.98618425 0.5 0.98618425 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01381575 0.5 -a2 0.98618425 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004144725 1 0.0004144725 -_jn1 0.0295855275 1 0.0295855275 -_jn2 0.0134012775 1 0.0134012775 -_jn3 0.9565987225 1 0.9565987225 - - - -******************************************************************************** - Iteration 85 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.03) + (0.99x0.97)]x0.5 -+ [(0.008x0.03) + (0.01x0.97)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.03) + (0.003x0.97)]x0.5 -+ [(0.8x0.03) + (0.997x0.97)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.03) + (0x0.97)]x1 -+ [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138158 = 0.01381575 -π_Jn(a2) = π(a2) = 0.986184 = 0.98618425 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.03) -+ (0.99x0.005x0.97) -+ (0.2x0.995x0.03) -+ (0.003x0.995x0.97) = 0.01381575 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.03) -+ (0.01x0.005x0.97) -+ (0.8x0.995x0.03) -+ (0.997x0.995x0.97) = 0.98618425 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 4.683753385e-17 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0004144725 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (1x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0295855275 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (1x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0134012775 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (1x0.97x0.986184) = 0.9565987225 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 7.278791285e-16 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005 0.5 -b2 0.995 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381575 0.5 0.01381575 -a2 0.98618425 0.5 0.98618425 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01381575 0.5 -a2 0.98618425 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004144725 1 0.0004144725 -_jn1 0.0295855275 1 0.0295855275 -_jn2 0.0134012775 1 0.0134012775 -_jn3 0.9565987225 1 0.9565987225 - - - -******************************************************************************** - Iteration 86 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.03) + (0.99x0.97)]x0.5 -+ [(0.008x0.03) + (0.01x0.97)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.03) + (0.003x0.97)]x0.5 -+ [(0.8x0.03) + (0.997x0.97)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.03) + (0x0.97)]x1 -+ [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138158 = 0.01381575 -π_Jn(a2) = π(a2) = 0.986184 = 0.98618425 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 8.67361738e-19 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.03) -+ (0.99x0.005x0.97) -+ (0.2x0.995x0.03) -+ (0.003x0.995x0.97) = 0.01381575 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.03) -+ (0.01x0.005x0.97) -+ (0.8x0.995x0.03) -+ (0.997x0.995x0.97) = 0.98618425 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 1.439820485e-16 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0004144725 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (1x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0295855275 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (1x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0134012775 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (1x0.97x0.986184) = 0.9565987225 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 4.857767834e-16 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005 0.5 -b2 0.995 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381575 0.5 0.01381575 -a2 0.98618425 0.5 0.98618425 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01381575 0.5 -a2 0.98618425 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004144725 1 0.0004144725 -_jn1 0.0295855275 1 0.0295855275 -_jn2 0.0134012775 1 0.0134012775 -_jn3 0.9565987225 1 0.9565987225 - - - -******************************************************************************** - Iteration 87 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.03) + (0.99x0.97)]x0.5 -+ [(0.008x0.03) + (0.01x0.97)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.03) + (0.003x0.97)]x0.5 -+ [(0.8x0.03) + (0.997x0.97)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.03) + (0x0.97)]x1 -+ [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138158 = 0.01381575 -π_Jn(a2) = π(a2) = 0.986184 = 0.98618425 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.03) -+ (0.99x0.005x0.97) -+ (0.2x0.995x0.03) -+ (0.003x0.995x0.97) = 0.01381575 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.03) -+ (0.01x0.005x0.97) -+ (0.8x0.995x0.03) -+ (0.997x0.995x0.97) = 0.98618425 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 2.255140519e-17 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0004144725 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (1x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0295855275 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (1x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0134012775 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (1x0.97x0.986184) = 0.9565987225 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 3.903127821e-16 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005 0.5 -b2 0.995 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381575 0.5 0.01381575 -a2 0.98618425 0.5 0.98618425 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01381575 0.5 -a2 0.98618425 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004144725 1 0.0004144725 -_jn1 0.0295855275 1 0.0295855275 -_jn2 0.0134012775 1 0.0134012775 -_jn3 0.9565987225 1 0.9565987225 - - - -******************************************************************************** - Iteration 88 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.03) + (0.99x0.97)]x0.5 -+ [(0.008x0.03) + (0.01x0.97)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.03) + (0.003x0.97)]x0.5 -+ [(0.8x0.03) + (0.997x0.97)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.03) + (0x0.97)]x1 -+ [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138158 = 0.01381575 -π_Jn(a2) = π(a2) = 0.986184 = 0.98618425 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.03) -+ (0.99x0.005x0.97) -+ (0.2x0.995x0.03) -+ (0.003x0.995x0.97) = 0.01381575 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.03) -+ (0.01x0.005x0.97) -+ (0.8x0.995x0.03) -+ (0.997x0.995x0.97) = 0.98618425 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 1.561251128e-17 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0004144725 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (1x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0295855275 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (1x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0134012775 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (1x0.97x0.986184) = 0.9565987225 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 2.243756396e-16 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005 0.5 -b2 0.995 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381575 0.5 0.01381575 -a2 0.98618425 0.5 0.98618425 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01381575 0.5 -a2 0.98618425 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004144725 1 0.0004144725 -_jn1 0.0295855275 1 0.0295855275 -_jn2 0.0134012775 1 0.0134012775 -_jn3 0.9565987225 1 0.9565987225 - - - -******************************************************************************** - Iteration 89 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.03) + (0.99x0.97)]x0.5 -+ [(0.008x0.03) + (0.01x0.97)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.03) + (0.003x0.97)]x0.5 -+ [(0.8x0.03) + (0.997x0.97)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.03) + (0x0.97)]x1 -+ [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138158 = 0.01381575 -π_Jn(a2) = π(a2) = 0.986184 = 0.98618425 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.03) -+ (0.99x0.005x0.97) -+ (0.2x0.995x0.03) -+ (0.003x0.995x0.97) = 0.01381575 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.03) -+ (0.01x0.005x0.97) -+ (0.8x0.995x0.03) -+ (0.997x0.995x0.97) = 0.98618425 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 8.67361738e-18 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0004144725 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (1x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0295855275 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (1x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0134012775 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (1x0.97x0.986184) = 0.9565987225 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 1.90656952e-16 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005 0.5 -b2 0.995 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381575 0.5 0.01381575 -a2 0.98618425 0.5 0.98618425 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01381575 0.5 -a2 0.98618425 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004144725 1 0.0004144725 -_jn1 0.0295855275 1 0.0295855275 -_jn2 0.0134012775 1 0.0134012775 -_jn3 0.9565987225 1 0.9565987225 - - - -******************************************************************************** - Iteration 90 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.03) + (0.99x0.97)]x0.5 -+ [(0.008x0.03) + (0.01x0.97)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.03) + (0.003x0.97)]x0.5 -+ [(0.8x0.03) + (0.997x0.97)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.03) + (0x0.97)]x1 -+ [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138158 = 0.01381575 -π_Jn(a2) = π(a2) = 0.986184 = 0.98618425 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.03) -+ (0.99x0.005x0.97) -+ (0.2x0.995x0.03) -+ (0.003x0.995x0.97) = 0.01381575 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.03) -+ (0.01x0.005x0.97) -+ (0.8x0.995x0.03) -+ (0.997x0.995x0.97) = 0.98618425 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 6.938893904e-18 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0004144725 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (1x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0295855275 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (1x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0134012775 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (1x0.97x0.986184) = 0.9565987225 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 5.838428699e-17 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005 0.5 -b2 0.995 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381575 0.5 0.01381575 -a2 0.98618425 0.5 0.98618425 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01381575 0.5 -a2 0.98618425 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004144725 1 0.0004144725 -_jn1 0.0295855275 1 0.0295855275 -_jn2 0.0134012775 1 0.0134012775 -_jn3 0.9565987225 1 0.9565987225 - - - -******************************************************************************** - Iteration 91 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.03) + (0.99x0.97)]x0.5 -+ [(0.008x0.03) + (0.01x0.97)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.03) + (0.003x0.97)]x0.5 -+ [(0.8x0.03) + (0.997x0.97)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.03) + (0x0.97)]x1 -+ [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138158 = 0.01381575 -π_Jn(a2) = π(a2) = 0.986184 = 0.98618425 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.03) -+ (0.99x0.005x0.97) -+ (0.2x0.995x0.03) -+ (0.003x0.995x0.97) = 0.01381575 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.03) -+ (0.01x0.005x0.97) -+ (0.8x0.995x0.03) -+ (0.997x0.995x0.97) = 0.98618425 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 6.938893904e-18 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0004144725 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (1x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0295855275 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (1x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0134012775 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (1x0.97x0.986184) = 0.9565987225 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 4.065758147e-17 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005 0.5 -b2 0.995 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381575 0.5 0.01381575 -a2 0.98618425 0.5 0.98618425 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01381575 0.5 -a2 0.98618425 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004144725 1 0.0004144725 -_jn1 0.0295855275 1 0.0295855275 -_jn2 0.0134012775 1 0.0134012775 -_jn3 0.9565987225 1 0.9565987225 - - - -******************************************************************************** - Iteration 92 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.03) + (0.99x0.97)]x0.5 -+ [(0.008x0.03) + (0.01x0.97)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.03) + (0.003x0.97)]x0.5 -+ [(0.8x0.03) + (0.997x0.97)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.03) + (0x0.97)]x1 -+ [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138158 = 0.01381575 -π_Jn(a2) = π(a2) = 0.986184 = 0.98618425 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.03) -+ (0.99x0.005x0.97) -+ (0.2x0.995x0.03) -+ (0.003x0.995x0.97) = 0.01381575 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.03) -+ (0.01x0.005x0.97) -+ (0.8x0.995x0.03) -+ (0.997x0.995x0.97) = 0.98618425 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 3.469446952e-18 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0004144725 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (1x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0295855275 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (1x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0134012775 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (1x0.97x0.986184) = 0.9565987225 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 1.341158087e-16 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005 0.5 -b2 0.995 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381575 0.5 0.01381575 -a2 0.98618425 0.5 0.98618425 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01381575 0.5 -a2 0.98618425 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004144725 1 0.0004144725 -_jn1 0.0295855275 1 0.0295855275 -_jn2 0.0134012775 1 0.0134012775 -_jn3 0.9565987225 1 0.9565987225 - - - -******************************************************************************** - Iteration 93 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.03) + (0.99x0.97)]x0.5 -+ [(0.008x0.03) + (0.01x0.97)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.03) + (0.003x0.97)]x0.5 -+ [(0.8x0.03) + (0.997x0.97)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.03) + (0x0.97)]x1 -+ [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138158 = 0.01381575 -π_Jn(a2) = π(a2) = 0.986184 = 0.98618425 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.03) -+ (0.99x0.005x0.97) -+ (0.2x0.995x0.03) -+ (0.003x0.995x0.97) = 0.01381575 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.03) -+ (0.01x0.005x0.97) -+ (0.8x0.995x0.03) -+ (0.997x0.995x0.97) = 0.98618425 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 1.127570259e-16 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0004144725 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (1x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0295855275 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (1x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0134012775 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (1x0.97x0.986184) = 0.9565987225 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 1.339531784e-16 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005 0.5 -b2 0.995 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381575 0.5 0.01381575 -a2 0.98618425 0.5 0.98618425 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01381575 0.5 -a2 0.98618425 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004144725 1 0.0004144725 -_jn1 0.0295855275 1 0.0295855275 -_jn2 0.0134012775 1 0.0134012775 -_jn3 0.9565987225 1 0.9565987225 - - - -******************************************************************************** - Iteration 94 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.03) + (0.99x0.97)]x0.5 -+ [(0.008x0.03) + (0.01x0.97)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.03) + (0.003x0.97)]x0.5 -+ [(0.8x0.03) + (0.997x0.97)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.03) + (0x0.97)]x1 -+ [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138158 = 0.01381575 -π_Jn(a2) = π(a2) = 0.986184 = 0.98618425 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 8.67361738e-19 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.03) -+ (0.99x0.005x0.97) -+ (0.2x0.995x0.03) -+ (0.003x0.995x0.97) = 0.01381575 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.03) -+ (0.01x0.005x0.97) -+ (0.8x0.995x0.03) -+ (0.997x0.995x0.97) = 0.98618425 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 1.734723476e-18 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0004144725 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (1x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0295855275 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (1x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0134012775 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (1x0.97x0.986184) = 0.9565987225 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 8.836247706e-18 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005 0.5 -b2 0.995 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381575 0.5 0.01381575 -a2 0.98618425 0.5 0.98618425 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01381575 0.5 -a2 0.98618425 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004144725 1 0.0004144725 -_jn1 0.0295855275 1 0.0295855275 -_jn2 0.0134012775 1 0.0134012775 -_jn3 0.9565987225 1 0.9565987225 - - - -******************************************************************************** - Iteration 95 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.03) + (0.99x0.97)]x0.5 -+ [(0.008x0.03) + (0.01x0.97)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.03) + (0.003x0.97)]x0.5 -+ [(0.8x0.03) + (0.997x0.97)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.03) + (0x0.97)]x1 -+ [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138158 = 0.01381575 -π_Jn(a2) = π(a2) = 0.986184 = 0.98618425 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.03) -+ (0.99x0.005x0.97) -+ (0.2x0.995x0.03) -+ (0.003x0.995x0.97) = 0.01381575 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.03) -+ (0.01x0.005x0.97) -+ (0.8x0.995x0.03) -+ (0.997x0.995x0.97) = 0.98618425 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 1.734723476e-18 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0004144725 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (1x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0295855275 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (1x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0134012775 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (1x0.97x0.986184) = 0.9565987225 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 8.836247706e-18 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005 0.5 -b2 0.995 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381575 0.5 0.01381575 -a2 0.98618425 0.5 0.98618425 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01381575 0.5 -a2 0.98618425 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004144725 1 0.0004144725 -_jn1 0.0295855275 1 0.0295855275 -_jn2 0.0134012775 1 0.0134012775 -_jn3 0.9565987225 1 0.9565987225 - - - -******************************************************************************** - Iteration 96 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.03) + (0.99x0.97)]x0.5 -+ [(0.008x0.03) + (0.01x0.97)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.03) + (0.003x0.97)]x0.5 -+ [(0.8x0.03) + (0.997x0.97)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.03) + (0x0.97)]x1 -+ [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138158 = 0.01381575 -π_Jn(a2) = π(a2) = 0.986184 = 0.98618425 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.03) -+ (0.99x0.005x0.97) -+ (0.2x0.995x0.03) -+ (0.003x0.995x0.97) = 0.01381575 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.03) -+ (0.01x0.005x0.97) -+ (0.8x0.995x0.03) -+ (0.997x0.995x0.97) = 0.98618425 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 0 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0004144725 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (1x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0295855275 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (1x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0134012775 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (1x0.97x0.986184) = 0.9565987225 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 1.788933585e-18 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005 0.5 -b2 0.995 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381575 0.5 0.01381575 -a2 0.98618425 0.5 0.98618425 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01381575 0.5 -a2 0.98618425 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004144725 1 0.0004144725 -_jn1 0.0295855275 1 0.0295855275 -_jn2 0.0134012775 1 0.0134012775 -_jn3 0.9565987225 1 0.9565987225 - - - -******************************************************************************** - Iteration 97 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.03) + (0.99x0.97)]x0.5 -+ [(0.008x0.03) + (0.01x0.97)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.03) + (0.003x0.97)]x0.5 -+ [(0.8x0.03) + (0.997x0.97)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.03) + (0x0.97)]x1 -+ [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138158 = 0.01381575 -π_Jn(a2) = π(a2) = 0.986184 = 0.98618425 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.03) -+ (0.99x0.005x0.97) -+ (0.2x0.995x0.03) -+ (0.003x0.995x0.97) = 0.01381575 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.03) -+ (0.01x0.005x0.97) -+ (0.8x0.995x0.03) -+ (0.997x0.995x0.97) = 0.98618425 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 0 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0004144725 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (1x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0295855275 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (1x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0134012775 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (1x0.97x0.986184) = 0.9565987225 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 1.788933585e-18 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005 0.5 -b2 0.995 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381575 0.5 0.01381575 -a2 0.98618425 0.5 0.98618425 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01381575 0.5 -a2 0.98618425 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004144725 1 0.0004144725 -_jn1 0.0295855275 1 0.0295855275 -_jn2 0.0134012775 1 0.0134012775 -_jn3 0.9565987225 1 0.9565987225 - - - -******************************************************************************** - Iteration 98 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.03) + (0.99x0.97)]x0.5 -+ [(0.008x0.03) + (0.01x0.97)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.03) + (0.003x0.97)]x0.5 -+ [(0.8x0.03) + (0.997x0.97)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.03) + (0x0.97)]x1 -+ [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138158 = 0.01381575 -π_Jn(a2) = π(a2) = 0.986184 = 0.98618425 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.03) -+ (0.99x0.005x0.97) -+ (0.2x0.995x0.03) -+ (0.003x0.995x0.97) = 0.01381575 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.03) -+ (0.01x0.005x0.97) -+ (0.8x0.995x0.03) -+ (0.997x0.995x0.97) = 0.98618425 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 0 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0004144725 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (1x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0295855275 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (1x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0134012775 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (1x0.97x0.986184) = 0.9565987225 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 0 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005 0.5 -b2 0.995 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381575 0.5 0.01381575 -a2 0.98618425 0.5 0.98618425 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01381575 0.5 -a2 0.98618425 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004144725 1 0.0004144725 -_jn1 0.0295855275 1 0.0295855275 -_jn2 0.0134012775 1 0.0134012775 -_jn3 0.9565987225 1 0.9565987225 - - -Iterative belief propagation converged in 98 iterations - diff --git a/packages/CLPBN/clpbn/bp/out.txt b/packages/CLPBN/clpbn/bp/out.txt deleted file mode 100644 index 78c46e813..000000000 --- a/packages/CLPBN/clpbn/bp/out.txt +++ /dev/null @@ -1,762 +0,0 @@ -Variable: Burglar -Domain: b1, b2 -Parents: -Childs: Alarm -cpt ----------------- -b1 0.005 -b2 0.995 - -Variable: FreightTruck -Domain: f1, f2 -Parents: -Childs: Alarm -cpt ----------------- -f1 0.03 -f2 0.97 - -Variable: Alarm -Domain: a1, a2 -Parents: Burglar, FreightTruck -Childs: -cpt b1,f1 b1,f2 b2,f1 b2,f2 ----------------------------------------------------- -a1 0.992 0.99 0.2 0.003 -a2 0.008 0.01 0.8 0.997 - -Variable: Burglar -Domain: b1, b2 -Parents: -Childs: Alarm -cpt ----------------- -b1 0.005 -b2 0.995 - -Variable: FreightTruck -Domain: f1, f2 -Parents: -Childs: Alarm, _Jn -cpt ----------------- -f1 0.03 -f2 0.97 - -Variable: Alarm -Domain: a1, a2 -Parents: Burglar, FreightTruck -Childs: _Jn -cpt b1,f1 b1,f2 b2,f1 b2,f2 ----------------------------------------------------- -a1 0.992 0.99 0.2 0.003 -a2 0.008 0.01 0.8 0.997 - -Variable: _Jn -Domain: _jn0, _jn1, _jn2, _jn3 -Parents: FreightTruck, Alarm -Childs: -cpt f1,a1 f1,a2 f2,a1 f2,a2 ----------------------------------------------------- -_jn0 1 0 0 0 -_jn1 0 1 0 0 -_jn2 0 0 1 0 -_jn3 0 0 0 1 - -The graph is not single connected. Iterative belief propagation will be used. - -Initializing solver --> schedule = parallel --> max iters = 100 --> stable threashold = 1e-20 --> query vars = FreightTruck Alarm -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 1 1 0.5 -b2 1 1 0.5 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.5 0.5 -b2 0.5 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 1 1 0.5 -f2 1 1 0.5 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.5 0.5 -f2 0.5 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.5 0.5 -f2 0.5 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 1 1 0.5 -a2 1 1 0.5 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.5 0.5 -a2 0.5 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 1 1 0.25 -_jn1 1 1 0.25 -_jn2 1 1 0.25 -_jn3 1 1 0.25 - - - -******************************************************************************** - Iteration 1 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.5) + (0.99x0.5)]x1 -+ [(0.008x0.5) + (0.01x0.5)]x1 = 1 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.5) + (0.003x0.5)]x1 -+ [(0.8x0.5) + (0.997x0.5)]x1 = 1 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.5) + (0.2x0.5)]x1 -+ [(0.008x0.5) + (0.8x0.5)]x1 = 1 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.5) + (0.003x0.5)]x1 -+ [(0.01x0.5) + (0.997x0.5)]x1 = 1 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.5) + (0x0.5)]x1 -+ [(0x0.5) + (1x0.5)]x1 -+ [(0x0.5) + (0x0.5)]x1 -+ [(0x0.5) + (0x0.5)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.5) + (0x0.5)]x1 -+ [(0x0.5) + (0x0.5)]x1 -+ [(1x0.5) + (0x0.5)]x1 -+ [(0x0.5) + (1x0.5)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.5) + (0x0.5)]x1 -+ [(0x0.5) + (0x0.5)]x1 -+ [(0x0.5) + (1x0.5)]x1 -+ [(0x0.5) + (0x0.5)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.5) + (0x0.5)]x1 -+ [(1x0.5) + (0x0.5)]x1 -+ [(0x0.5) + (0x0.5)]x1 -+ [(0x0.5) + (1x0.5)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 1 = 1 -π_Jn(a2) = π(a2) = 1 = 1 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 1 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 1 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.03) -+ (0.99x0.005x0.97) -+ (0.2x0.995x0.03) -+ (0.003x0.995x0.97) = 0.01381575 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.03) -+ (0.01x0.005x0.97) -+ (0.8x0.995x0.03) -+ (0.997x0.995x0.97) = 0.98618425 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 1 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.03x0.5) -+ (0x0.03x0.5) -+ (0x0.97x0.5) -+ (0x0.97x0.5) = 0.015 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.5) -+ (1x0.03x0.5) -+ (0x0.97x0.5) -+ (0x0.97x0.5) = 0.015 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.5) -+ (0x0.03x0.5) -+ (1x0.97x0.5) -+ (0x0.97x0.5) = 0.485 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.5) -+ (0x0.03x0.5) -+ (0x0.97x0.5) -+ (1x0.97x0.5) = 0.485 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 1 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005 0.5 -b2 0.995 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381575 0.5 0.01381575 -a2 0.98618425 0.5 0.98618425 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.5 0.5 -a2 0.5 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.015 1 0.015 -_jn1 0.015 1 0.015 -_jn2 0.485 1 0.485 -_jn3 0.485 1 0.485 - - - -******************************************************************************** - Iteration 2 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.03) + (0.99x0.97)]x0.5 -+ [(0.008x0.03) + (0.01x0.97)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.03) + (0.003x0.97)]x0.5 -+ [(0.8x0.03) + (0.997x0.97)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.5) + (0x0.5)]x1 -+ [(0x0.5) + (1x0.5)]x1 -+ [(0x0.5) + (0x0.5)]x1 -+ [(0x0.5) + (0x0.5)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.5) + (0x0.5)]x1 -+ [(0x0.5) + (0x0.5)]x1 -+ [(1x0.5) + (0x0.5)]x1 -+ [(0x0.5) + (1x0.5)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.03) + (0x0.97)]x1 -+ [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138158 = 0.01381575 -π_Jn(a2) = π(a2) = 0.986184 = 0.98618425 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 8.67361738e-19 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.03) -+ (0.99x0.005x0.97) -+ (0.2x0.995x0.03) -+ (0.003x0.995x0.97) = 0.01381575 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.03) -+ (0.01x0.005x0.97) -+ (0.8x0.995x0.03) -+ (0.997x0.995x0.97) = 0.98618425 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 0 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0004144725 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (1x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0295855275 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (1x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0134012775 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (1x0.97x0.986184) = 0.9565987225 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 0.9723685 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005 0.5 -b2 0.995 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381575 0.5 0.01381575 -a2 0.98618425 0.5 0.98618425 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01381575 0.5 -a2 0.98618425 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004144725 1 0.0004144725 -_jn1 0.0295855275 1 0.0295855275 -_jn2 0.0134012775 1 0.0134012775 -_jn3 0.9565987225 1 0.9565987225 - - - -******************************************************************************** - Iteration 3 -******************************************************************************** -λ message Alarm --> Burglar -λAlarm(b1) -= [p(a1|b1,f1).πAlarm(f1) + p(a1|b1,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(f1) + p(a2|b1,f2).πAlarm(f2)].λ(a2) -= [(0.992x0.03) + (0.99x0.97)]x0.5 -+ [(0.008x0.03) + (0.01x0.97)]x0.5 = 0.5 -λAlarm(b2) -= [p(a1|b2,f1).πAlarm(f1) + p(a1|b2,f2).πAlarm(f2)].λ(a1) -+ [p(a2|b2,f1).πAlarm(f1) + p(a2|b2,f2).πAlarm(f2)].λ(a2) -= [(0.2x0.03) + (0.003x0.97)]x0.5 -+ [(0.8x0.03) + (0.997x0.97)]x0.5 = 0.5 - -λ message Alarm --> FreightTruck -λAlarm(f1) -= [p(a1|b1,f1).πAlarm(b1) + p(a1|b2,f1).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f1).πAlarm(b1) + p(a2|b2,f1).πAlarm(b2)].λ(a2) -= [(0.992x0.005) + (0.2x0.995)]x0.5 -+ [(0.008x0.005) + (0.8x0.995)]x0.5 = 0.5 -λAlarm(f2) -= [p(a1|b1,f2).πAlarm(b1) + p(a1|b2,f2).πAlarm(b2)].λ(a1) -+ [p(a2|b1,f2).πAlarm(b1) + p(a2|b2,f2).πAlarm(b2)].λ(a2) -= [(0.99x0.005) + (0.003x0.995)]x0.5 -+ [(0.01x0.005) + (0.997x0.995)]x0.5 = 0.5 - -λ message _Jn --> FreightTruck -λ_Jn(f1) -= [p(_jn0|f1,a1).π_Jn(a1) + p(_jn0|f1,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(a1) + p(_jn1|f1,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(a1) + p(_jn2|f1,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(a1) + p(_jn3|f1,a2).π_Jn(a2)].λ(_jn3) -= [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 = 1 -λ_Jn(f2) -= [p(_jn0|f2,a1).π_Jn(a1) + p(_jn0|f2,a2).π_Jn(a2)].λ(_jn0) -+ [p(_jn1|f2,a1).π_Jn(a1) + p(_jn1|f2,a2).π_Jn(a2)].λ(_jn1) -+ [p(_jn2|f2,a1).π_Jn(a1) + p(_jn2|f2,a2).π_Jn(a2)].λ(_jn2) -+ [p(_jn3|f2,a1).π_Jn(a1) + p(_jn3|f2,a2).π_Jn(a2)].λ(_jn3) -= [(0x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (0x0.986184)]x1 -+ [(1x0.0138158) + (0x0.986184)]x1 -+ [(0x0.0138158) + (1x0.986184)]x1 = 1 - -λ message _Jn --> Alarm -λ_Jn(a1) -= [p(_jn0|f1,a1).π_Jn(f1) + p(_jn0|f2,a1).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a1).π_Jn(f1) + p(_jn1|f2,a1).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a1).π_Jn(f1) + p(_jn2|f2,a1).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a1).π_Jn(f1) + p(_jn3|f2,a1).π_Jn(f2)].λ(_jn3) -= [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 = 1 -λ_Jn(a2) -= [p(_jn0|f1,a2).π_Jn(f1) + p(_jn0|f2,a2).π_Jn(f2)].λ(_jn0) -+ [p(_jn1|f1,a2).π_Jn(f1) + p(_jn1|f2,a2).π_Jn(f2)].λ(_jn1) -+ [p(_jn2|f1,a2).π_Jn(f1) + p(_jn2|f2,a2).π_Jn(f2)].λ(_jn2) -+ [p(_jn3|f1,a2).π_Jn(f1) + p(_jn3|f2,a2).π_Jn(f2)].λ(_jn3) -= [(0x0.03) + (0x0.97)]x1 -+ [(1x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (0x0.97)]x1 -+ [(0x0.03) + (1x0.97)]x1 = 1 - -π message Burglar --> Alarm -πAlarm(b1) = π(b1) = 0.005 = 0.005 -πAlarm(b2) = π(b2) = 0.995 = 0.995 - -π message FreightTruck --> Alarm -πAlarm(f1) = π(f1).λ_Jn(f1) = 0.03 x 0.5 = 0.015 -πAlarm(f2) = π(f2).λ_Jn(f2) = 0.97 x 0.5 = 0.485 - -π message FreightTruck --> _Jn -π_Jn(f1) = π(f1).λAlarm(f1) = 0.03 x 0.5 = 0.015 -π_Jn(f2) = π(f2).λAlarm(f2) = 0.97 x 0.5 = 0.485 - -π message Alarm --> _Jn -π_Jn(a1) = π(a1) = 0.0138158 = 0.01381575 -π_Jn(a2) = π(a2) = 0.986184 = 0.98618425 - -var Burglar: -π(b1) -= p(b1) -= (0.005) = 0.005 -π(b2) -= p(b2) -= (0.995) = 0.995 -λ(b1) = λAlarm(b1) = 0.5 = 0.5 -λ(b2) = λAlarm(b2) = 0.5 = 0.5 -belief change = 0 - -var FreightTruck: -π(f1) -= p(f1) -= (0.03) = 0.03 -π(f2) -= p(f2) -= (0.97) = 0.97 -λ(f1) = λAlarm(f1).λ_Jn(f1) = 0.5 x 0.5 = 0.25 -λ(f2) = λAlarm(f2).λ_Jn(f2) = 0.5 x 0.5 = 0.25 -belief change = 0 - -var Alarm: -π(a1) -= p(a1|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a1|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a1|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a1|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.992x0.005x0.03) -+ (0.99x0.005x0.97) -+ (0.2x0.995x0.03) -+ (0.003x0.995x0.97) = 0.01381575 -π(a2) -= p(a2|b1,f1).πAlarm(b1).πAlarm(f1) -+ p(a2|b1,f2).πAlarm(b1).πAlarm(f2) -+ p(a2|b2,f1).πAlarm(b2).πAlarm(f1) -+ p(a2|b2,f2).πAlarm(b2).πAlarm(f2) -= (0.008x0.005x0.03) -+ (0.01x0.005x0.97) -+ (0.8x0.995x0.03) -+ (0.997x0.995x0.97) = 0.98618425 -λ(a1) = λ_Jn(a1) = 0.5 = 0.5 -λ(a2) = λ_Jn(a2) = 0.5 = 0.5 -belief change = 0 - -var _Jn: -π(_jn0) -= p(_jn0|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn0|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn0|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn0|f2,a2).π_Jn(f2).π_Jn(a2) -= (1x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0004144725 -π(_jn1) -= p(_jn1|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn1|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn1|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn1|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (1x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0295855275 -π(_jn2) -= p(_jn2|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn2|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn2|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn2|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (1x0.97x0.0138158) -+ (0x0.97x0.986184) = 0.0134012775 -π(_jn3) -= p(_jn3|f1,a1).π_Jn(f1).π_Jn(a1) -+ p(_jn3|f1,a2).π_Jn(f1).π_Jn(a2) -+ p(_jn3|f2,a1).π_Jn(f2).π_Jn(a1) -+ p(_jn3|f2,a2).π_Jn(f2).π_Jn(a2) -= (0x0.03x0.0138158) -+ (0x0.03x0.986184) -+ (0x0.97x0.0138158) -+ (1x0.97x0.986184) = 0.9565987225 -λ(_jn0) = 1 -λ(_jn1) = 1 -λ(_jn2) = 1 -λ(_jn3) = 1 -belief change = 0 - -domain π(Burglar) λ(Burglar) belief ----------------------------------------------------------------- -b1 0.005 0.5 0.005 -b2 0.995 0.5 0.995 - -domain πAlarm(Burglar) λAlarm(Burglar) ----------------------------------------------------------------- -b1 0.005 0.5 -b2 0.995 0.5 - -domain π(FreightTruck) λ(FreightTruck) belief ----------------------------------------------------------------- -f1 0.03 0.25 0.03 -f2 0.97 0.25 0.97 - -domain πAlarm(FreightTruck) λAlarm(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π_Jn(FreightTruck) λ_Jn(FreightTruck) ----------------------------------------------------------------- -f1 0.03 0.5 -f2 0.97 0.5 - -domain π(Alarm) λ(Alarm) belief ----------------------------------------------------------------- -a1 0.01381575 0.5 0.01381575 -a2 0.98618425 0.5 0.98618425 - -domain π_Jn(Alarm) λ_Jn(Alarm) ----------------------------------------------------------------- -a1 0.01381575 0.5 -a2 0.98618425 0.5 - -domain π(_Jn) λ(_Jn) belief ----------------------------------------------------------------- -_jn0 0.0004144725 1 0.0004144725 -_jn1 0.0295855275 1 0.0295855275 -_jn2 0.0134012775 1 0.0134012775 -_jn3 0.9565987225 1 0.9565987225 - - -Iterative belief propagation converged in 3 iterations - diff --git a/packages/CLPBN/clpbn/bp/simple-loop.par.txt b/packages/CLPBN/clpbn/bp/simple-loop.par.txt deleted file mode 100644 index 25bab238e..000000000 --- a/packages/CLPBN/clpbn/bp/simple-loop.par.txt +++ /dev/null @@ -1,10366 +0,0 @@ -Variable: A -Domain: a1, a2 -Parents: -Childs: B, C -cpt ----------------- -a1 0.01 -a2 0.09 - -Variable: B -Domain: b1, b2 -Parents: A -Childs: D -cpt a1, a2, ----------------------------- -b1 0.03 0.6 -b2 0.97 0.4 - -Variable: C -Domain: c1, c2 -Parents: A -Childs: D -cpt a1, a2, ----------------------------- -c1 0.24 0.12 -c2 0.76 0.88 - -Variable: D -Domain: d1, d2 -Parents: B, C -Childs: -cpt b1,c1, b1,c2, b2,c1, b2,c2, ----------------------------------------------------- -d1 0.2 0.7 0.45 0.22 -d2 0.8 0.3 0.55 0.78 - -initializing solver - schedule = parallel - maxIter = 100 - accuracy = 0 - - -******************************************************************************** -Iteration 0 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 1 0.1 - a2 0.09 1 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 1 1 - a2 1 1 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 1 1 - a2 1 1 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 1 1 0.5 - b2 1 1 0.5 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 1 1 - b2 1 1 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 1 1 0.5 - c2 1 1 0.5 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 1 1 - c2 1 1 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 1 1 0.5 - d2 1 1 0.5 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x1 + [(0.97)]x1 = 1 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x1 + [(0.4)]x1 = 1 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x1 + [(0.76)]x1 = 1 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x1 + [(0.88)]x1 = 1 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x1) + (0.7x1)]x1 + [(0.8x1) + (0.3x1)]x1 = 2 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x1) + (0.22x1)]x1 + [(0.55x1) + (0.78x1)]x1 = 2 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x1) + (0.45x1)]x1 + [(0.8x1) + (0.55x1)]x1 = 2 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x1) + (0.22x1)]x1 + [(0.3x1) + (0.78x1)]x1 = 2 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 1 = 0.01 - πB(a2) = π(a2).λC(a2) = 0.09 x 1 = 0.09 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 1 = 0.01 - πC(a2) = π(a2).λB(a2) = 0.09 x 1 = 0.09 -π message B --> D - πD(b1) = π(b1) = 1 = 1 - πD(b2) = π(b2) = 1 = 1 -π message C --> D - πD(c1) = π(c1) = 1 = 1 - πD(c2) = π(c2) = 1 = 1 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 1 x 1 = 1 - λ(a2) = λB(a2).λC(a2) = 1 x 1 = 1 - belief change = 1 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 0.01) + (0.6 x 0.09) = 0.0543 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 0.01) + (0.4 x 0.09) = 0.0457 - λ(b1) = λD(b1) = 2 = 2 - λ(b2) = λD(b2) = 2 = 2 - belief change = 1 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 0.01) + (0.12 x 0.09) = 0.0132 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 0.01) + (0.88 x 0.09) = 0.0868 - λ(c1) = λD(c1) = 2 = 2 - λ(c2) = λD(c2) = 2 = 2 - belief change = 1 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 1 x 1) + (0.7 x 1 x 1) + (0.45 x 1 x 1) + (0.22 x 1 x 1) = 1.57 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 1 x 1) + (0.3 x 1 x 1) + (0.55 x 1 x 1) + (0.78 x 1 x 1) = 2.43 - λ(d1) = 1 - λ(d2) = 1 - belief change = 1 - - -******************************************************************************** -Iteration 1 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 1 0.1 - a2 0.09 1 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 0.01 1 - a2 0.09 1 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 0.01 1 - a2 0.09 1 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 0.0543 2 0.543 - b2 0.0457 2 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 1 2 - b2 1 2 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 0.0132 2 0.132 - c2 0.0868 2 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 1 2 - c2 1 2 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 1.57 1 0.3925 - d2 2.43 1 0.6075 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x2 + [(0.97)]x2 = 2 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x2 + [(0.4)]x2 = 2 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x2 + [(0.76)]x2 = 2 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x2 + [(0.88)]x2 = 2 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x1) + (0.7x1)]x1 + [(0.8x1) + (0.3x1)]x1 = 2 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x1) + (0.22x1)]x1 + [(0.55x1) + (0.78x1)]x1 = 2 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x1) + (0.45x1)]x1 + [(0.8x1) + (0.55x1)]x1 = 2 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x1) + (0.22x1)]x1 + [(0.3x1) + (0.78x1)]x1 = 2 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 1 = 0.01 - πB(a2) = π(a2).λC(a2) = 0.09 x 1 = 0.09 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 1 = 0.01 - πC(a2) = π(a2).λB(a2) = 0.09 x 1 = 0.09 -π message B --> D - πD(b1) = π(b1) = 0.0543 = 0.0543 - πD(b2) = π(b2) = 0.0457 = 0.0457 -π message C --> D - πD(c1) = π(c1) = 0.0132 = 0.0132 - πD(c2) = π(c2) = 0.0868 = 0.0868 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 2 x 2 = 4 - λ(a2) = λB(a2).λC(a2) = 2 x 2 = 4 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 0.01) + (0.6 x 0.09) = 0.0543 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 0.01) + (0.4 x 0.09) = 0.0457 - λ(b1) = λD(b1) = 2 = 2 - λ(b2) = λD(b2) = 2 = 2 - belief change = 0 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 0.01) + (0.12 x 0.09) = 0.0132 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 0.01) + (0.88 x 0.09) = 0.0868 - λ(c1) = λD(c1) = 2 = 2 - λ(c2) = λD(c2) = 2 = 2 - belief change = 0 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 0.0543 x 0.0132) + (0.7 x 0.0543 x 0.0868) + (0.45 x 0.0457 x 0.0132) + (0.22 x 0.0457 x 0.0868) = 0.0045867652 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 0.0543 x 0.0132) + (0.3 x 0.0543 x 0.0868) + (0.55 x 0.0457 x 0.0132) + (0.78 x 0.0457 x 0.0868) = 0.0054132348 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0.13235304 - - -******************************************************************************** -Iteration 2 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 4 0.1 - a2 0.09 4 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 0.01 2 - a2 0.09 2 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 0.01 2 - a2 0.09 2 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 0.0543 2 0.543 - b2 0.0457 2 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 0.0543 2 - b2 0.0457 2 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 0.0132 2 0.132 - c2 0.0868 2 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 0.0132 2 - c2 0.0868 2 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 0.0045867652 1 0.45867652 - d2 0.0054132348 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x2 + [(0.97)]x2 = 2 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x2 + [(0.4)]x2 = 2 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x2 + [(0.76)]x2 = 2 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x2 + [(0.88)]x2 = 2 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x0.0132) + (0.7x0.0868)]x1 + [(0.8x0.0132) + (0.3x0.0868)]x1 = 0.1 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x0.0132) + (0.22x0.0868)]x1 + [(0.55x0.0132) + (0.78x0.0868)]x1 = 0.1 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x0.0543) + (0.45x0.0457)]x1 + [(0.8x0.0543) + (0.55x0.0457)]x1 = 0.1 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x0.0543) + (0.22x0.0457)]x1 + [(0.3x0.0543) + (0.78x0.0457)]x1 = 0.1 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 2 = 0.02 - πB(a2) = π(a2).λC(a2) = 0.09 x 2 = 0.18 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 2 = 0.02 - πC(a2) = π(a2).λB(a2) = 0.09 x 2 = 0.18 -π message B --> D - πD(b1) = π(b1) = 0.0543 = 0.0543 - πD(b2) = π(b2) = 0.0457 = 0.0457 -π message C --> D - πD(c1) = π(c1) = 0.0132 = 0.0132 - πD(c2) = π(c2) = 0.0868 = 0.0868 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 2 x 2 = 4 - λ(a2) = λB(a2).λC(a2) = 2 x 2 = 4 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 0.02) + (0.6 x 0.18) = 0.1086 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 0.02) + (0.4 x 0.18) = 0.0914 - λ(b1) = λD(b1) = 0.1 = 0.1 - λ(b2) = λD(b2) = 0.1 = 0.1 - belief change = 1.665334537e-16 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 0.02) + (0.12 x 0.18) = 0.0264 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 0.02) + (0.88 x 0.18) = 0.1736 - λ(c1) = λD(c1) = 0.1 = 0.1 - λ(c2) = λD(c2) = 0.1 = 0.1 - belief change = 0 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 0.0543 x 0.0132) + (0.7 x 0.0543 x 0.0868) + (0.45 x 0.0457 x 0.0132) + (0.22 x 0.0457 x 0.0868) = 0.0045867652 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 0.0543 x 0.0132) + (0.3 x 0.0543 x 0.0868) + (0.55 x 0.0457 x 0.0132) + (0.78 x 0.0457 x 0.0868) = 0.0054132348 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 3 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 4 0.1 - a2 0.09 4 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 0.02 2 - a2 0.18 2 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 0.02 2 - a2 0.18 2 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 0.1086 0.1 0.543 - b2 0.0914 0.1 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 0.0543 0.1 - b2 0.0457 0.1 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 0.0264 0.1 0.132 - c2 0.1736 0.1 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 0.0132 0.1 - c2 0.0868 0.1 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 0.0045867652 1 0.45867652 - d2 0.0054132348 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x0.1 + [(0.97)]x0.1 = 0.1 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x0.1 + [(0.4)]x0.1 = 0.1 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x0.1 + [(0.76)]x0.1 = 0.1 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x0.1 + [(0.88)]x0.1 = 0.1 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x0.0132) + (0.7x0.0868)]x1 + [(0.8x0.0132) + (0.3x0.0868)]x1 = 0.1 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x0.0132) + (0.22x0.0868)]x1 + [(0.55x0.0132) + (0.78x0.0868)]x1 = 0.1 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x0.0543) + (0.45x0.0457)]x1 + [(0.8x0.0543) + (0.55x0.0457)]x1 = 0.1 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x0.0543) + (0.22x0.0457)]x1 + [(0.3x0.0543) + (0.78x0.0457)]x1 = 0.1 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 2 = 0.02 - πB(a2) = π(a2).λC(a2) = 0.09 x 2 = 0.18 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 2 = 0.02 - πC(a2) = π(a2).λB(a2) = 0.09 x 2 = 0.18 -π message B --> D - πD(b1) = π(b1) = 0.1086 = 0.1086 - πD(b2) = π(b2) = 0.0914 = 0.0914 -π message C --> D - πD(c1) = π(c1) = 0.0264 = 0.0264 - πD(c2) = π(c2) = 0.1736 = 0.1736 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 0.1 x 0.1 = 0.01 - λ(a2) = λB(a2).λC(a2) = 0.1 x 0.1 = 0.01 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 0.02) + (0.6 x 0.18) = 0.1086 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 0.02) + (0.4 x 0.18) = 0.0914 - λ(b1) = λD(b1) = 0.1 = 0.1 - λ(b2) = λD(b2) = 0.1 = 0.1 - belief change = 0 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 0.02) + (0.12 x 0.18) = 0.0264 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 0.02) + (0.88 x 0.18) = 0.1736 - λ(c1) = λD(c1) = 0.1 = 0.1 - λ(c2) = λD(c2) = 0.1 = 0.1 - belief change = 0 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 0.1086 x 0.0264) + (0.7 x 0.1086 x 0.1736) + (0.45 x 0.0914 x 0.0264) + (0.22 x 0.0914 x 0.1736) = 0.0183470608 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 0.1086 x 0.0264) + (0.3 x 0.1086 x 0.1736) + (0.55 x 0.0914 x 0.0264) + (0.78 x 0.0914 x 0.1736) = 0.0216529392 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 4 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 0.01 0.1 - a2 0.09 0.01 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 0.02 0.1 - a2 0.18 0.1 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 0.02 0.1 - a2 0.18 0.1 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 0.1086 0.1 0.543 - b2 0.0914 0.1 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 0.1086 0.1 - b2 0.0914 0.1 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 0.0264 0.1 0.132 - c2 0.1736 0.1 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 0.0264 0.1 - c2 0.1736 0.1 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 0.0183470608 1 0.45867652 - d2 0.0216529392 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x0.1 + [(0.97)]x0.1 = 0.1 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x0.1 + [(0.4)]x0.1 = 0.1 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x0.1 + [(0.76)]x0.1 = 0.1 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x0.1 + [(0.88)]x0.1 = 0.1 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x0.0264) + (0.7x0.1736)]x1 + [(0.8x0.0264) + (0.3x0.1736)]x1 = 0.2 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x0.0264) + (0.22x0.1736)]x1 + [(0.55x0.0264) + (0.78x0.1736)]x1 = 0.2 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x0.1086) + (0.45x0.0914)]x1 + [(0.8x0.1086) + (0.55x0.0914)]x1 = 0.2 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x0.1086) + (0.22x0.0914)]x1 + [(0.3x0.1086) + (0.78x0.0914)]x1 = 0.2 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 0.1 = 0.001 - πB(a2) = π(a2).λC(a2) = 0.09 x 0.1 = 0.009 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 0.1 = 0.001 - πC(a2) = π(a2).λB(a2) = 0.09 x 0.1 = 0.009 -π message B --> D - πD(b1) = π(b1) = 0.1086 = 0.1086 - πD(b2) = π(b2) = 0.0914 = 0.0914 -π message C --> D - πD(c1) = π(c1) = 0.0264 = 0.0264 - πD(c2) = π(c2) = 0.1736 = 0.1736 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 0.1 x 0.1 = 0.01 - λ(a2) = λB(a2).λC(a2) = 0.1 x 0.1 = 0.01 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 0.001) + (0.6 x 0.009) = 0.00543 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 0.001) + (0.4 x 0.009) = 0.00457 - λ(b1) = λD(b1) = 0.2 = 0.2 - λ(b2) = λD(b2) = 0.2 = 0.2 - belief change = 2.220446049e-16 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 0.001) + (0.12 x 0.009) = 0.00132 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 0.001) + (0.88 x 0.009) = 0.00868 - λ(c1) = λD(c1) = 0.2 = 0.2 - λ(c2) = λD(c2) = 0.2 = 0.2 - belief change = 1.387778781e-16 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 0.1086 x 0.0264) + (0.7 x 0.1086 x 0.1736) + (0.45 x 0.0914 x 0.0264) + (0.22 x 0.0914 x 0.1736) = 0.0183470608 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 0.1086 x 0.0264) + (0.3 x 0.1086 x 0.1736) + (0.55 x 0.0914 x 0.0264) + (0.78 x 0.0914 x 0.1736) = 0.0216529392 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 5 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 0.01 0.1 - a2 0.09 0.01 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 0.001 0.1 - a2 0.009 0.1 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 0.001 0.1 - a2 0.009 0.1 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 0.00543 0.2 0.543 - b2 0.00457 0.2 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 0.1086 0.2 - b2 0.0914 0.2 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 0.00132 0.2 0.132 - c2 0.00868 0.2 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 0.0264 0.2 - c2 0.1736 0.2 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 0.0183470608 1 0.45867652 - d2 0.0216529392 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x0.2 + [(0.97)]x0.2 = 0.2 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x0.2 + [(0.4)]x0.2 = 0.2 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x0.2 + [(0.76)]x0.2 = 0.2 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x0.2 + [(0.88)]x0.2 = 0.2 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x0.0264) + (0.7x0.1736)]x1 + [(0.8x0.0264) + (0.3x0.1736)]x1 = 0.2 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x0.0264) + (0.22x0.1736)]x1 + [(0.55x0.0264) + (0.78x0.1736)]x1 = 0.2 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x0.1086) + (0.45x0.0914)]x1 + [(0.8x0.1086) + (0.55x0.0914)]x1 = 0.2 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x0.1086) + (0.22x0.0914)]x1 + [(0.3x0.1086) + (0.78x0.0914)]x1 = 0.2 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 0.1 = 0.001 - πB(a2) = π(a2).λC(a2) = 0.09 x 0.1 = 0.009 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 0.1 = 0.001 - πC(a2) = π(a2).λB(a2) = 0.09 x 0.1 = 0.009 -π message B --> D - πD(b1) = π(b1) = 0.00543 = 0.00543 - πD(b2) = π(b2) = 0.00457 = 0.00457 -π message C --> D - πD(c1) = π(c1) = 0.00132 = 0.00132 - πD(c2) = π(c2) = 0.00868 = 0.00868 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 0.2 x 0.2 = 0.04 - λ(a2) = λB(a2).λC(a2) = 0.2 x 0.2 = 0.04 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 0.001) + (0.6 x 0.009) = 0.00543 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 0.001) + (0.4 x 0.009) = 0.00457 - λ(b1) = λD(b1) = 0.2 = 0.2 - λ(b2) = λD(b2) = 0.2 = 0.2 - belief change = 0 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 0.001) + (0.12 x 0.009) = 0.00132 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 0.001) + (0.88 x 0.009) = 0.00868 - λ(c1) = λD(c1) = 0.2 = 0.2 - λ(c2) = λD(c2) = 0.2 = 0.2 - belief change = 0 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 0.00543 x 0.00132) + (0.7 x 0.00543 x 0.00868) + (0.45 x 0.00457 x 0.00132) + (0.22 x 0.00457 x 0.00868) = 4.5867652e-05 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 0.00543 x 0.00132) + (0.3 x 0.00543 x 0.00868) + (0.55 x 0.00457 x 0.00132) + (0.78 x 0.00457 x 0.00868) = 5.4132348e-05 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 6 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 0.04 0.1 - a2 0.09 0.04 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 0.001 0.2 - a2 0.009 0.2 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 0.001 0.2 - a2 0.009 0.2 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 0.00543 0.2 0.543 - b2 0.00457 0.2 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 0.00543 0.2 - b2 0.00457 0.2 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 0.00132 0.2 0.132 - c2 0.00868 0.2 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 0.00132 0.2 - c2 0.00868 0.2 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 4.5867652e-05 1 0.45867652 - d2 5.4132348e-05 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x0.2 + [(0.97)]x0.2 = 0.2 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x0.2 + [(0.4)]x0.2 = 0.2 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x0.2 + [(0.76)]x0.2 = 0.2 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x0.2 + [(0.88)]x0.2 = 0.2 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x0.00132) + (0.7x0.00868)]x1 + [(0.8x0.00132) + (0.3x0.00868)]x1 = 0.01 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x0.00132) + (0.22x0.00868)]x1 + [(0.55x0.00132) + (0.78x0.00868)]x1 = 0.01 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x0.00543) + (0.45x0.00457)]x1 + [(0.8x0.00543) + (0.55x0.00457)]x1 = 0.01 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x0.00543) + (0.22x0.00457)]x1 + [(0.3x0.00543) + (0.78x0.00457)]x1 = 0.01 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 0.2 = 0.002 - πB(a2) = π(a2).λC(a2) = 0.09 x 0.2 = 0.018 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 0.2 = 0.002 - πC(a2) = π(a2).λB(a2) = 0.09 x 0.2 = 0.018 -π message B --> D - πD(b1) = π(b1) = 0.00543 = 0.00543 - πD(b2) = π(b2) = 0.00457 = 0.00457 -π message C --> D - πD(c1) = π(c1) = 0.00132 = 0.00132 - πD(c2) = π(c2) = 0.00868 = 0.00868 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 0.2 x 0.2 = 0.04 - λ(a2) = λB(a2).λC(a2) = 0.2 x 0.2 = 0.04 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 0.002) + (0.6 x 0.018) = 0.01086 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 0.002) + (0.4 x 0.018) = 0.00914 - λ(b1) = λD(b1) = 0.01 = 0.01 - λ(b2) = λD(b2) = 0.01 = 0.01 - belief change = 5.551115123e-17 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 0.002) + (0.12 x 0.018) = 0.00264 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 0.002) + (0.88 x 0.018) = 0.01736 - λ(c1) = λD(c1) = 0.01 = 0.01 - λ(c2) = λD(c2) = 0.01 = 0.01 - belief change = 1.110223025e-16 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 0.00543 x 0.00132) + (0.7 x 0.00543 x 0.00868) + (0.45 x 0.00457 x 0.00132) + (0.22 x 0.00457 x 0.00868) = 4.5867652e-05 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 0.00543 x 0.00132) + (0.3 x 0.00543 x 0.00868) + (0.55 x 0.00457 x 0.00132) + (0.78 x 0.00457 x 0.00868) = 5.4132348e-05 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 7 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 0.04 0.1 - a2 0.09 0.04 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 0.002 0.2 - a2 0.018 0.2 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 0.002 0.2 - a2 0.018 0.2 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 0.01086 0.01 0.543 - b2 0.00914 0.01 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 0.00543 0.01 - b2 0.00457 0.01 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 0.00264 0.01 0.132 - c2 0.01736 0.01 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 0.00132 0.01 - c2 0.00868 0.01 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 4.5867652e-05 1 0.45867652 - d2 5.4132348e-05 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x0.01 + [(0.97)]x0.01 = 0.01 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x0.01 + [(0.4)]x0.01 = 0.01 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x0.01 + [(0.76)]x0.01 = 0.01 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x0.01 + [(0.88)]x0.01 = 0.01 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x0.00132) + (0.7x0.00868)]x1 + [(0.8x0.00132) + (0.3x0.00868)]x1 = 0.01 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x0.00132) + (0.22x0.00868)]x1 + [(0.55x0.00132) + (0.78x0.00868)]x1 = 0.01 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x0.00543) + (0.45x0.00457)]x1 + [(0.8x0.00543) + (0.55x0.00457)]x1 = 0.01 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x0.00543) + (0.22x0.00457)]x1 + [(0.3x0.00543) + (0.78x0.00457)]x1 = 0.01 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 0.2 = 0.002 - πB(a2) = π(a2).λC(a2) = 0.09 x 0.2 = 0.018 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 0.2 = 0.002 - πC(a2) = π(a2).λB(a2) = 0.09 x 0.2 = 0.018 -π message B --> D - πD(b1) = π(b1) = 0.01086 = 0.01086 - πD(b2) = π(b2) = 0.00914 = 0.00914 -π message C --> D - πD(c1) = π(c1) = 0.00264 = 0.00264 - πD(c2) = π(c2) = 0.01736 = 0.01736 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 0.01 x 0.01 = 0.0001 - λ(a2) = λB(a2).λC(a2) = 0.01 x 0.01 = 0.0001 - belief change = 1.387778781e-17 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 0.002) + (0.6 x 0.018) = 0.01086 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 0.002) + (0.4 x 0.018) = 0.00914 - λ(b1) = λD(b1) = 0.01 = 0.01 - λ(b2) = λD(b2) = 0.01 = 0.01 - belief change = 0 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 0.002) + (0.12 x 0.018) = 0.00264 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 0.002) + (0.88 x 0.018) = 0.01736 - λ(c1) = λD(c1) = 0.01 = 0.01 - λ(c2) = λD(c2) = 0.01 = 0.01 - belief change = 0 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 0.01086 x 0.00264) + (0.7 x 0.01086 x 0.01736) + (0.45 x 0.00914 x 0.00264) + (0.22 x 0.00914 x 0.01736) = 0.000183470608 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 0.01086 x 0.00264) + (0.3 x 0.01086 x 0.01736) + (0.55 x 0.00914 x 0.00264) + (0.78 x 0.00914 x 0.01736) = 0.000216529392 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 8 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 0.0001 0.1 - a2 0.09 0.0001 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 0.002 0.01 - a2 0.018 0.01 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 0.002 0.01 - a2 0.018 0.01 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 0.01086 0.01 0.543 - b2 0.00914 0.01 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 0.01086 0.01 - b2 0.00914 0.01 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 0.00264 0.01 0.132 - c2 0.01736 0.01 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 0.00264 0.01 - c2 0.01736 0.01 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 0.000183470608 1 0.45867652 - d2 0.000216529392 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x0.01 + [(0.97)]x0.01 = 0.01 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x0.01 + [(0.4)]x0.01 = 0.01 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x0.01 + [(0.76)]x0.01 = 0.01 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x0.01 + [(0.88)]x0.01 = 0.01 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x0.00264) + (0.7x0.01736)]x1 + [(0.8x0.00264) + (0.3x0.01736)]x1 = 0.02 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x0.00264) + (0.22x0.01736)]x1 + [(0.55x0.00264) + (0.78x0.01736)]x1 = 0.02 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x0.01086) + (0.45x0.00914)]x1 + [(0.8x0.01086) + (0.55x0.00914)]x1 = 0.02 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x0.01086) + (0.22x0.00914)]x1 + [(0.3x0.01086) + (0.78x0.00914)]x1 = 0.02 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 0.01 = 0.0001 - πB(a2) = π(a2).λC(a2) = 0.09 x 0.01 = 0.0009 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 0.01 = 0.0001 - πC(a2) = π(a2).λB(a2) = 0.09 x 0.01 = 0.0009 -π message B --> D - πD(b1) = π(b1) = 0.01086 = 0.01086 - πD(b2) = π(b2) = 0.00914 = 0.00914 -π message C --> D - πD(c1) = π(c1) = 0.00264 = 0.00264 - πD(c2) = π(c2) = 0.01736 = 0.01736 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 0.01 x 0.01 = 0.0001 - λ(a2) = λB(a2).λC(a2) = 0.01 x 0.01 = 0.0001 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 0.0001) + (0.6 x 0.0009) = 0.000543 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 0.0001) + (0.4 x 0.0009) = 0.000457 - λ(b1) = λD(b1) = 0.02 = 0.02 - λ(b2) = λD(b2) = 0.02 = 0.02 - belief change = 0 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 0.0001) + (0.12 x 0.0009) = 0.000132 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 0.0001) + (0.88 x 0.0009) = 0.000868 - λ(c1) = λD(c1) = 0.02 = 0.02 - λ(c2) = λD(c2) = 0.02 = 0.02 - belief change = 1.387778781e-16 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 0.01086 x 0.00264) + (0.7 x 0.01086 x 0.01736) + (0.45 x 0.00914 x 0.00264) + (0.22 x 0.00914 x 0.01736) = 0.000183470608 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 0.01086 x 0.00264) + (0.3 x 0.01086 x 0.01736) + (0.55 x 0.00914 x 0.00264) + (0.78 x 0.00914 x 0.01736) = 0.000216529392 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 9 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 0.0001 0.1 - a2 0.09 0.0001 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 0.0001 0.01 - a2 0.0009 0.01 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 0.0001 0.01 - a2 0.0009 0.01 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 0.000543 0.02 0.543 - b2 0.000457 0.02 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 0.01086 0.02 - b2 0.00914 0.02 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 0.000132 0.02 0.132 - c2 0.000868 0.02 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 0.00264 0.02 - c2 0.01736 0.02 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 0.000183470608 1 0.45867652 - d2 0.000216529392 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x0.02 + [(0.97)]x0.02 = 0.02 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x0.02 + [(0.4)]x0.02 = 0.02 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x0.02 + [(0.76)]x0.02 = 0.02 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x0.02 + [(0.88)]x0.02 = 0.02 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x0.00264) + (0.7x0.01736)]x1 + [(0.8x0.00264) + (0.3x0.01736)]x1 = 0.02 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x0.00264) + (0.22x0.01736)]x1 + [(0.55x0.00264) + (0.78x0.01736)]x1 = 0.02 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x0.01086) + (0.45x0.00914)]x1 + [(0.8x0.01086) + (0.55x0.00914)]x1 = 0.02 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x0.01086) + (0.22x0.00914)]x1 + [(0.3x0.01086) + (0.78x0.00914)]x1 = 0.02 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 0.01 = 0.0001 - πB(a2) = π(a2).λC(a2) = 0.09 x 0.01 = 0.0009 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 0.01 = 0.0001 - πC(a2) = π(a2).λB(a2) = 0.09 x 0.01 = 0.0009 -π message B --> D - πD(b1) = π(b1) = 0.000543 = 0.000543 - πD(b2) = π(b2) = 0.000457 = 0.000457 -π message C --> D - πD(c1) = π(c1) = 0.000132 = 0.000132 - πD(c2) = π(c2) = 0.000868 = 0.000868 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 0.02 x 0.02 = 0.0004 - λ(a2) = λB(a2).λC(a2) = 0.02 x 0.02 = 0.0004 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 0.0001) + (0.6 x 0.0009) = 0.000543 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 0.0001) + (0.4 x 0.0009) = 0.000457 - λ(b1) = λD(b1) = 0.02 = 0.02 - λ(b2) = λD(b2) = 0.02 = 0.02 - belief change = 0 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 0.0001) + (0.12 x 0.0009) = 0.000132 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 0.0001) + (0.88 x 0.0009) = 0.000868 - λ(c1) = λD(c1) = 0.02 = 0.02 - λ(c2) = λD(c2) = 0.02 = 0.02 - belief change = 0 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 0.000543 x 0.000132) + (0.7 x 0.000543 x 0.000868) + (0.45 x 0.000457 x 0.000132) + (0.22 x 0.000457 x 0.000868) = 4.5867652e-07 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 0.000543 x 0.000132) + (0.3 x 0.000543 x 0.000868) + (0.55 x 0.000457 x 0.000132) + (0.78 x 0.000457 x 0.000868) = 5.4132348e-07 - λ(d1) = 1 - λ(d2) = 1 - belief change = 5.551115123e-17 - - -******************************************************************************** -Iteration 10 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 0.0004 0.1 - a2 0.09 0.0004 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 0.0001 0.02 - a2 0.0009 0.02 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 0.0001 0.02 - a2 0.0009 0.02 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 0.000543 0.02 0.543 - b2 0.000457 0.02 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 0.000543 0.02 - b2 0.000457 0.02 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 0.000132 0.02 0.132 - c2 0.000868 0.02 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 0.000132 0.02 - c2 0.000868 0.02 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 4.5867652e-07 1 0.45867652 - d2 5.4132348e-07 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x0.02 + [(0.97)]x0.02 = 0.02 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x0.02 + [(0.4)]x0.02 = 0.02 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x0.02 + [(0.76)]x0.02 = 0.02 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x0.02 + [(0.88)]x0.02 = 0.02 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x0.000132) + (0.7x0.000868)]x1 + [(0.8x0.000132) + (0.3x0.000868)]x1 = 0.001 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x0.000132) + (0.22x0.000868)]x1 + [(0.55x0.000132) + (0.78x0.000868)]x1 = 0.001 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x0.000543) + (0.45x0.000457)]x1 + [(0.8x0.000543) + (0.55x0.000457)]x1 = 0.001 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x0.000543) + (0.22x0.000457)]x1 + [(0.3x0.000543) + (0.78x0.000457)]x1 = 0.001 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 0.02 = 0.0002 - πB(a2) = π(a2).λC(a2) = 0.09 x 0.02 = 0.0018 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 0.02 = 0.0002 - πC(a2) = π(a2).λB(a2) = 0.09 x 0.02 = 0.0018 -π message B --> D - πD(b1) = π(b1) = 0.000543 = 0.000543 - πD(b2) = π(b2) = 0.000457 = 0.000457 -π message C --> D - πD(c1) = π(c1) = 0.000132 = 0.000132 - πD(c2) = π(c2) = 0.000868 = 0.000868 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 0.02 x 0.02 = 0.0004 - λ(a2) = λB(a2).λC(a2) = 0.02 x 0.02 = 0.0004 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 0.0002) + (0.6 x 0.0018) = 0.001086 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 0.0002) + (0.4 x 0.0018) = 0.000914 - λ(b1) = λD(b1) = 0.001 = 0.001 - λ(b2) = λD(b2) = 0.001 = 0.001 - belief change = 3.330669074e-16 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 0.0002) + (0.12 x 0.0018) = 0.000264 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 0.0002) + (0.88 x 0.0018) = 0.001736 - λ(c1) = λD(c1) = 0.001 = 0.001 - λ(c2) = λD(c2) = 0.001 = 0.001 - belief change = 2.775557562e-17 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 0.000543 x 0.000132) + (0.7 x 0.000543 x 0.000868) + (0.45 x 0.000457 x 0.000132) + (0.22 x 0.000457 x 0.000868) = 4.5867652e-07 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 0.000543 x 0.000132) + (0.3 x 0.000543 x 0.000868) + (0.55 x 0.000457 x 0.000132) + (0.78 x 0.000457 x 0.000868) = 5.4132348e-07 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 11 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 0.0004 0.1 - a2 0.09 0.0004 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 0.0002 0.02 - a2 0.0018 0.02 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 0.0002 0.02 - a2 0.0018 0.02 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 0.001086 0.001 0.543 - b2 0.000914 0.001 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 0.000543 0.001 - b2 0.000457 0.001 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 0.000264 0.001 0.132 - c2 0.001736 0.001 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 0.000132 0.001 - c2 0.000868 0.001 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 4.5867652e-07 1 0.45867652 - d2 5.4132348e-07 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x0.001 + [(0.97)]x0.001 = 0.001 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x0.001 + [(0.4)]x0.001 = 0.001 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x0.001 + [(0.76)]x0.001 = 0.001 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x0.001 + [(0.88)]x0.001 = 0.001 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x0.000132) + (0.7x0.000868)]x1 + [(0.8x0.000132) + (0.3x0.000868)]x1 = 0.001 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x0.000132) + (0.22x0.000868)]x1 + [(0.55x0.000132) + (0.78x0.000868)]x1 = 0.001 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x0.000543) + (0.45x0.000457)]x1 + [(0.8x0.000543) + (0.55x0.000457)]x1 = 0.001 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x0.000543) + (0.22x0.000457)]x1 + [(0.3x0.000543) + (0.78x0.000457)]x1 = 0.001 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 0.02 = 0.0002 - πB(a2) = π(a2).λC(a2) = 0.09 x 0.02 = 0.0018 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 0.02 = 0.0002 - πC(a2) = π(a2).λB(a2) = 0.09 x 0.02 = 0.0018 -π message B --> D - πD(b1) = π(b1) = 0.001086 = 0.001086 - πD(b2) = π(b2) = 0.000914 = 0.000914 -π message C --> D - πD(c1) = π(c1) = 0.000264 = 0.000264 - πD(c2) = π(c2) = 0.001736 = 0.001736 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 0.001 x 0.001 = 1e-06 - λ(a2) = λB(a2).λC(a2) = 0.001 x 0.001 = 1e-06 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 0.0002) + (0.6 x 0.0018) = 0.001086 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 0.0002) + (0.4 x 0.0018) = 0.000914 - λ(b1) = λD(b1) = 0.001 = 0.001 - λ(b2) = λD(b2) = 0.001 = 0.001 - belief change = 0 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 0.0002) + (0.12 x 0.0018) = 0.000264 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 0.0002) + (0.88 x 0.0018) = 0.001736 - λ(c1) = λD(c1) = 0.001 = 0.001 - λ(c2) = λD(c2) = 0.001 = 0.001 - belief change = 0 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 0.001086 x 0.000264) + (0.7 x 0.001086 x 0.001736) + (0.45 x 0.000914 x 0.000264) + (0.22 x 0.000914 x 0.001736) = 1.83470608e-06 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 0.001086 x 0.000264) + (0.3 x 0.001086 x 0.001736) + (0.55 x 0.000914 x 0.000264) + (0.78 x 0.000914 x 0.001736) = 2.16529392e-06 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 12 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 1e-06 0.1 - a2 0.09 1e-06 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 0.0002 0.001 - a2 0.0018 0.001 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 0.0002 0.001 - a2 0.0018 0.001 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 0.001086 0.001 0.543 - b2 0.000914 0.001 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 0.001086 0.001 - b2 0.000914 0.001 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 0.000264 0.001 0.132 - c2 0.001736 0.001 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 0.000264 0.001 - c2 0.001736 0.001 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 1.83470608e-06 1 0.45867652 - d2 2.16529392e-06 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x0.001 + [(0.97)]x0.001 = 0.001 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x0.001 + [(0.4)]x0.001 = 0.001 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x0.001 + [(0.76)]x0.001 = 0.001 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x0.001 + [(0.88)]x0.001 = 0.001 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x0.000264) + (0.7x0.001736)]x1 + [(0.8x0.000264) + (0.3x0.001736)]x1 = 0.002 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x0.000264) + (0.22x0.001736)]x1 + [(0.55x0.000264) + (0.78x0.001736)]x1 = 0.002 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x0.001086) + (0.45x0.000914)]x1 + [(0.8x0.001086) + (0.55x0.000914)]x1 = 0.002 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x0.001086) + (0.22x0.000914)]x1 + [(0.3x0.001086) + (0.78x0.000914)]x1 = 0.002 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 0.001 = 1e-05 - πB(a2) = π(a2).λC(a2) = 0.09 x 0.001 = 9e-05 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 0.001 = 1e-05 - πC(a2) = π(a2).λB(a2) = 0.09 x 0.001 = 9e-05 -π message B --> D - πD(b1) = π(b1) = 0.001086 = 0.001086 - πD(b2) = π(b2) = 0.000914 = 0.000914 -π message C --> D - πD(c1) = π(c1) = 0.000264 = 0.000264 - πD(c2) = π(c2) = 0.001736 = 0.001736 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 0.001 x 0.001 = 1e-06 - λ(a2) = λB(a2).λC(a2) = 0.001 x 0.001 = 1e-06 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 1e-05) + (0.6 x 9e-05) = 5.43e-05 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 1e-05) + (0.4 x 9e-05) = 4.57e-05 - λ(b1) = λD(b1) = 0.002 = 0.002 - λ(b2) = λD(b2) = 0.002 = 0.002 - belief change = 1.665334537e-16 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 1e-05) + (0.12 x 9e-05) = 1.32e-05 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 1e-05) + (0.88 x 9e-05) = 8.68e-05 - λ(c1) = λD(c1) = 0.002 = 0.002 - λ(c2) = λD(c2) = 0.002 = 0.002 - belief change = 1.387778781e-16 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 0.001086 x 0.000264) + (0.7 x 0.001086 x 0.001736) + (0.45 x 0.000914 x 0.000264) + (0.22 x 0.000914 x 0.001736) = 1.83470608e-06 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 0.001086 x 0.000264) + (0.3 x 0.001086 x 0.001736) + (0.55 x 0.000914 x 0.000264) + (0.78 x 0.000914 x 0.001736) = 2.16529392e-06 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 13 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 1e-06 0.1 - a2 0.09 1e-06 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 1e-05 0.001 - a2 9e-05 0.001 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 1e-05 0.001 - a2 9e-05 0.001 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 5.43e-05 0.002 0.543 - b2 4.57e-05 0.002 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 0.001086 0.002 - b2 0.000914 0.002 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 1.32e-05 0.002 0.132 - c2 8.68e-05 0.002 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 0.000264 0.002 - c2 0.001736 0.002 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 1.83470608e-06 1 0.45867652 - d2 2.16529392e-06 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x0.002 + [(0.97)]x0.002 = 0.002 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x0.002 + [(0.4)]x0.002 = 0.002 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x0.002 + [(0.76)]x0.002 = 0.002 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x0.002 + [(0.88)]x0.002 = 0.002 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x0.000264) + (0.7x0.001736)]x1 + [(0.8x0.000264) + (0.3x0.001736)]x1 = 0.002 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x0.000264) + (0.22x0.001736)]x1 + [(0.55x0.000264) + (0.78x0.001736)]x1 = 0.002 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x0.001086) + (0.45x0.000914)]x1 + [(0.8x0.001086) + (0.55x0.000914)]x1 = 0.002 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x0.001086) + (0.22x0.000914)]x1 + [(0.3x0.001086) + (0.78x0.000914)]x1 = 0.002 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 0.001 = 1e-05 - πB(a2) = π(a2).λC(a2) = 0.09 x 0.001 = 9e-05 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 0.001 = 1e-05 - πC(a2) = π(a2).λB(a2) = 0.09 x 0.001 = 9e-05 -π message B --> D - πD(b1) = π(b1) = 5.43e-05 = 5.43e-05 - πD(b2) = π(b2) = 4.57e-05 = 4.57e-05 -π message C --> D - πD(c1) = π(c1) = 1.32e-05 = 1.32e-05 - πD(c2) = π(c2) = 8.68e-05 = 8.68e-05 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 0.002 x 0.002 = 4e-06 - λ(a2) = λB(a2).λC(a2) = 0.002 x 0.002 = 4e-06 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 1e-05) + (0.6 x 9e-05) = 5.43e-05 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 1e-05) + (0.4 x 9e-05) = 4.57e-05 - λ(b1) = λD(b1) = 0.002 = 0.002 - λ(b2) = λD(b2) = 0.002 = 0.002 - belief change = 0 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 1e-05) + (0.12 x 9e-05) = 1.32e-05 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 1e-05) + (0.88 x 9e-05) = 8.68e-05 - λ(c1) = λD(c1) = 0.002 = 0.002 - λ(c2) = λD(c2) = 0.002 = 0.002 - belief change = 0 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 5.43e-05 x 1.32e-05) + (0.7 x 5.43e-05 x 8.68e-05) + (0.45 x 4.57e-05 x 1.32e-05) + (0.22 x 4.57e-05 x 8.68e-05) = 4.5867652e-09 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 5.43e-05 x 1.32e-05) + (0.3 x 5.43e-05 x 8.68e-05) + (0.55 x 4.57e-05 x 1.32e-05) + (0.78 x 4.57e-05 x 8.68e-05) = 5.4132348e-09 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 14 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 4e-06 0.1 - a2 0.09 4e-06 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 1e-05 0.002 - a2 9e-05 0.002 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 1e-05 0.002 - a2 9e-05 0.002 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 5.43e-05 0.002 0.543 - b2 4.57e-05 0.002 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 5.43e-05 0.002 - b2 4.57e-05 0.002 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 1.32e-05 0.002 0.132 - c2 8.68e-05 0.002 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 1.32e-05 0.002 - c2 8.68e-05 0.002 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 4.5867652e-09 1 0.45867652 - d2 5.4132348e-09 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x0.002 + [(0.97)]x0.002 = 0.002 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x0.002 + [(0.4)]x0.002 = 0.002 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x0.002 + [(0.76)]x0.002 = 0.002 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x0.002 + [(0.88)]x0.002 = 0.002 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x1.32e-05) + (0.7x8.68e-05)]x1 + [(0.8x1.32e-05) + (0.3x8.68e-05)]x1 = 0.0001 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x1.32e-05) + (0.22x8.68e-05)]x1 + [(0.55x1.32e-05) + (0.78x8.68e-05)]x1 = 0.0001 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x5.43e-05) + (0.45x4.57e-05)]x1 + [(0.8x5.43e-05) + (0.55x4.57e-05)]x1 = 0.0001 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x5.43e-05) + (0.22x4.57e-05)]x1 + [(0.3x5.43e-05) + (0.78x4.57e-05)]x1 = 0.0001 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 0.002 = 2e-05 - πB(a2) = π(a2).λC(a2) = 0.09 x 0.002 = 0.00018 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 0.002 = 2e-05 - πC(a2) = π(a2).λB(a2) = 0.09 x 0.002 = 0.00018 -π message B --> D - πD(b1) = π(b1) = 5.43e-05 = 5.43e-05 - πD(b2) = π(b2) = 4.57e-05 = 4.57e-05 -π message C --> D - πD(c1) = π(c1) = 1.32e-05 = 1.32e-05 - πD(c2) = π(c2) = 8.68e-05 = 8.68e-05 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 0.002 x 0.002 = 4e-06 - λ(a2) = λB(a2).λC(a2) = 0.002 x 0.002 = 4e-06 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 2e-05) + (0.6 x 0.00018) = 0.0001086 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 2e-05) + (0.4 x 0.00018) = 9.14e-05 - λ(b1) = λD(b1) = 0.0001 = 0.0001 - λ(b2) = λD(b2) = 0.0001 = 0.0001 - belief change = 1.110223025e-16 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 2e-05) + (0.12 x 0.00018) = 2.64e-05 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 2e-05) + (0.88 x 0.00018) = 0.0001736 - λ(c1) = λD(c1) = 0.0001 = 0.0001 - λ(c2) = λD(c2) = 0.0001 = 0.0001 - belief change = 2.775557562e-17 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 5.43e-05 x 1.32e-05) + (0.7 x 5.43e-05 x 8.68e-05) + (0.45 x 4.57e-05 x 1.32e-05) + (0.22 x 4.57e-05 x 8.68e-05) = 4.5867652e-09 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 5.43e-05 x 1.32e-05) + (0.3 x 5.43e-05 x 8.68e-05) + (0.55 x 4.57e-05 x 1.32e-05) + (0.78 x 4.57e-05 x 8.68e-05) = 5.4132348e-09 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 15 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 4e-06 0.1 - a2 0.09 4e-06 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 2e-05 0.002 - a2 0.00018 0.002 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 2e-05 0.002 - a2 0.00018 0.002 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 0.0001086 0.0001 0.543 - b2 9.14e-05 0.0001 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 5.43e-05 0.0001 - b2 4.57e-05 0.0001 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 2.64e-05 0.0001 0.132 - c2 0.0001736 0.0001 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 1.32e-05 0.0001 - c2 8.68e-05 0.0001 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 4.5867652e-09 1 0.45867652 - d2 5.4132348e-09 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x0.0001 + [(0.97)]x0.0001 = 0.0001 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x0.0001 + [(0.4)]x0.0001 = 0.0001 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x0.0001 + [(0.76)]x0.0001 = 0.0001 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x0.0001 + [(0.88)]x0.0001 = 0.0001 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x1.32e-05) + (0.7x8.68e-05)]x1 + [(0.8x1.32e-05) + (0.3x8.68e-05)]x1 = 0.0001 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x1.32e-05) + (0.22x8.68e-05)]x1 + [(0.55x1.32e-05) + (0.78x8.68e-05)]x1 = 0.0001 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x5.43e-05) + (0.45x4.57e-05)]x1 + [(0.8x5.43e-05) + (0.55x4.57e-05)]x1 = 0.0001 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x5.43e-05) + (0.22x4.57e-05)]x1 + [(0.3x5.43e-05) + (0.78x4.57e-05)]x1 = 0.0001 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 0.002 = 2e-05 - πB(a2) = π(a2).λC(a2) = 0.09 x 0.002 = 0.00018 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 0.002 = 2e-05 - πC(a2) = π(a2).λB(a2) = 0.09 x 0.002 = 0.00018 -π message B --> D - πD(b1) = π(b1) = 0.0001086 = 0.0001086 - πD(b2) = π(b2) = 9.14e-05 = 9.14e-05 -π message C --> D - πD(c1) = π(c1) = 2.64e-05 = 2.64e-05 - πD(c2) = π(c2) = 0.0001736 = 0.0001736 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 0.0001 x 0.0001 = 1e-08 - λ(a2) = λB(a2).λC(a2) = 0.0001 x 0.0001 = 1e-08 - belief change = 1.387778781e-17 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 2e-05) + (0.6 x 0.00018) = 0.0001086 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 2e-05) + (0.4 x 0.00018) = 9.14e-05 - λ(b1) = λD(b1) = 0.0001 = 0.0001 - λ(b2) = λD(b2) = 0.0001 = 0.0001 - belief change = 0 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 2e-05) + (0.12 x 0.00018) = 2.64e-05 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 2e-05) + (0.88 x 0.00018) = 0.0001736 - λ(c1) = λD(c1) = 0.0001 = 0.0001 - λ(c2) = λD(c2) = 0.0001 = 0.0001 - belief change = 0 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 0.0001086 x 2.64e-05) + (0.7 x 0.0001086 x 0.0001736) + (0.45 x 9.14e-05 x 2.64e-05) + (0.22 x 9.14e-05 x 0.0001736) = 1.83470608e-08 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 0.0001086 x 2.64e-05) + (0.3 x 0.0001086 x 0.0001736) + (0.55 x 9.14e-05 x 2.64e-05) + (0.78 x 9.14e-05 x 0.0001736) = 2.16529392e-08 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 16 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 1e-08 0.1 - a2 0.09 1e-08 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 2e-05 0.0001 - a2 0.00018 0.0001 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 2e-05 0.0001 - a2 0.00018 0.0001 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 0.0001086 0.0001 0.543 - b2 9.14e-05 0.0001 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 0.0001086 0.0001 - b2 9.14e-05 0.0001 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 2.64e-05 0.0001 0.132 - c2 0.0001736 0.0001 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 2.64e-05 0.0001 - c2 0.0001736 0.0001 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 1.83470608e-08 1 0.45867652 - d2 2.16529392e-08 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x0.0001 + [(0.97)]x0.0001 = 0.0001 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x0.0001 + [(0.4)]x0.0001 = 0.0001 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x0.0001 + [(0.76)]x0.0001 = 0.0001 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x0.0001 + [(0.88)]x0.0001 = 0.0001 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x2.64e-05) + (0.7x0.0001736)]x1 + [(0.8x2.64e-05) + (0.3x0.0001736)]x1 = 0.0002 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x2.64e-05) + (0.22x0.0001736)]x1 + [(0.55x2.64e-05) + (0.78x0.0001736)]x1 = 0.0002 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x0.0001086) + (0.45x9.14e-05)]x1 + [(0.8x0.0001086) + (0.55x9.14e-05)]x1 = 0.0002 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x0.0001086) + (0.22x9.14e-05)]x1 + [(0.3x0.0001086) + (0.78x9.14e-05)]x1 = 0.0002 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 0.0001 = 1e-06 - πB(a2) = π(a2).λC(a2) = 0.09 x 0.0001 = 9e-06 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 0.0001 = 1e-06 - πC(a2) = π(a2).λB(a2) = 0.09 x 0.0001 = 9e-06 -π message B --> D - πD(b1) = π(b1) = 0.0001086 = 0.0001086 - πD(b2) = π(b2) = 9.14e-05 = 9.14e-05 -π message C --> D - πD(c1) = π(c1) = 2.64e-05 = 2.64e-05 - πD(c2) = π(c2) = 0.0001736 = 0.0001736 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 0.0001 x 0.0001 = 1e-08 - λ(a2) = λB(a2).λC(a2) = 0.0001 x 0.0001 = 1e-08 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 1e-06) + (0.6 x 9e-06) = 5.43e-06 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 1e-06) + (0.4 x 9e-06) = 4.57e-06 - λ(b1) = λD(b1) = 0.0002 = 0.0002 - λ(b2) = λD(b2) = 0.0002 = 0.0002 - belief change = 5.551115123e-17 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 1e-06) + (0.12 x 9e-06) = 1.32e-06 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 1e-06) + (0.88 x 9e-06) = 8.68e-06 - λ(c1) = λD(c1) = 0.0002 = 0.0002 - λ(c2) = λD(c2) = 0.0002 = 0.0002 - belief change = 1.387778781e-16 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 0.0001086 x 2.64e-05) + (0.7 x 0.0001086 x 0.0001736) + (0.45 x 9.14e-05 x 2.64e-05) + (0.22 x 9.14e-05 x 0.0001736) = 1.83470608e-08 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 0.0001086 x 2.64e-05) + (0.3 x 0.0001086 x 0.0001736) + (0.55 x 9.14e-05 x 2.64e-05) + (0.78 x 9.14e-05 x 0.0001736) = 2.16529392e-08 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 17 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 1e-08 0.1 - a2 0.09 1e-08 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 1e-06 0.0001 - a2 9e-06 0.0001 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 1e-06 0.0001 - a2 9e-06 0.0001 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 5.43e-06 0.0002 0.543 - b2 4.57e-06 0.0002 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 0.0001086 0.0002 - b2 9.14e-05 0.0002 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 1.32e-06 0.0002 0.132 - c2 8.68e-06 0.0002 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 2.64e-05 0.0002 - c2 0.0001736 0.0002 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 1.83470608e-08 1 0.45867652 - d2 2.16529392e-08 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x0.0002 + [(0.97)]x0.0002 = 0.0002 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x0.0002 + [(0.4)]x0.0002 = 0.0002 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x0.0002 + [(0.76)]x0.0002 = 0.0002 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x0.0002 + [(0.88)]x0.0002 = 0.0002 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x2.64e-05) + (0.7x0.0001736)]x1 + [(0.8x2.64e-05) + (0.3x0.0001736)]x1 = 0.0002 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x2.64e-05) + (0.22x0.0001736)]x1 + [(0.55x2.64e-05) + (0.78x0.0001736)]x1 = 0.0002 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x0.0001086) + (0.45x9.14e-05)]x1 + [(0.8x0.0001086) + (0.55x9.14e-05)]x1 = 0.0002 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x0.0001086) + (0.22x9.14e-05)]x1 + [(0.3x0.0001086) + (0.78x9.14e-05)]x1 = 0.0002 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 0.0001 = 1e-06 - πB(a2) = π(a2).λC(a2) = 0.09 x 0.0001 = 9e-06 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 0.0001 = 1e-06 - πC(a2) = π(a2).λB(a2) = 0.09 x 0.0001 = 9e-06 -π message B --> D - πD(b1) = π(b1) = 5.43e-06 = 5.43e-06 - πD(b2) = π(b2) = 4.57e-06 = 4.57e-06 -π message C --> D - πD(c1) = π(c1) = 1.32e-06 = 1.32e-06 - πD(c2) = π(c2) = 8.68e-06 = 8.68e-06 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 0.0002 x 0.0002 = 4e-08 - λ(a2) = λB(a2).λC(a2) = 0.0002 x 0.0002 = 4e-08 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 1e-06) + (0.6 x 9e-06) = 5.43e-06 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 1e-06) + (0.4 x 9e-06) = 4.57e-06 - λ(b1) = λD(b1) = 0.0002 = 0.0002 - λ(b2) = λD(b2) = 0.0002 = 0.0002 - belief change = 0 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 1e-06) + (0.12 x 9e-06) = 1.32e-06 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 1e-06) + (0.88 x 9e-06) = 8.68e-06 - λ(c1) = λD(c1) = 0.0002 = 0.0002 - λ(c2) = λD(c2) = 0.0002 = 0.0002 - belief change = 0 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 5.43e-06 x 1.32e-06) + (0.7 x 5.43e-06 x 8.68e-06) + (0.45 x 4.57e-06 x 1.32e-06) + (0.22 x 4.57e-06 x 8.68e-06) = 4.5867652e-11 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 5.43e-06 x 1.32e-06) + (0.3 x 5.43e-06 x 8.68e-06) + (0.55 x 4.57e-06 x 1.32e-06) + (0.78 x 4.57e-06 x 8.68e-06) = 5.4132348e-11 - λ(d1) = 1 - λ(d2) = 1 - belief change = 1.665334537e-16 - - -******************************************************************************** -Iteration 18 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 4e-08 0.1 - a2 0.09 4e-08 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 1e-06 0.0002 - a2 9e-06 0.0002 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 1e-06 0.0002 - a2 9e-06 0.0002 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 5.43e-06 0.0002 0.543 - b2 4.57e-06 0.0002 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 5.43e-06 0.0002 - b2 4.57e-06 0.0002 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 1.32e-06 0.0002 0.132 - c2 8.68e-06 0.0002 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 1.32e-06 0.0002 - c2 8.68e-06 0.0002 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 4.5867652e-11 1 0.45867652 - d2 5.4132348e-11 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x0.0002 + [(0.97)]x0.0002 = 0.0002 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x0.0002 + [(0.4)]x0.0002 = 0.0002 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x0.0002 + [(0.76)]x0.0002 = 0.0002 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x0.0002 + [(0.88)]x0.0002 = 0.0002 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x1.32e-06) + (0.7x8.68e-06)]x1 + [(0.8x1.32e-06) + (0.3x8.68e-06)]x1 = 1e-05 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x1.32e-06) + (0.22x8.68e-06)]x1 + [(0.55x1.32e-06) + (0.78x8.68e-06)]x1 = 1e-05 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x5.43e-06) + (0.45x4.57e-06)]x1 + [(0.8x5.43e-06) + (0.55x4.57e-06)]x1 = 1e-05 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x5.43e-06) + (0.22x4.57e-06)]x1 + [(0.3x5.43e-06) + (0.78x4.57e-06)]x1 = 1e-05 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 0.0002 = 2e-06 - πB(a2) = π(a2).λC(a2) = 0.09 x 0.0002 = 1.8e-05 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 0.0002 = 2e-06 - πC(a2) = π(a2).λB(a2) = 0.09 x 0.0002 = 1.8e-05 -π message B --> D - πD(b1) = π(b1) = 5.43e-06 = 5.43e-06 - πD(b2) = π(b2) = 4.57e-06 = 4.57e-06 -π message C --> D - πD(c1) = π(c1) = 1.32e-06 = 1.32e-06 - πD(c2) = π(c2) = 8.68e-06 = 8.68e-06 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 0.0002 x 0.0002 = 4e-08 - λ(a2) = λB(a2).λC(a2) = 0.0002 x 0.0002 = 4e-08 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 2e-06) + (0.6 x 1.8e-05) = 1.086e-05 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 2e-06) + (0.4 x 1.8e-05) = 9.14e-06 - λ(b1) = λD(b1) = 1e-05 = 1e-05 - λ(b2) = λD(b2) = 1e-05 = 1e-05 - belief change = 5.551115123e-17 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 2e-06) + (0.12 x 1.8e-05) = 2.64e-06 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 2e-06) + (0.88 x 1.8e-05) = 1.736e-05 - λ(c1) = λD(c1) = 1e-05 = 1e-05 - λ(c2) = λD(c2) = 1e-05 = 1e-05 - belief change = 1.387778781e-16 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 5.43e-06 x 1.32e-06) + (0.7 x 5.43e-06 x 8.68e-06) + (0.45 x 4.57e-06 x 1.32e-06) + (0.22 x 4.57e-06 x 8.68e-06) = 4.5867652e-11 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 5.43e-06 x 1.32e-06) + (0.3 x 5.43e-06 x 8.68e-06) + (0.55 x 4.57e-06 x 1.32e-06) + (0.78 x 4.57e-06 x 8.68e-06) = 5.4132348e-11 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 19 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 4e-08 0.1 - a2 0.09 4e-08 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 2e-06 0.0002 - a2 1.8e-05 0.0002 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 2e-06 0.0002 - a2 1.8e-05 0.0002 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 1.086e-05 1e-05 0.543 - b2 9.14e-06 1e-05 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 5.43e-06 1e-05 - b2 4.57e-06 1e-05 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 2.64e-06 1e-05 0.132 - c2 1.736e-05 1e-05 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 1.32e-06 1e-05 - c2 8.68e-06 1e-05 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 4.5867652e-11 1 0.45867652 - d2 5.4132348e-11 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x1e-05 + [(0.97)]x1e-05 = 1e-05 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x1e-05 + [(0.4)]x1e-05 = 1e-05 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x1e-05 + [(0.76)]x1e-05 = 1e-05 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x1e-05 + [(0.88)]x1e-05 = 1e-05 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x1.32e-06) + (0.7x8.68e-06)]x1 + [(0.8x1.32e-06) + (0.3x8.68e-06)]x1 = 1e-05 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x1.32e-06) + (0.22x8.68e-06)]x1 + [(0.55x1.32e-06) + (0.78x8.68e-06)]x1 = 1e-05 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x5.43e-06) + (0.45x4.57e-06)]x1 + [(0.8x5.43e-06) + (0.55x4.57e-06)]x1 = 1e-05 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x5.43e-06) + (0.22x4.57e-06)]x1 + [(0.3x5.43e-06) + (0.78x4.57e-06)]x1 = 1e-05 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 0.0002 = 2e-06 - πB(a2) = π(a2).λC(a2) = 0.09 x 0.0002 = 1.8e-05 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 0.0002 = 2e-06 - πC(a2) = π(a2).λB(a2) = 0.09 x 0.0002 = 1.8e-05 -π message B --> D - πD(b1) = π(b1) = 1.086e-05 = 1.086e-05 - πD(b2) = π(b2) = 9.14e-06 = 9.14e-06 -π message C --> D - πD(c1) = π(c1) = 2.64e-06 = 2.64e-06 - πD(c2) = π(c2) = 1.736e-05 = 1.736e-05 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 1e-05 x 1e-05 = 1e-10 - λ(a2) = λB(a2).λC(a2) = 1e-05 x 1e-05 = 1e-10 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 2e-06) + (0.6 x 1.8e-05) = 1.086e-05 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 2e-06) + (0.4 x 1.8e-05) = 9.14e-06 - λ(b1) = λD(b1) = 1e-05 = 1e-05 - λ(b2) = λD(b2) = 1e-05 = 1e-05 - belief change = 0 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 2e-06) + (0.12 x 1.8e-05) = 2.64e-06 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 2e-06) + (0.88 x 1.8e-05) = 1.736e-05 - λ(c1) = λD(c1) = 1e-05 = 1e-05 - λ(c2) = λD(c2) = 1e-05 = 1e-05 - belief change = 0 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 1.086e-05 x 2.64e-06) + (0.7 x 1.086e-05 x 1.736e-05) + (0.45 x 9.14e-06 x 2.64e-06) + (0.22 x 9.14e-06 x 1.736e-05) = 1.83470608e-10 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 1.086e-05 x 2.64e-06) + (0.3 x 1.086e-05 x 1.736e-05) + (0.55 x 9.14e-06 x 2.64e-06) + (0.78 x 9.14e-06 x 1.736e-05) = 2.16529392e-10 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 20 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 1e-10 0.1 - a2 0.09 1e-10 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 2e-06 1e-05 - a2 1.8e-05 1e-05 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 2e-06 1e-05 - a2 1.8e-05 1e-05 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 1.086e-05 1e-05 0.543 - b2 9.14e-06 1e-05 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 1.086e-05 1e-05 - b2 9.14e-06 1e-05 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 2.64e-06 1e-05 0.132 - c2 1.736e-05 1e-05 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 2.64e-06 1e-05 - c2 1.736e-05 1e-05 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 1.83470608e-10 1 0.45867652 - d2 2.16529392e-10 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x1e-05 + [(0.97)]x1e-05 = 1e-05 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x1e-05 + [(0.4)]x1e-05 = 1e-05 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x1e-05 + [(0.76)]x1e-05 = 1e-05 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x1e-05 + [(0.88)]x1e-05 = 1e-05 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x2.64e-06) + (0.7x1.736e-05)]x1 + [(0.8x2.64e-06) + (0.3x1.736e-05)]x1 = 2e-05 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x2.64e-06) + (0.22x1.736e-05)]x1 + [(0.55x2.64e-06) + (0.78x1.736e-05)]x1 = 2e-05 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x1.086e-05) + (0.45x9.14e-06)]x1 + [(0.8x1.086e-05) + (0.55x9.14e-06)]x1 = 2e-05 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x1.086e-05) + (0.22x9.14e-06)]x1 + [(0.3x1.086e-05) + (0.78x9.14e-06)]x1 = 2e-05 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 1e-05 = 1e-07 - πB(a2) = π(a2).λC(a2) = 0.09 x 1e-05 = 9e-07 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 1e-05 = 1e-07 - πC(a2) = π(a2).λB(a2) = 0.09 x 1e-05 = 9e-07 -π message B --> D - πD(b1) = π(b1) = 1.086e-05 = 1.086e-05 - πD(b2) = π(b2) = 9.14e-06 = 9.14e-06 -π message C --> D - πD(c1) = π(c1) = 2.64e-06 = 2.64e-06 - πD(c2) = π(c2) = 1.736e-05 = 1.736e-05 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 1e-05 x 1e-05 = 1e-10 - λ(a2) = λB(a2).λC(a2) = 1e-05 x 1e-05 = 1e-10 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 1e-07) + (0.6 x 9e-07) = 5.43e-07 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 1e-07) + (0.4 x 9e-07) = 4.57e-07 - λ(b1) = λD(b1) = 2e-05 = 2e-05 - λ(b2) = λD(b2) = 2e-05 = 2e-05 - belief change = 0 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 1e-07) + (0.12 x 9e-07) = 1.32e-07 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 1e-07) + (0.88 x 9e-07) = 8.68e-07 - λ(c1) = λD(c1) = 2e-05 = 2e-05 - λ(c2) = λD(c2) = 2e-05 = 2e-05 - belief change = 1.110223025e-16 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 1.086e-05 x 2.64e-06) + (0.7 x 1.086e-05 x 1.736e-05) + (0.45 x 9.14e-06 x 2.64e-06) + (0.22 x 9.14e-06 x 1.736e-05) = 1.83470608e-10 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 1.086e-05 x 2.64e-06) + (0.3 x 1.086e-05 x 1.736e-05) + (0.55 x 9.14e-06 x 2.64e-06) + (0.78 x 9.14e-06 x 1.736e-05) = 2.16529392e-10 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 21 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 1e-10 0.1 - a2 0.09 1e-10 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 1e-07 1e-05 - a2 9e-07 1e-05 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 1e-07 1e-05 - a2 9e-07 1e-05 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 5.43e-07 2e-05 0.543 - b2 4.57e-07 2e-05 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 1.086e-05 2e-05 - b2 9.14e-06 2e-05 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 1.32e-07 2e-05 0.132 - c2 8.68e-07 2e-05 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 2.64e-06 2e-05 - c2 1.736e-05 2e-05 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 1.83470608e-10 1 0.45867652 - d2 2.16529392e-10 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x2e-05 + [(0.97)]x2e-05 = 2e-05 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x2e-05 + [(0.4)]x2e-05 = 2e-05 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x2e-05 + [(0.76)]x2e-05 = 2e-05 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x2e-05 + [(0.88)]x2e-05 = 2e-05 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x2.64e-06) + (0.7x1.736e-05)]x1 + [(0.8x2.64e-06) + (0.3x1.736e-05)]x1 = 2e-05 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x2.64e-06) + (0.22x1.736e-05)]x1 + [(0.55x2.64e-06) + (0.78x1.736e-05)]x1 = 2e-05 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x1.086e-05) + (0.45x9.14e-06)]x1 + [(0.8x1.086e-05) + (0.55x9.14e-06)]x1 = 2e-05 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x1.086e-05) + (0.22x9.14e-06)]x1 + [(0.3x1.086e-05) + (0.78x9.14e-06)]x1 = 2e-05 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 1e-05 = 1e-07 - πB(a2) = π(a2).λC(a2) = 0.09 x 1e-05 = 9e-07 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 1e-05 = 1e-07 - πC(a2) = π(a2).λB(a2) = 0.09 x 1e-05 = 9e-07 -π message B --> D - πD(b1) = π(b1) = 5.43e-07 = 5.43e-07 - πD(b2) = π(b2) = 4.57e-07 = 4.57e-07 -π message C --> D - πD(c1) = π(c1) = 1.32e-07 = 1.32e-07 - πD(c2) = π(c2) = 8.68e-07 = 8.68e-07 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 2e-05 x 2e-05 = 4e-10 - λ(a2) = λB(a2).λC(a2) = 2e-05 x 2e-05 = 4e-10 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 1e-07) + (0.6 x 9e-07) = 5.43e-07 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 1e-07) + (0.4 x 9e-07) = 4.57e-07 - λ(b1) = λD(b1) = 2e-05 = 2e-05 - λ(b2) = λD(b2) = 2e-05 = 2e-05 - belief change = 0 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 1e-07) + (0.12 x 9e-07) = 1.32e-07 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 1e-07) + (0.88 x 9e-07) = 8.68e-07 - λ(c1) = λD(c1) = 2e-05 = 2e-05 - λ(c2) = λD(c2) = 2e-05 = 2e-05 - belief change = 0 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 5.43e-07 x 1.32e-07) + (0.7 x 5.43e-07 x 8.68e-07) + (0.45 x 4.57e-07 x 1.32e-07) + (0.22 x 4.57e-07 x 8.68e-07) = 4.5867652e-13 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 5.43e-07 x 1.32e-07) + (0.3 x 5.43e-07 x 8.68e-07) + (0.55 x 4.57e-07 x 1.32e-07) + (0.78 x 4.57e-07 x 8.68e-07) = 5.4132348e-13 - λ(d1) = 1 - λ(d2) = 1 - belief change = 1.110223025e-16 - - -******************************************************************************** -Iteration 22 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 4e-10 0.1 - a2 0.09 4e-10 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 1e-07 2e-05 - a2 9e-07 2e-05 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 1e-07 2e-05 - a2 9e-07 2e-05 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 5.43e-07 2e-05 0.543 - b2 4.57e-07 2e-05 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 5.43e-07 2e-05 - b2 4.57e-07 2e-05 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 1.32e-07 2e-05 0.132 - c2 8.68e-07 2e-05 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 1.32e-07 2e-05 - c2 8.68e-07 2e-05 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 4.5867652e-13 1 0.45867652 - d2 5.4132348e-13 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x2e-05 + [(0.97)]x2e-05 = 2e-05 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x2e-05 + [(0.4)]x2e-05 = 2e-05 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x2e-05 + [(0.76)]x2e-05 = 2e-05 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x2e-05 + [(0.88)]x2e-05 = 2e-05 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x1.32e-07) + (0.7x8.68e-07)]x1 + [(0.8x1.32e-07) + (0.3x8.68e-07)]x1 = 1e-06 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x1.32e-07) + (0.22x8.68e-07)]x1 + [(0.55x1.32e-07) + (0.78x8.68e-07)]x1 = 1e-06 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x5.43e-07) + (0.45x4.57e-07)]x1 + [(0.8x5.43e-07) + (0.55x4.57e-07)]x1 = 1e-06 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x5.43e-07) + (0.22x4.57e-07)]x1 + [(0.3x5.43e-07) + (0.78x4.57e-07)]x1 = 1e-06 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 2e-05 = 2e-07 - πB(a2) = π(a2).λC(a2) = 0.09 x 2e-05 = 1.8e-06 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 2e-05 = 2e-07 - πC(a2) = π(a2).λB(a2) = 0.09 x 2e-05 = 1.8e-06 -π message B --> D - πD(b1) = π(b1) = 5.43e-07 = 5.43e-07 - πD(b2) = π(b2) = 4.57e-07 = 4.57e-07 -π message C --> D - πD(c1) = π(c1) = 1.32e-07 = 1.32e-07 - πD(c2) = π(c2) = 8.68e-07 = 8.68e-07 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 2e-05 x 2e-05 = 4e-10 - λ(a2) = λB(a2).λC(a2) = 2e-05 x 2e-05 = 4e-10 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 2e-07) + (0.6 x 1.8e-06) = 1.086e-06 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 2e-07) + (0.4 x 1.8e-06) = 9.14e-07 - λ(b1) = λD(b1) = 1e-06 = 1e-06 - λ(b2) = λD(b2) = 1e-06 = 1e-06 - belief change = 5.551115123e-17 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 2e-07) + (0.12 x 1.8e-06) = 2.64e-07 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 2e-07) + (0.88 x 1.8e-06) = 1.736e-06 - λ(c1) = λD(c1) = 1e-06 = 1e-06 - λ(c2) = λD(c2) = 1e-06 = 1e-06 - belief change = 2.498001805e-16 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 5.43e-07 x 1.32e-07) + (0.7 x 5.43e-07 x 8.68e-07) + (0.45 x 4.57e-07 x 1.32e-07) + (0.22 x 4.57e-07 x 8.68e-07) = 4.5867652e-13 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 5.43e-07 x 1.32e-07) + (0.3 x 5.43e-07 x 8.68e-07) + (0.55 x 4.57e-07 x 1.32e-07) + (0.78 x 4.57e-07 x 8.68e-07) = 5.4132348e-13 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 23 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 4e-10 0.1 - a2 0.09 4e-10 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 2e-07 2e-05 - a2 1.8e-06 2e-05 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 2e-07 2e-05 - a2 1.8e-06 2e-05 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 1.086e-06 1e-06 0.543 - b2 9.14e-07 1e-06 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 5.43e-07 1e-06 - b2 4.57e-07 1e-06 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 2.64e-07 1e-06 0.132 - c2 1.736e-06 1e-06 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 1.32e-07 1e-06 - c2 8.68e-07 1e-06 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 4.5867652e-13 1 0.45867652 - d2 5.4132348e-13 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x1e-06 + [(0.97)]x1e-06 = 1e-06 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x1e-06 + [(0.4)]x1e-06 = 1e-06 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x1e-06 + [(0.76)]x1e-06 = 1e-06 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x1e-06 + [(0.88)]x1e-06 = 1e-06 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x1.32e-07) + (0.7x8.68e-07)]x1 + [(0.8x1.32e-07) + (0.3x8.68e-07)]x1 = 1e-06 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x1.32e-07) + (0.22x8.68e-07)]x1 + [(0.55x1.32e-07) + (0.78x8.68e-07)]x1 = 1e-06 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x5.43e-07) + (0.45x4.57e-07)]x1 + [(0.8x5.43e-07) + (0.55x4.57e-07)]x1 = 1e-06 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x5.43e-07) + (0.22x4.57e-07)]x1 + [(0.3x5.43e-07) + (0.78x4.57e-07)]x1 = 1e-06 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 2e-05 = 2e-07 - πB(a2) = π(a2).λC(a2) = 0.09 x 2e-05 = 1.8e-06 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 2e-05 = 2e-07 - πC(a2) = π(a2).λB(a2) = 0.09 x 2e-05 = 1.8e-06 -π message B --> D - πD(b1) = π(b1) = 1.086e-06 = 1.086e-06 - πD(b2) = π(b2) = 9.14e-07 = 9.14e-07 -π message C --> D - πD(c1) = π(c1) = 2.64e-07 = 2.64e-07 - πD(c2) = π(c2) = 1.736e-06 = 1.736e-06 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 1e-06 x 1e-06 = 1e-12 - λ(a2) = λB(a2).λC(a2) = 1e-06 x 1e-06 = 1e-12 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 2e-07) + (0.6 x 1.8e-06) = 1.086e-06 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 2e-07) + (0.4 x 1.8e-06) = 9.14e-07 - λ(b1) = λD(b1) = 1e-06 = 1e-06 - λ(b2) = λD(b2) = 1e-06 = 1e-06 - belief change = 0 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 2e-07) + (0.12 x 1.8e-06) = 2.64e-07 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 2e-07) + (0.88 x 1.8e-06) = 1.736e-06 - λ(c1) = λD(c1) = 1e-06 = 1e-06 - λ(c2) = λD(c2) = 1e-06 = 1e-06 - belief change = 0 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 1.086e-06 x 2.64e-07) + (0.7 x 1.086e-06 x 1.736e-06) + (0.45 x 9.14e-07 x 2.64e-07) + (0.22 x 9.14e-07 x 1.736e-06) = 1.83470608e-12 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 1.086e-06 x 2.64e-07) + (0.3 x 1.086e-06 x 1.736e-06) + (0.55 x 9.14e-07 x 2.64e-07) + (0.78 x 9.14e-07 x 1.736e-06) = 2.16529392e-12 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 24 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 1e-12 0.1 - a2 0.09 1e-12 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 2e-07 1e-06 - a2 1.8e-06 1e-06 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 2e-07 1e-06 - a2 1.8e-06 1e-06 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 1.086e-06 1e-06 0.543 - b2 9.14e-07 1e-06 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 1.086e-06 1e-06 - b2 9.14e-07 1e-06 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 2.64e-07 1e-06 0.132 - c2 1.736e-06 1e-06 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 2.64e-07 1e-06 - c2 1.736e-06 1e-06 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 1.83470608e-12 1 0.45867652 - d2 2.16529392e-12 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x1e-06 + [(0.97)]x1e-06 = 1e-06 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x1e-06 + [(0.4)]x1e-06 = 1e-06 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x1e-06 + [(0.76)]x1e-06 = 1e-06 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x1e-06 + [(0.88)]x1e-06 = 1e-06 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x2.64e-07) + (0.7x1.736e-06)]x1 + [(0.8x2.64e-07) + (0.3x1.736e-06)]x1 = 2e-06 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x2.64e-07) + (0.22x1.736e-06)]x1 + [(0.55x2.64e-07) + (0.78x1.736e-06)]x1 = 2e-06 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x1.086e-06) + (0.45x9.14e-07)]x1 + [(0.8x1.086e-06) + (0.55x9.14e-07)]x1 = 2e-06 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x1.086e-06) + (0.22x9.14e-07)]x1 + [(0.3x1.086e-06) + (0.78x9.14e-07)]x1 = 2e-06 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 1e-06 = 1e-08 - πB(a2) = π(a2).λC(a2) = 0.09 x 1e-06 = 9e-08 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 1e-06 = 1e-08 - πC(a2) = π(a2).λB(a2) = 0.09 x 1e-06 = 9e-08 -π message B --> D - πD(b1) = π(b1) = 1.086e-06 = 1.086e-06 - πD(b2) = π(b2) = 9.14e-07 = 9.14e-07 -π message C --> D - πD(c1) = π(c1) = 2.64e-07 = 2.64e-07 - πD(c2) = π(c2) = 1.736e-06 = 1.736e-06 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 1e-06 x 1e-06 = 1e-12 - λ(a2) = λB(a2).λC(a2) = 1e-06 x 1e-06 = 1e-12 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 1e-08) + (0.6 x 9e-08) = 5.43e-08 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 1e-08) + (0.4 x 9e-08) = 4.57e-08 - λ(b1) = λD(b1) = 2e-06 = 2e-06 - λ(b2) = λD(b2) = 2e-06 = 2e-06 - belief change = 5.551115123e-17 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 1e-08) + (0.12 x 9e-08) = 1.32e-08 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 1e-08) + (0.88 x 9e-08) = 8.68e-08 - λ(c1) = λD(c1) = 2e-06 = 2e-06 - λ(c2) = λD(c2) = 2e-06 = 2e-06 - belief change = 1.387778781e-16 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 1.086e-06 x 2.64e-07) + (0.7 x 1.086e-06 x 1.736e-06) + (0.45 x 9.14e-07 x 2.64e-07) + (0.22 x 9.14e-07 x 1.736e-06) = 1.83470608e-12 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 1.086e-06 x 2.64e-07) + (0.3 x 1.086e-06 x 1.736e-06) + (0.55 x 9.14e-07 x 2.64e-07) + (0.78 x 9.14e-07 x 1.736e-06) = 2.16529392e-12 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 25 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 1e-12 0.1 - a2 0.09 1e-12 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 1e-08 1e-06 - a2 9e-08 1e-06 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 1e-08 1e-06 - a2 9e-08 1e-06 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 5.43e-08 2e-06 0.543 - b2 4.57e-08 2e-06 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 1.086e-06 2e-06 - b2 9.14e-07 2e-06 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 1.32e-08 2e-06 0.132 - c2 8.68e-08 2e-06 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 2.64e-07 2e-06 - c2 1.736e-06 2e-06 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 1.83470608e-12 1 0.45867652 - d2 2.16529392e-12 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x2e-06 + [(0.97)]x2e-06 = 2e-06 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x2e-06 + [(0.4)]x2e-06 = 2e-06 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x2e-06 + [(0.76)]x2e-06 = 2e-06 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x2e-06 + [(0.88)]x2e-06 = 2e-06 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x2.64e-07) + (0.7x1.736e-06)]x1 + [(0.8x2.64e-07) + (0.3x1.736e-06)]x1 = 2e-06 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x2.64e-07) + (0.22x1.736e-06)]x1 + [(0.55x2.64e-07) + (0.78x1.736e-06)]x1 = 2e-06 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x1.086e-06) + (0.45x9.14e-07)]x1 + [(0.8x1.086e-06) + (0.55x9.14e-07)]x1 = 2e-06 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x1.086e-06) + (0.22x9.14e-07)]x1 + [(0.3x1.086e-06) + (0.78x9.14e-07)]x1 = 2e-06 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 1e-06 = 1e-08 - πB(a2) = π(a2).λC(a2) = 0.09 x 1e-06 = 9e-08 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 1e-06 = 1e-08 - πC(a2) = π(a2).λB(a2) = 0.09 x 1e-06 = 9e-08 -π message B --> D - πD(b1) = π(b1) = 5.43e-08 = 5.43e-08 - πD(b2) = π(b2) = 4.57e-08 = 4.57e-08 -π message C --> D - πD(c1) = π(c1) = 1.32e-08 = 1.32e-08 - πD(c2) = π(c2) = 8.68e-08 = 8.68e-08 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 2e-06 x 2e-06 = 4e-12 - λ(a2) = λB(a2).λC(a2) = 2e-06 x 2e-06 = 4e-12 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 1e-08) + (0.6 x 9e-08) = 5.43e-08 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 1e-08) + (0.4 x 9e-08) = 4.57e-08 - λ(b1) = λD(b1) = 2e-06 = 2e-06 - λ(b2) = λD(b2) = 2e-06 = 2e-06 - belief change = 0 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 1e-08) + (0.12 x 9e-08) = 1.32e-08 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 1e-08) + (0.88 x 9e-08) = 8.68e-08 - λ(c1) = λD(c1) = 2e-06 = 2e-06 - λ(c2) = λD(c2) = 2e-06 = 2e-06 - belief change = 0 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 5.43e-08 x 1.32e-08) + (0.7 x 5.43e-08 x 8.68e-08) + (0.45 x 4.57e-08 x 1.32e-08) + (0.22 x 4.57e-08 x 8.68e-08) = 4.5867652e-15 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 5.43e-08 x 1.32e-08) + (0.3 x 5.43e-08 x 8.68e-08) + (0.55 x 4.57e-08 x 1.32e-08) + (0.78 x 4.57e-08 x 8.68e-08) = 5.4132348e-15 - λ(d1) = 1 - λ(d2) = 1 - belief change = 5.551115123e-17 - - -******************************************************************************** -Iteration 26 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 4e-12 0.1 - a2 0.09 4e-12 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 1e-08 2e-06 - a2 9e-08 2e-06 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 1e-08 2e-06 - a2 9e-08 2e-06 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 5.43e-08 2e-06 0.543 - b2 4.57e-08 2e-06 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 5.43e-08 2e-06 - b2 4.57e-08 2e-06 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 1.32e-08 2e-06 0.132 - c2 8.68e-08 2e-06 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 1.32e-08 2e-06 - c2 8.68e-08 2e-06 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 4.5867652e-15 1 0.45867652 - d2 5.4132348e-15 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x2e-06 + [(0.97)]x2e-06 = 2e-06 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x2e-06 + [(0.4)]x2e-06 = 2e-06 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x2e-06 + [(0.76)]x2e-06 = 2e-06 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x2e-06 + [(0.88)]x2e-06 = 2e-06 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x1.32e-08) + (0.7x8.68e-08)]x1 + [(0.8x1.32e-08) + (0.3x8.68e-08)]x1 = 1e-07 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x1.32e-08) + (0.22x8.68e-08)]x1 + [(0.55x1.32e-08) + (0.78x8.68e-08)]x1 = 1e-07 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x5.43e-08) + (0.45x4.57e-08)]x1 + [(0.8x5.43e-08) + (0.55x4.57e-08)]x1 = 1e-07 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x5.43e-08) + (0.22x4.57e-08)]x1 + [(0.3x5.43e-08) + (0.78x4.57e-08)]x1 = 1e-07 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 2e-06 = 2e-08 - πB(a2) = π(a2).λC(a2) = 0.09 x 2e-06 = 1.8e-07 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 2e-06 = 2e-08 - πC(a2) = π(a2).λB(a2) = 0.09 x 2e-06 = 1.8e-07 -π message B --> D - πD(b1) = π(b1) = 5.43e-08 = 5.43e-08 - πD(b2) = π(b2) = 4.57e-08 = 4.57e-08 -π message C --> D - πD(c1) = π(c1) = 1.32e-08 = 1.32e-08 - πD(c2) = π(c2) = 8.68e-08 = 8.68e-08 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 2e-06 x 2e-06 = 4e-12 - λ(a2) = λB(a2).λC(a2) = 2e-06 x 2e-06 = 4e-12 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 2e-08) + (0.6 x 1.8e-07) = 1.086e-07 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 2e-08) + (0.4 x 1.8e-07) = 9.14e-08 - λ(b1) = λD(b1) = 1e-07 = 1e-07 - λ(b2) = λD(b2) = 1e-07 = 1e-07 - belief change = 1.110223025e-16 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 2e-08) + (0.12 x 1.8e-07) = 2.64e-08 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 2e-08) + (0.88 x 1.8e-07) = 1.736e-07 - λ(c1) = λD(c1) = 1e-07 = 1e-07 - λ(c2) = λD(c2) = 1e-07 = 1e-07 - belief change = 2.775557562e-17 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 5.43e-08 x 1.32e-08) + (0.7 x 5.43e-08 x 8.68e-08) + (0.45 x 4.57e-08 x 1.32e-08) + (0.22 x 4.57e-08 x 8.68e-08) = 4.5867652e-15 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 5.43e-08 x 1.32e-08) + (0.3 x 5.43e-08 x 8.68e-08) + (0.55 x 4.57e-08 x 1.32e-08) + (0.78 x 4.57e-08 x 8.68e-08) = 5.4132348e-15 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 27 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 4e-12 0.1 - a2 0.09 4e-12 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 2e-08 2e-06 - a2 1.8e-07 2e-06 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 2e-08 2e-06 - a2 1.8e-07 2e-06 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 1.086e-07 1e-07 0.543 - b2 9.14e-08 1e-07 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 5.43e-08 1e-07 - b2 4.57e-08 1e-07 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 2.64e-08 1e-07 0.132 - c2 1.736e-07 1e-07 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 1.32e-08 1e-07 - c2 8.68e-08 1e-07 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 4.5867652e-15 1 0.45867652 - d2 5.4132348e-15 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x1e-07 + [(0.97)]x1e-07 = 1e-07 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x1e-07 + [(0.4)]x1e-07 = 1e-07 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x1e-07 + [(0.76)]x1e-07 = 1e-07 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x1e-07 + [(0.88)]x1e-07 = 1e-07 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x1.32e-08) + (0.7x8.68e-08)]x1 + [(0.8x1.32e-08) + (0.3x8.68e-08)]x1 = 1e-07 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x1.32e-08) + (0.22x8.68e-08)]x1 + [(0.55x1.32e-08) + (0.78x8.68e-08)]x1 = 1e-07 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x5.43e-08) + (0.45x4.57e-08)]x1 + [(0.8x5.43e-08) + (0.55x4.57e-08)]x1 = 1e-07 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x5.43e-08) + (0.22x4.57e-08)]x1 + [(0.3x5.43e-08) + (0.78x4.57e-08)]x1 = 1e-07 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 2e-06 = 2e-08 - πB(a2) = π(a2).λC(a2) = 0.09 x 2e-06 = 1.8e-07 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 2e-06 = 2e-08 - πC(a2) = π(a2).λB(a2) = 0.09 x 2e-06 = 1.8e-07 -π message B --> D - πD(b1) = π(b1) = 1.086e-07 = 1.086e-07 - πD(b2) = π(b2) = 9.14e-08 = 9.14e-08 -π message C --> D - πD(c1) = π(c1) = 2.64e-08 = 2.64e-08 - πD(c2) = π(c2) = 1.736e-07 = 1.736e-07 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 1e-07 x 1e-07 = 1e-14 - λ(a2) = λB(a2).λC(a2) = 1e-07 x 1e-07 = 1e-14 - belief change = 1.249000903e-16 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 2e-08) + (0.6 x 1.8e-07) = 1.086e-07 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 2e-08) + (0.4 x 1.8e-07) = 9.14e-08 - λ(b1) = λD(b1) = 1e-07 = 1e-07 - λ(b2) = λD(b2) = 1e-07 = 1e-07 - belief change = 0 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 2e-08) + (0.12 x 1.8e-07) = 2.64e-08 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 2e-08) + (0.88 x 1.8e-07) = 1.736e-07 - λ(c1) = λD(c1) = 1e-07 = 1e-07 - λ(c2) = λD(c2) = 1e-07 = 1e-07 - belief change = 0 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 1.086e-07 x 2.64e-08) + (0.7 x 1.086e-07 x 1.736e-07) + (0.45 x 9.14e-08 x 2.64e-08) + (0.22 x 9.14e-08 x 1.736e-07) = 1.83470608e-14 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 1.086e-07 x 2.64e-08) + (0.3 x 1.086e-07 x 1.736e-07) + (0.55 x 9.14e-08 x 2.64e-08) + (0.78 x 9.14e-08 x 1.736e-07) = 2.16529392e-14 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 28 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 1e-14 0.1 - a2 0.09 1e-14 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 2e-08 1e-07 - a2 1.8e-07 1e-07 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 2e-08 1e-07 - a2 1.8e-07 1e-07 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 1.086e-07 1e-07 0.543 - b2 9.14e-08 1e-07 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 1.086e-07 1e-07 - b2 9.14e-08 1e-07 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 2.64e-08 1e-07 0.132 - c2 1.736e-07 1e-07 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 2.64e-08 1e-07 - c2 1.736e-07 1e-07 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 1.83470608e-14 1 0.45867652 - d2 2.16529392e-14 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x1e-07 + [(0.97)]x1e-07 = 1e-07 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x1e-07 + [(0.4)]x1e-07 = 1e-07 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x1e-07 + [(0.76)]x1e-07 = 1e-07 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x1e-07 + [(0.88)]x1e-07 = 1e-07 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x2.64e-08) + (0.7x1.736e-07)]x1 + [(0.8x2.64e-08) + (0.3x1.736e-07)]x1 = 2e-07 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x2.64e-08) + (0.22x1.736e-07)]x1 + [(0.55x2.64e-08) + (0.78x1.736e-07)]x1 = 2e-07 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x1.086e-07) + (0.45x9.14e-08)]x1 + [(0.8x1.086e-07) + (0.55x9.14e-08)]x1 = 2e-07 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x1.086e-07) + (0.22x9.14e-08)]x1 + [(0.3x1.086e-07) + (0.78x9.14e-08)]x1 = 2e-07 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 1e-07 = 1e-09 - πB(a2) = π(a2).λC(a2) = 0.09 x 1e-07 = 9e-09 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 1e-07 = 1e-09 - πC(a2) = π(a2).λB(a2) = 0.09 x 1e-07 = 9e-09 -π message B --> D - πD(b1) = π(b1) = 1.086e-07 = 1.086e-07 - πD(b2) = π(b2) = 9.14e-08 = 9.14e-08 -π message C --> D - πD(c1) = π(c1) = 2.64e-08 = 2.64e-08 - πD(c2) = π(c2) = 1.736e-07 = 1.736e-07 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 1e-07 x 1e-07 = 1e-14 - λ(a2) = λB(a2).λC(a2) = 1e-07 x 1e-07 = 1e-14 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 1e-09) + (0.6 x 9e-09) = 5.43e-09 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 1e-09) + (0.4 x 9e-09) = 4.57e-09 - λ(b1) = λD(b1) = 2e-07 = 2e-07 - λ(b2) = λD(b2) = 2e-07 = 2e-07 - belief change = 5.551115123e-17 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 1e-09) + (0.12 x 9e-09) = 1.32e-09 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 1e-09) + (0.88 x 9e-09) = 8.68e-09 - λ(c1) = λD(c1) = 2e-07 = 2e-07 - λ(c2) = λD(c2) = 2e-07 = 2e-07 - belief change = 0 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 1.086e-07 x 2.64e-08) + (0.7 x 1.086e-07 x 1.736e-07) + (0.45 x 9.14e-08 x 2.64e-08) + (0.22 x 9.14e-08 x 1.736e-07) = 1.83470608e-14 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 1.086e-07 x 2.64e-08) + (0.3 x 1.086e-07 x 1.736e-07) + (0.55 x 9.14e-08 x 2.64e-08) + (0.78 x 9.14e-08 x 1.736e-07) = 2.16529392e-14 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 29 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 1e-14 0.1 - a2 0.09 1e-14 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 1e-09 1e-07 - a2 9e-09 1e-07 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 1e-09 1e-07 - a2 9e-09 1e-07 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 5.43e-09 2e-07 0.543 - b2 4.57e-09 2e-07 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 1.086e-07 2e-07 - b2 9.14e-08 2e-07 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 1.32e-09 2e-07 0.132 - c2 8.68e-09 2e-07 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 2.64e-08 2e-07 - c2 1.736e-07 2e-07 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 1.83470608e-14 1 0.45867652 - d2 2.16529392e-14 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x2e-07 + [(0.97)]x2e-07 = 2e-07 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x2e-07 + [(0.4)]x2e-07 = 2e-07 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x2e-07 + [(0.76)]x2e-07 = 2e-07 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x2e-07 + [(0.88)]x2e-07 = 2e-07 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x2.64e-08) + (0.7x1.736e-07)]x1 + [(0.8x2.64e-08) + (0.3x1.736e-07)]x1 = 2e-07 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x2.64e-08) + (0.22x1.736e-07)]x1 + [(0.55x2.64e-08) + (0.78x1.736e-07)]x1 = 2e-07 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x1.086e-07) + (0.45x9.14e-08)]x1 + [(0.8x1.086e-07) + (0.55x9.14e-08)]x1 = 2e-07 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x1.086e-07) + (0.22x9.14e-08)]x1 + [(0.3x1.086e-07) + (0.78x9.14e-08)]x1 = 2e-07 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 1e-07 = 1e-09 - πB(a2) = π(a2).λC(a2) = 0.09 x 1e-07 = 9e-09 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 1e-07 = 1e-09 - πC(a2) = π(a2).λB(a2) = 0.09 x 1e-07 = 9e-09 -π message B --> D - πD(b1) = π(b1) = 5.43e-09 = 5.43e-09 - πD(b2) = π(b2) = 4.57e-09 = 4.57e-09 -π message C --> D - πD(c1) = π(c1) = 1.32e-09 = 1.32e-09 - πD(c2) = π(c2) = 8.68e-09 = 8.68e-09 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 2e-07 x 2e-07 = 4e-14 - λ(a2) = λB(a2).λC(a2) = 2e-07 x 2e-07 = 4e-14 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 1e-09) + (0.6 x 9e-09) = 5.43e-09 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 1e-09) + (0.4 x 9e-09) = 4.57e-09 - λ(b1) = λD(b1) = 2e-07 = 2e-07 - λ(b2) = λD(b2) = 2e-07 = 2e-07 - belief change = 0 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 1e-09) + (0.12 x 9e-09) = 1.32e-09 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 1e-09) + (0.88 x 9e-09) = 8.68e-09 - λ(c1) = λD(c1) = 2e-07 = 2e-07 - λ(c2) = λD(c2) = 2e-07 = 2e-07 - belief change = 0 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 5.43e-09 x 1.32e-09) + (0.7 x 5.43e-09 x 8.68e-09) + (0.45 x 4.57e-09 x 1.32e-09) + (0.22 x 4.57e-09 x 8.68e-09) = 4.5867652e-17 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 5.43e-09 x 1.32e-09) + (0.3 x 5.43e-09 x 8.68e-09) + (0.55 x 4.57e-09 x 1.32e-09) + (0.78 x 4.57e-09 x 8.68e-09) = 5.4132348e-17 - λ(d1) = 1 - λ(d2) = 1 - belief change = 5.551115123e-17 - - -******************************************************************************** -Iteration 30 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 4e-14 0.1 - a2 0.09 4e-14 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 1e-09 2e-07 - a2 9e-09 2e-07 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 1e-09 2e-07 - a2 9e-09 2e-07 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 5.43e-09 2e-07 0.543 - b2 4.57e-09 2e-07 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 5.43e-09 2e-07 - b2 4.57e-09 2e-07 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 1.32e-09 2e-07 0.132 - c2 8.68e-09 2e-07 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 1.32e-09 2e-07 - c2 8.68e-09 2e-07 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 4.5867652e-17 1 0.45867652 - d2 5.4132348e-17 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x2e-07 + [(0.97)]x2e-07 = 2e-07 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x2e-07 + [(0.4)]x2e-07 = 2e-07 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x2e-07 + [(0.76)]x2e-07 = 2e-07 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x2e-07 + [(0.88)]x2e-07 = 2e-07 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x1.32e-09) + (0.7x8.68e-09)]x1 + [(0.8x1.32e-09) + (0.3x8.68e-09)]x1 = 1e-08 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x1.32e-09) + (0.22x8.68e-09)]x1 + [(0.55x1.32e-09) + (0.78x8.68e-09)]x1 = 1e-08 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x5.43e-09) + (0.45x4.57e-09)]x1 + [(0.8x5.43e-09) + (0.55x4.57e-09)]x1 = 1e-08 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x5.43e-09) + (0.22x4.57e-09)]x1 + [(0.3x5.43e-09) + (0.78x4.57e-09)]x1 = 1e-08 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 2e-07 = 2e-09 - πB(a2) = π(a2).λC(a2) = 0.09 x 2e-07 = 1.8e-08 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 2e-07 = 2e-09 - πC(a2) = π(a2).λB(a2) = 0.09 x 2e-07 = 1.8e-08 -π message B --> D - πD(b1) = π(b1) = 5.43e-09 = 5.43e-09 - πD(b2) = π(b2) = 4.57e-09 = 4.57e-09 -π message C --> D - πD(c1) = π(c1) = 1.32e-09 = 1.32e-09 - πD(c2) = π(c2) = 8.68e-09 = 8.68e-09 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 2e-07 x 2e-07 = 4e-14 - λ(a2) = λB(a2).λC(a2) = 2e-07 x 2e-07 = 4e-14 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 2e-09) + (0.6 x 1.8e-08) = 1.086e-08 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 2e-09) + (0.4 x 1.8e-08) = 9.14e-09 - λ(b1) = λD(b1) = 1e-08 = 1e-08 - λ(b2) = λD(b2) = 1e-08 = 1e-08 - belief change = 2.220446049e-16 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 2e-09) + (0.12 x 1.8e-08) = 2.64e-09 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 2e-09) + (0.88 x 1.8e-08) = 1.736e-08 - λ(c1) = λD(c1) = 1e-08 = 1e-08 - λ(c2) = λD(c2) = 1e-08 = 1e-08 - belief change = 1.387778781e-16 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 5.43e-09 x 1.32e-09) + (0.7 x 5.43e-09 x 8.68e-09) + (0.45 x 4.57e-09 x 1.32e-09) + (0.22 x 4.57e-09 x 8.68e-09) = 4.5867652e-17 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 5.43e-09 x 1.32e-09) + (0.3 x 5.43e-09 x 8.68e-09) + (0.55 x 4.57e-09 x 1.32e-09) + (0.78 x 4.57e-09 x 8.68e-09) = 5.4132348e-17 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 31 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 4e-14 0.1 - a2 0.09 4e-14 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 2e-09 2e-07 - a2 1.8e-08 2e-07 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 2e-09 2e-07 - a2 1.8e-08 2e-07 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 1.086e-08 1e-08 0.543 - b2 9.14e-09 1e-08 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 5.43e-09 1e-08 - b2 4.57e-09 1e-08 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 2.64e-09 1e-08 0.132 - c2 1.736e-08 1e-08 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 1.32e-09 1e-08 - c2 8.68e-09 1e-08 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 4.5867652e-17 1 0.45867652 - d2 5.4132348e-17 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x1e-08 + [(0.97)]x1e-08 = 1e-08 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x1e-08 + [(0.4)]x1e-08 = 1e-08 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x1e-08 + [(0.76)]x1e-08 = 1e-08 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x1e-08 + [(0.88)]x1e-08 = 1e-08 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x1.32e-09) + (0.7x8.68e-09)]x1 + [(0.8x1.32e-09) + (0.3x8.68e-09)]x1 = 1e-08 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x1.32e-09) + (0.22x8.68e-09)]x1 + [(0.55x1.32e-09) + (0.78x8.68e-09)]x1 = 1e-08 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x5.43e-09) + (0.45x4.57e-09)]x1 + [(0.8x5.43e-09) + (0.55x4.57e-09)]x1 = 1e-08 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x5.43e-09) + (0.22x4.57e-09)]x1 + [(0.3x5.43e-09) + (0.78x4.57e-09)]x1 = 1e-08 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 2e-07 = 2e-09 - πB(a2) = π(a2).λC(a2) = 0.09 x 2e-07 = 1.8e-08 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 2e-07 = 2e-09 - πC(a2) = π(a2).λB(a2) = 0.09 x 2e-07 = 1.8e-08 -π message B --> D - πD(b1) = π(b1) = 1.086e-08 = 1.086e-08 - πD(b2) = π(b2) = 9.14e-09 = 9.14e-09 -π message C --> D - πD(c1) = π(c1) = 2.64e-09 = 2.64e-09 - πD(c2) = π(c2) = 1.736e-08 = 1.736e-08 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 1e-08 x 1e-08 = 1e-16 - λ(a2) = λB(a2).λC(a2) = 1e-08 x 1e-08 = 1e-16 - belief change = 1.249000903e-16 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 2e-09) + (0.6 x 1.8e-08) = 1.086e-08 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 2e-09) + (0.4 x 1.8e-08) = 9.14e-09 - λ(b1) = λD(b1) = 1e-08 = 1e-08 - λ(b2) = λD(b2) = 1e-08 = 1e-08 - belief change = 0 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 2e-09) + (0.12 x 1.8e-08) = 2.64e-09 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 2e-09) + (0.88 x 1.8e-08) = 1.736e-08 - λ(c1) = λD(c1) = 1e-08 = 1e-08 - λ(c2) = λD(c2) = 1e-08 = 1e-08 - belief change = 0 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 1.086e-08 x 2.64e-09) + (0.7 x 1.086e-08 x 1.736e-08) + (0.45 x 9.14e-09 x 2.64e-09) + (0.22 x 9.14e-09 x 1.736e-08) = 1.83470608e-16 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 1.086e-08 x 2.64e-09) + (0.3 x 1.086e-08 x 1.736e-08) + (0.55 x 9.14e-09 x 2.64e-09) + (0.78 x 9.14e-09 x 1.736e-08) = 2.16529392e-16 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 32 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 1e-16 0.1 - a2 0.09 1e-16 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 2e-09 1e-08 - a2 1.8e-08 1e-08 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 2e-09 1e-08 - a2 1.8e-08 1e-08 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 1.086e-08 1e-08 0.543 - b2 9.14e-09 1e-08 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 1.086e-08 1e-08 - b2 9.14e-09 1e-08 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 2.64e-09 1e-08 0.132 - c2 1.736e-08 1e-08 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 2.64e-09 1e-08 - c2 1.736e-08 1e-08 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 1.83470608e-16 1 0.45867652 - d2 2.16529392e-16 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x1e-08 + [(0.97)]x1e-08 = 1e-08 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x1e-08 + [(0.4)]x1e-08 = 1e-08 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x1e-08 + [(0.76)]x1e-08 = 1e-08 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x1e-08 + [(0.88)]x1e-08 = 1e-08 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x2.64e-09) + (0.7x1.736e-08)]x1 + [(0.8x2.64e-09) + (0.3x1.736e-08)]x1 = 2e-08 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x2.64e-09) + (0.22x1.736e-08)]x1 + [(0.55x2.64e-09) + (0.78x1.736e-08)]x1 = 2e-08 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x1.086e-08) + (0.45x9.14e-09)]x1 + [(0.8x1.086e-08) + (0.55x9.14e-09)]x1 = 2e-08 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x1.086e-08) + (0.22x9.14e-09)]x1 + [(0.3x1.086e-08) + (0.78x9.14e-09)]x1 = 2e-08 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 1e-08 = 1e-10 - πB(a2) = π(a2).λC(a2) = 0.09 x 1e-08 = 9e-10 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 1e-08 = 1e-10 - πC(a2) = π(a2).λB(a2) = 0.09 x 1e-08 = 9e-10 -π message B --> D - πD(b1) = π(b1) = 1.086e-08 = 1.086e-08 - πD(b2) = π(b2) = 9.14e-09 = 9.14e-09 -π message C --> D - πD(c1) = π(c1) = 2.64e-09 = 2.64e-09 - πD(c2) = π(c2) = 1.736e-08 = 1.736e-08 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 1e-08 x 1e-08 = 1e-16 - λ(a2) = λB(a2).λC(a2) = 1e-08 x 1e-08 = 1e-16 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 1e-10) + (0.6 x 9e-10) = 5.43e-10 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 1e-10) + (0.4 x 9e-10) = 4.57e-10 - λ(b1) = λD(b1) = 2e-08 = 2e-08 - λ(b2) = λD(b2) = 2e-08 = 2e-08 - belief change = 1.665334537e-16 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 1e-10) + (0.12 x 9e-10) = 1.32e-10 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 1e-10) + (0.88 x 9e-10) = 8.68e-10 - λ(c1) = λD(c1) = 2e-08 = 2e-08 - λ(c2) = λD(c2) = 2e-08 = 2e-08 - belief change = 1.387778781e-16 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 1.086e-08 x 2.64e-09) + (0.7 x 1.086e-08 x 1.736e-08) + (0.45 x 9.14e-09 x 2.64e-09) + (0.22 x 9.14e-09 x 1.736e-08) = 1.83470608e-16 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 1.086e-08 x 2.64e-09) + (0.3 x 1.086e-08 x 1.736e-08) + (0.55 x 9.14e-09 x 2.64e-09) + (0.78 x 9.14e-09 x 1.736e-08) = 2.16529392e-16 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 33 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 1e-16 0.1 - a2 0.09 1e-16 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 1e-10 1e-08 - a2 9e-10 1e-08 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 1e-10 1e-08 - a2 9e-10 1e-08 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 5.43e-10 2e-08 0.543 - b2 4.57e-10 2e-08 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 1.086e-08 2e-08 - b2 9.14e-09 2e-08 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 1.32e-10 2e-08 0.132 - c2 8.68e-10 2e-08 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 2.64e-09 2e-08 - c2 1.736e-08 2e-08 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 1.83470608e-16 1 0.45867652 - d2 2.16529392e-16 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x2e-08 + [(0.97)]x2e-08 = 2e-08 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x2e-08 + [(0.4)]x2e-08 = 2e-08 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x2e-08 + [(0.76)]x2e-08 = 2e-08 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x2e-08 + [(0.88)]x2e-08 = 2e-08 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x2.64e-09) + (0.7x1.736e-08)]x1 + [(0.8x2.64e-09) + (0.3x1.736e-08)]x1 = 2e-08 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x2.64e-09) + (0.22x1.736e-08)]x1 + [(0.55x2.64e-09) + (0.78x1.736e-08)]x1 = 2e-08 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x1.086e-08) + (0.45x9.14e-09)]x1 + [(0.8x1.086e-08) + (0.55x9.14e-09)]x1 = 2e-08 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x1.086e-08) + (0.22x9.14e-09)]x1 + [(0.3x1.086e-08) + (0.78x9.14e-09)]x1 = 2e-08 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 1e-08 = 1e-10 - πB(a2) = π(a2).λC(a2) = 0.09 x 1e-08 = 9e-10 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 1e-08 = 1e-10 - πC(a2) = π(a2).λB(a2) = 0.09 x 1e-08 = 9e-10 -π message B --> D - πD(b1) = π(b1) = 5.43e-10 = 5.43e-10 - πD(b2) = π(b2) = 4.57e-10 = 4.57e-10 -π message C --> D - πD(c1) = π(c1) = 1.32e-10 = 1.32e-10 - πD(c2) = π(c2) = 8.68e-10 = 8.68e-10 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 2e-08 x 2e-08 = 4e-16 - λ(a2) = λB(a2).λC(a2) = 2e-08 x 2e-08 = 4e-16 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 1e-10) + (0.6 x 9e-10) = 5.43e-10 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 1e-10) + (0.4 x 9e-10) = 4.57e-10 - λ(b1) = λD(b1) = 2e-08 = 2e-08 - λ(b2) = λD(b2) = 2e-08 = 2e-08 - belief change = 0 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 1e-10) + (0.12 x 9e-10) = 1.32e-10 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 1e-10) + (0.88 x 9e-10) = 8.68e-10 - λ(c1) = λD(c1) = 2e-08 = 2e-08 - λ(c2) = λD(c2) = 2e-08 = 2e-08 - belief change = 0 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 5.43e-10 x 1.32e-10) + (0.7 x 5.43e-10 x 8.68e-10) + (0.45 x 4.57e-10 x 1.32e-10) + (0.22 x 4.57e-10 x 8.68e-10) = 4.5867652e-19 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 5.43e-10 x 1.32e-10) + (0.3 x 5.43e-10 x 8.68e-10) + (0.55 x 4.57e-10 x 1.32e-10) + (0.78 x 4.57e-10 x 8.68e-10) = 5.4132348e-19 - λ(d1) = 1 - λ(d2) = 1 - belief change = 1.665334537e-16 - - -******************************************************************************** -Iteration 34 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 4e-16 0.1 - a2 0.09 4e-16 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 1e-10 2e-08 - a2 9e-10 2e-08 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 1e-10 2e-08 - a2 9e-10 2e-08 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 5.43e-10 2e-08 0.543 - b2 4.57e-10 2e-08 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 5.43e-10 2e-08 - b2 4.57e-10 2e-08 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 1.32e-10 2e-08 0.132 - c2 8.68e-10 2e-08 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 1.32e-10 2e-08 - c2 8.68e-10 2e-08 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 4.5867652e-19 1 0.45867652 - d2 5.4132348e-19 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x2e-08 + [(0.97)]x2e-08 = 2e-08 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x2e-08 + [(0.4)]x2e-08 = 2e-08 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x2e-08 + [(0.76)]x2e-08 = 2e-08 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x2e-08 + [(0.88)]x2e-08 = 2e-08 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x1.32e-10) + (0.7x8.68e-10)]x1 + [(0.8x1.32e-10) + (0.3x8.68e-10)]x1 = 1e-09 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x1.32e-10) + (0.22x8.68e-10)]x1 + [(0.55x1.32e-10) + (0.78x8.68e-10)]x1 = 1e-09 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x5.43e-10) + (0.45x4.57e-10)]x1 + [(0.8x5.43e-10) + (0.55x4.57e-10)]x1 = 1e-09 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x5.43e-10) + (0.22x4.57e-10)]x1 + [(0.3x5.43e-10) + (0.78x4.57e-10)]x1 = 1e-09 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 2e-08 = 2e-10 - πB(a2) = π(a2).λC(a2) = 0.09 x 2e-08 = 1.8e-09 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 2e-08 = 2e-10 - πC(a2) = π(a2).λB(a2) = 0.09 x 2e-08 = 1.8e-09 -π message B --> D - πD(b1) = π(b1) = 5.43e-10 = 5.43e-10 - πD(b2) = π(b2) = 4.57e-10 = 4.57e-10 -π message C --> D - πD(c1) = π(c1) = 1.32e-10 = 1.32e-10 - πD(c2) = π(c2) = 8.68e-10 = 8.68e-10 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 2e-08 x 2e-08 = 4e-16 - λ(a2) = λB(a2).λC(a2) = 2e-08 x 2e-08 = 4e-16 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 2e-10) + (0.6 x 1.8e-09) = 1.086e-09 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 2e-10) + (0.4 x 1.8e-09) = 9.14e-10 - λ(b1) = λD(b1) = 1e-09 = 1e-09 - λ(b2) = λD(b2) = 1e-09 = 1e-09 - belief change = 1.665334537e-16 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 2e-10) + (0.12 x 1.8e-09) = 2.64e-10 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 2e-10) + (0.88 x 1.8e-09) = 1.736e-09 - λ(c1) = λD(c1) = 1e-09 = 1e-09 - λ(c2) = λD(c2) = 1e-09 = 1e-09 - belief change = 2.775557562e-17 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 5.43e-10 x 1.32e-10) + (0.7 x 5.43e-10 x 8.68e-10) + (0.45 x 4.57e-10 x 1.32e-10) + (0.22 x 4.57e-10 x 8.68e-10) = 4.5867652e-19 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 5.43e-10 x 1.32e-10) + (0.3 x 5.43e-10 x 8.68e-10) + (0.55 x 4.57e-10 x 1.32e-10) + (0.78 x 4.57e-10 x 8.68e-10) = 5.4132348e-19 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 35 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 4e-16 0.1 - a2 0.09 4e-16 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 2e-10 2e-08 - a2 1.8e-09 2e-08 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 2e-10 2e-08 - a2 1.8e-09 2e-08 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 1.086e-09 1e-09 0.543 - b2 9.14e-10 1e-09 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 5.43e-10 1e-09 - b2 4.57e-10 1e-09 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 2.64e-10 1e-09 0.132 - c2 1.736e-09 1e-09 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 1.32e-10 1e-09 - c2 8.68e-10 1e-09 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 4.5867652e-19 1 0.45867652 - d2 5.4132348e-19 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x1e-09 + [(0.97)]x1e-09 = 1e-09 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x1e-09 + [(0.4)]x1e-09 = 1e-09 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x1e-09 + [(0.76)]x1e-09 = 1e-09 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x1e-09 + [(0.88)]x1e-09 = 1e-09 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x1.32e-10) + (0.7x8.68e-10)]x1 + [(0.8x1.32e-10) + (0.3x8.68e-10)]x1 = 1e-09 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x1.32e-10) + (0.22x8.68e-10)]x1 + [(0.55x1.32e-10) + (0.78x8.68e-10)]x1 = 1e-09 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x5.43e-10) + (0.45x4.57e-10)]x1 + [(0.8x5.43e-10) + (0.55x4.57e-10)]x1 = 1e-09 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x5.43e-10) + (0.22x4.57e-10)]x1 + [(0.3x5.43e-10) + (0.78x4.57e-10)]x1 = 1e-09 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 2e-08 = 2e-10 - πB(a2) = π(a2).λC(a2) = 0.09 x 2e-08 = 1.8e-09 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 2e-08 = 2e-10 - πC(a2) = π(a2).λB(a2) = 0.09 x 2e-08 = 1.8e-09 -π message B --> D - πD(b1) = π(b1) = 1.086e-09 = 1.086e-09 - πD(b2) = π(b2) = 9.14e-10 = 9.14e-10 -π message C --> D - πD(c1) = π(c1) = 2.64e-10 = 2.64e-10 - πD(c2) = π(c2) = 1.736e-09 = 1.736e-09 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 1e-09 x 1e-09 = 1e-18 - λ(a2) = λB(a2).λC(a2) = 1e-09 x 1e-09 = 1e-18 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 2e-10) + (0.6 x 1.8e-09) = 1.086e-09 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 2e-10) + (0.4 x 1.8e-09) = 9.14e-10 - λ(b1) = λD(b1) = 1e-09 = 1e-09 - λ(b2) = λD(b2) = 1e-09 = 1e-09 - belief change = 0 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 2e-10) + (0.12 x 1.8e-09) = 2.64e-10 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 2e-10) + (0.88 x 1.8e-09) = 1.736e-09 - λ(c1) = λD(c1) = 1e-09 = 1e-09 - λ(c2) = λD(c2) = 1e-09 = 1e-09 - belief change = 0 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 1.086e-09 x 2.64e-10) + (0.7 x 1.086e-09 x 1.736e-09) + (0.45 x 9.14e-10 x 2.64e-10) + (0.22 x 9.14e-10 x 1.736e-09) = 1.83470608e-18 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 1.086e-09 x 2.64e-10) + (0.3 x 1.086e-09 x 1.736e-09) + (0.55 x 9.14e-10 x 2.64e-10) + (0.78 x 9.14e-10 x 1.736e-09) = 2.16529392e-18 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 36 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 1e-18 0.1 - a2 0.09 1e-18 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 2e-10 1e-09 - a2 1.8e-09 1e-09 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 2e-10 1e-09 - a2 1.8e-09 1e-09 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 1.086e-09 1e-09 0.543 - b2 9.14e-10 1e-09 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 1.086e-09 1e-09 - b2 9.14e-10 1e-09 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 2.64e-10 1e-09 0.132 - c2 1.736e-09 1e-09 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 2.64e-10 1e-09 - c2 1.736e-09 1e-09 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 1.83470608e-18 1 0.45867652 - d2 2.16529392e-18 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x1e-09 + [(0.97)]x1e-09 = 1e-09 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x1e-09 + [(0.4)]x1e-09 = 1e-09 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x1e-09 + [(0.76)]x1e-09 = 1e-09 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x1e-09 + [(0.88)]x1e-09 = 1e-09 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x2.64e-10) + (0.7x1.736e-09)]x1 + [(0.8x2.64e-10) + (0.3x1.736e-09)]x1 = 2e-09 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x2.64e-10) + (0.22x1.736e-09)]x1 + [(0.55x2.64e-10) + (0.78x1.736e-09)]x1 = 2e-09 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x1.086e-09) + (0.45x9.14e-10)]x1 + [(0.8x1.086e-09) + (0.55x9.14e-10)]x1 = 2e-09 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x1.086e-09) + (0.22x9.14e-10)]x1 + [(0.3x1.086e-09) + (0.78x9.14e-10)]x1 = 2e-09 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 1e-09 = 1e-11 - πB(a2) = π(a2).λC(a2) = 0.09 x 1e-09 = 9e-11 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 1e-09 = 1e-11 - πC(a2) = π(a2).λB(a2) = 0.09 x 1e-09 = 9e-11 -π message B --> D - πD(b1) = π(b1) = 1.086e-09 = 1.086e-09 - πD(b2) = π(b2) = 9.14e-10 = 9.14e-10 -π message C --> D - πD(c1) = π(c1) = 2.64e-10 = 2.64e-10 - πD(c2) = π(c2) = 1.736e-09 = 1.736e-09 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 1e-09 x 1e-09 = 1e-18 - λ(a2) = λB(a2).λC(a2) = 1e-09 x 1e-09 = 1e-18 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 1e-11) + (0.6 x 9e-11) = 5.43e-11 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 1e-11) + (0.4 x 9e-11) = 4.57e-11 - λ(b1) = λD(b1) = 2e-09 = 2e-09 - λ(b2) = λD(b2) = 2e-09 = 2e-09 - belief change = 0 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 1e-11) + (0.12 x 9e-11) = 1.32e-11 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 1e-11) + (0.88 x 9e-11) = 8.68e-11 - λ(c1) = λD(c1) = 2e-09 = 2e-09 - λ(c2) = λD(c2) = 2e-09 = 2e-09 - belief change = 2.775557562e-17 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 1.086e-09 x 2.64e-10) + (0.7 x 1.086e-09 x 1.736e-09) + (0.45 x 9.14e-10 x 2.64e-10) + (0.22 x 9.14e-10 x 1.736e-09) = 1.83470608e-18 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 1.086e-09 x 2.64e-10) + (0.3 x 1.086e-09 x 1.736e-09) + (0.55 x 9.14e-10 x 2.64e-10) + (0.78 x 9.14e-10 x 1.736e-09) = 2.16529392e-18 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 37 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 1e-18 0.1 - a2 0.09 1e-18 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 1e-11 1e-09 - a2 9e-11 1e-09 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 1e-11 1e-09 - a2 9e-11 1e-09 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 5.43e-11 2e-09 0.543 - b2 4.57e-11 2e-09 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 1.086e-09 2e-09 - b2 9.14e-10 2e-09 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 1.32e-11 2e-09 0.132 - c2 8.68e-11 2e-09 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 2.64e-10 2e-09 - c2 1.736e-09 2e-09 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 1.83470608e-18 1 0.45867652 - d2 2.16529392e-18 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x2e-09 + [(0.97)]x2e-09 = 2e-09 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x2e-09 + [(0.4)]x2e-09 = 2e-09 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x2e-09 + [(0.76)]x2e-09 = 2e-09 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x2e-09 + [(0.88)]x2e-09 = 2e-09 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x2.64e-10) + (0.7x1.736e-09)]x1 + [(0.8x2.64e-10) + (0.3x1.736e-09)]x1 = 2e-09 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x2.64e-10) + (0.22x1.736e-09)]x1 + [(0.55x2.64e-10) + (0.78x1.736e-09)]x1 = 2e-09 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x1.086e-09) + (0.45x9.14e-10)]x1 + [(0.8x1.086e-09) + (0.55x9.14e-10)]x1 = 2e-09 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x1.086e-09) + (0.22x9.14e-10)]x1 + [(0.3x1.086e-09) + (0.78x9.14e-10)]x1 = 2e-09 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 1e-09 = 1e-11 - πB(a2) = π(a2).λC(a2) = 0.09 x 1e-09 = 9e-11 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 1e-09 = 1e-11 - πC(a2) = π(a2).λB(a2) = 0.09 x 1e-09 = 9e-11 -π message B --> D - πD(b1) = π(b1) = 5.43e-11 = 5.43e-11 - πD(b2) = π(b2) = 4.57e-11 = 4.57e-11 -π message C --> D - πD(c1) = π(c1) = 1.32e-11 = 1.32e-11 - πD(c2) = π(c2) = 8.68e-11 = 8.68e-11 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 2e-09 x 2e-09 = 4e-18 - λ(a2) = λB(a2).λC(a2) = 2e-09 x 2e-09 = 4e-18 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 1e-11) + (0.6 x 9e-11) = 5.43e-11 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 1e-11) + (0.4 x 9e-11) = 4.57e-11 - λ(b1) = λD(b1) = 2e-09 = 2e-09 - λ(b2) = λD(b2) = 2e-09 = 2e-09 - belief change = 0 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 1e-11) + (0.12 x 9e-11) = 1.32e-11 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 1e-11) + (0.88 x 9e-11) = 8.68e-11 - λ(c1) = λD(c1) = 2e-09 = 2e-09 - λ(c2) = λD(c2) = 2e-09 = 2e-09 - belief change = 0 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 5.43e-11 x 1.32e-11) + (0.7 x 5.43e-11 x 8.68e-11) + (0.45 x 4.57e-11 x 1.32e-11) + (0.22 x 4.57e-11 x 8.68e-11) = 4.5867652e-21 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 5.43e-11 x 1.32e-11) + (0.3 x 5.43e-11 x 8.68e-11) + (0.55 x 4.57e-11 x 1.32e-11) + (0.78 x 4.57e-11 x 8.68e-11) = 5.4132348e-21 - λ(d1) = 1 - λ(d2) = 1 - belief change = 2.220446049e-16 - - -******************************************************************************** -Iteration 38 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 4e-18 0.1 - a2 0.09 4e-18 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 1e-11 2e-09 - a2 9e-11 2e-09 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 1e-11 2e-09 - a2 9e-11 2e-09 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 5.43e-11 2e-09 0.543 - b2 4.57e-11 2e-09 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 5.43e-11 2e-09 - b2 4.57e-11 2e-09 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 1.32e-11 2e-09 0.132 - c2 8.68e-11 2e-09 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 1.32e-11 2e-09 - c2 8.68e-11 2e-09 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 4.5867652e-21 1 0.45867652 - d2 5.4132348e-21 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x2e-09 + [(0.97)]x2e-09 = 2e-09 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x2e-09 + [(0.4)]x2e-09 = 2e-09 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x2e-09 + [(0.76)]x2e-09 = 2e-09 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x2e-09 + [(0.88)]x2e-09 = 2e-09 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x1.32e-11) + (0.7x8.68e-11)]x1 + [(0.8x1.32e-11) + (0.3x8.68e-11)]x1 = 1e-10 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x1.32e-11) + (0.22x8.68e-11)]x1 + [(0.55x1.32e-11) + (0.78x8.68e-11)]x1 = 1e-10 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x5.43e-11) + (0.45x4.57e-11)]x1 + [(0.8x5.43e-11) + (0.55x4.57e-11)]x1 = 1e-10 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x5.43e-11) + (0.22x4.57e-11)]x1 + [(0.3x5.43e-11) + (0.78x4.57e-11)]x1 = 1e-10 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 2e-09 = 2e-11 - πB(a2) = π(a2).λC(a2) = 0.09 x 2e-09 = 1.8e-10 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 2e-09 = 2e-11 - πC(a2) = π(a2).λB(a2) = 0.09 x 2e-09 = 1.8e-10 -π message B --> D - πD(b1) = π(b1) = 5.43e-11 = 5.43e-11 - πD(b2) = π(b2) = 4.57e-11 = 4.57e-11 -π message C --> D - πD(c1) = π(c1) = 1.32e-11 = 1.32e-11 - πD(c2) = π(c2) = 8.68e-11 = 8.68e-11 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 2e-09 x 2e-09 = 4e-18 - λ(a2) = λB(a2).λC(a2) = 2e-09 x 2e-09 = 4e-18 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 2e-11) + (0.6 x 1.8e-10) = 1.086e-10 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 2e-11) + (0.4 x 1.8e-10) = 9.14e-11 - λ(b1) = λD(b1) = 1e-10 = 1e-10 - λ(b2) = λD(b2) = 1e-10 = 1e-10 - belief change = 1.110223025e-16 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 2e-11) + (0.12 x 1.8e-10) = 2.64e-11 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 2e-11) + (0.88 x 1.8e-10) = 1.736e-10 - λ(c1) = λD(c1) = 1e-10 = 1e-10 - λ(c2) = λD(c2) = 1e-10 = 1e-10 - belief change = 2.775557562e-17 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 5.43e-11 x 1.32e-11) + (0.7 x 5.43e-11 x 8.68e-11) + (0.45 x 4.57e-11 x 1.32e-11) + (0.22 x 4.57e-11 x 8.68e-11) = 4.5867652e-21 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 5.43e-11 x 1.32e-11) + (0.3 x 5.43e-11 x 8.68e-11) + (0.55 x 4.57e-11 x 1.32e-11) + (0.78 x 4.57e-11 x 8.68e-11) = 5.4132348e-21 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 39 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 4e-18 0.1 - a2 0.09 4e-18 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 2e-11 2e-09 - a2 1.8e-10 2e-09 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 2e-11 2e-09 - a2 1.8e-10 2e-09 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 1.086e-10 1e-10 0.543 - b2 9.14e-11 1e-10 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 5.43e-11 1e-10 - b2 4.57e-11 1e-10 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 2.64e-11 1e-10 0.132 - c2 1.736e-10 1e-10 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 1.32e-11 1e-10 - c2 8.68e-11 1e-10 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 4.5867652e-21 1 0.45867652 - d2 5.4132348e-21 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x1e-10 + [(0.97)]x1e-10 = 1e-10 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x1e-10 + [(0.4)]x1e-10 = 1e-10 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x1e-10 + [(0.76)]x1e-10 = 1e-10 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x1e-10 + [(0.88)]x1e-10 = 1e-10 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x1.32e-11) + (0.7x8.68e-11)]x1 + [(0.8x1.32e-11) + (0.3x8.68e-11)]x1 = 1e-10 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x1.32e-11) + (0.22x8.68e-11)]x1 + [(0.55x1.32e-11) + (0.78x8.68e-11)]x1 = 1e-10 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x5.43e-11) + (0.45x4.57e-11)]x1 + [(0.8x5.43e-11) + (0.55x4.57e-11)]x1 = 1e-10 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x5.43e-11) + (0.22x4.57e-11)]x1 + [(0.3x5.43e-11) + (0.78x4.57e-11)]x1 = 1e-10 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 2e-09 = 2e-11 - πB(a2) = π(a2).λC(a2) = 0.09 x 2e-09 = 1.8e-10 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 2e-09 = 2e-11 - πC(a2) = π(a2).λB(a2) = 0.09 x 2e-09 = 1.8e-10 -π message B --> D - πD(b1) = π(b1) = 1.086e-10 = 1.086e-10 - πD(b2) = π(b2) = 9.14e-11 = 9.14e-11 -π message C --> D - πD(c1) = π(c1) = 2.64e-11 = 2.64e-11 - πD(c2) = π(c2) = 1.736e-10 = 1.736e-10 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 1e-10 x 1e-10 = 1e-20 - λ(a2) = λB(a2).λC(a2) = 1e-10 x 1e-10 = 1e-20 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 2e-11) + (0.6 x 1.8e-10) = 1.086e-10 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 2e-11) + (0.4 x 1.8e-10) = 9.14e-11 - λ(b1) = λD(b1) = 1e-10 = 1e-10 - λ(b2) = λD(b2) = 1e-10 = 1e-10 - belief change = 0 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 2e-11) + (0.12 x 1.8e-10) = 2.64e-11 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 2e-11) + (0.88 x 1.8e-10) = 1.736e-10 - λ(c1) = λD(c1) = 1e-10 = 1e-10 - λ(c2) = λD(c2) = 1e-10 = 1e-10 - belief change = 0 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 1.086e-10 x 2.64e-11) + (0.7 x 1.086e-10 x 1.736e-10) + (0.45 x 9.14e-11 x 2.64e-11) + (0.22 x 9.14e-11 x 1.736e-10) = 1.83470608e-20 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 1.086e-10 x 2.64e-11) + (0.3 x 1.086e-10 x 1.736e-10) + (0.55 x 9.14e-11 x 2.64e-11) + (0.78 x 9.14e-11 x 1.736e-10) = 2.16529392e-20 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 40 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 1e-20 0.1 - a2 0.09 1e-20 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 2e-11 1e-10 - a2 1.8e-10 1e-10 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 2e-11 1e-10 - a2 1.8e-10 1e-10 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 1.086e-10 1e-10 0.543 - b2 9.14e-11 1e-10 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 1.086e-10 1e-10 - b2 9.14e-11 1e-10 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 2.64e-11 1e-10 0.132 - c2 1.736e-10 1e-10 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 2.64e-11 1e-10 - c2 1.736e-10 1e-10 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 1.83470608e-20 1 0.45867652 - d2 2.16529392e-20 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x1e-10 + [(0.97)]x1e-10 = 1e-10 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x1e-10 + [(0.4)]x1e-10 = 1e-10 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x1e-10 + [(0.76)]x1e-10 = 1e-10 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x1e-10 + [(0.88)]x1e-10 = 1e-10 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x2.64e-11) + (0.7x1.736e-10)]x1 + [(0.8x2.64e-11) + (0.3x1.736e-10)]x1 = 2e-10 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x2.64e-11) + (0.22x1.736e-10)]x1 + [(0.55x2.64e-11) + (0.78x1.736e-10)]x1 = 2e-10 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x1.086e-10) + (0.45x9.14e-11)]x1 + [(0.8x1.086e-10) + (0.55x9.14e-11)]x1 = 2e-10 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x1.086e-10) + (0.22x9.14e-11)]x1 + [(0.3x1.086e-10) + (0.78x9.14e-11)]x1 = 2e-10 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 1e-10 = 1e-12 - πB(a2) = π(a2).λC(a2) = 0.09 x 1e-10 = 9e-12 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 1e-10 = 1e-12 - πC(a2) = π(a2).λB(a2) = 0.09 x 1e-10 = 9e-12 -π message B --> D - πD(b1) = π(b1) = 1.086e-10 = 1.086e-10 - πD(b2) = π(b2) = 9.14e-11 = 9.14e-11 -π message C --> D - πD(c1) = π(c1) = 2.64e-11 = 2.64e-11 - πD(c2) = π(c2) = 1.736e-10 = 1.736e-10 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 1e-10 x 1e-10 = 1e-20 - λ(a2) = λB(a2).λC(a2) = 1e-10 x 1e-10 = 1e-20 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 1e-12) + (0.6 x 9e-12) = 5.43e-12 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 1e-12) + (0.4 x 9e-12) = 4.57e-12 - λ(b1) = λD(b1) = 2e-10 = 2e-10 - λ(b2) = λD(b2) = 2e-10 = 2e-10 - belief change = 1.110223025e-16 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 1e-12) + (0.12 x 9e-12) = 1.32e-12 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 1e-12) + (0.88 x 9e-12) = 8.68e-12 - λ(c1) = λD(c1) = 2e-10 = 2e-10 - λ(c2) = λD(c2) = 2e-10 = 2e-10 - belief change = 2.775557562e-17 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 1.086e-10 x 2.64e-11) + (0.7 x 1.086e-10 x 1.736e-10) + (0.45 x 9.14e-11 x 2.64e-11) + (0.22 x 9.14e-11 x 1.736e-10) = 1.83470608e-20 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 1.086e-10 x 2.64e-11) + (0.3 x 1.086e-10 x 1.736e-10) + (0.55 x 9.14e-11 x 2.64e-11) + (0.78 x 9.14e-11 x 1.736e-10) = 2.16529392e-20 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 41 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 1e-20 0.1 - a2 0.09 1e-20 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 1e-12 1e-10 - a2 9e-12 1e-10 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 1e-12 1e-10 - a2 9e-12 1e-10 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 5.43e-12 2e-10 0.543 - b2 4.57e-12 2e-10 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 1.086e-10 2e-10 - b2 9.14e-11 2e-10 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 1.32e-12 2e-10 0.132 - c2 8.68e-12 2e-10 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 2.64e-11 2e-10 - c2 1.736e-10 2e-10 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 1.83470608e-20 1 0.45867652 - d2 2.16529392e-20 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x2e-10 + [(0.97)]x2e-10 = 2e-10 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x2e-10 + [(0.4)]x2e-10 = 2e-10 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x2e-10 + [(0.76)]x2e-10 = 2e-10 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x2e-10 + [(0.88)]x2e-10 = 2e-10 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x2.64e-11) + (0.7x1.736e-10)]x1 + [(0.8x2.64e-11) + (0.3x1.736e-10)]x1 = 2e-10 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x2.64e-11) + (0.22x1.736e-10)]x1 + [(0.55x2.64e-11) + (0.78x1.736e-10)]x1 = 2e-10 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x1.086e-10) + (0.45x9.14e-11)]x1 + [(0.8x1.086e-10) + (0.55x9.14e-11)]x1 = 2e-10 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x1.086e-10) + (0.22x9.14e-11)]x1 + [(0.3x1.086e-10) + (0.78x9.14e-11)]x1 = 2e-10 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 1e-10 = 1e-12 - πB(a2) = π(a2).λC(a2) = 0.09 x 1e-10 = 9e-12 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 1e-10 = 1e-12 - πC(a2) = π(a2).λB(a2) = 0.09 x 1e-10 = 9e-12 -π message B --> D - πD(b1) = π(b1) = 5.43e-12 = 5.43e-12 - πD(b2) = π(b2) = 4.57e-12 = 4.57e-12 -π message C --> D - πD(c1) = π(c1) = 1.32e-12 = 1.32e-12 - πD(c2) = π(c2) = 8.68e-12 = 8.68e-12 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 2e-10 x 2e-10 = 4e-20 - λ(a2) = λB(a2).λC(a2) = 2e-10 x 2e-10 = 4e-20 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 1e-12) + (0.6 x 9e-12) = 5.43e-12 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 1e-12) + (0.4 x 9e-12) = 4.57e-12 - λ(b1) = λD(b1) = 2e-10 = 2e-10 - λ(b2) = λD(b2) = 2e-10 = 2e-10 - belief change = 0 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 1e-12) + (0.12 x 9e-12) = 1.32e-12 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 1e-12) + (0.88 x 9e-12) = 8.68e-12 - λ(c1) = λD(c1) = 2e-10 = 2e-10 - λ(c2) = λD(c2) = 2e-10 = 2e-10 - belief change = 0 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 5.43e-12 x 1.32e-12) + (0.7 x 5.43e-12 x 8.68e-12) + (0.45 x 4.57e-12 x 1.32e-12) + (0.22 x 4.57e-12 x 8.68e-12) = 4.5867652e-23 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 5.43e-12 x 1.32e-12) + (0.3 x 5.43e-12 x 8.68e-12) + (0.55 x 4.57e-12 x 1.32e-12) + (0.78 x 4.57e-12 x 8.68e-12) = 5.4132348e-23 - λ(d1) = 1 - λ(d2) = 1 - belief change = 5.551115123e-17 - - -******************************************************************************** -Iteration 42 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 4e-20 0.1 - a2 0.09 4e-20 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 1e-12 2e-10 - a2 9e-12 2e-10 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 1e-12 2e-10 - a2 9e-12 2e-10 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 5.43e-12 2e-10 0.543 - b2 4.57e-12 2e-10 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 5.43e-12 2e-10 - b2 4.57e-12 2e-10 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 1.32e-12 2e-10 0.132 - c2 8.68e-12 2e-10 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 1.32e-12 2e-10 - c2 8.68e-12 2e-10 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 4.5867652e-23 1 0.45867652 - d2 5.4132348e-23 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x2e-10 + [(0.97)]x2e-10 = 2e-10 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x2e-10 + [(0.4)]x2e-10 = 2e-10 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x2e-10 + [(0.76)]x2e-10 = 2e-10 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x2e-10 + [(0.88)]x2e-10 = 2e-10 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x1.32e-12) + (0.7x8.68e-12)]x1 + [(0.8x1.32e-12) + (0.3x8.68e-12)]x1 = 1e-11 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x1.32e-12) + (0.22x8.68e-12)]x1 + [(0.55x1.32e-12) + (0.78x8.68e-12)]x1 = 1e-11 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x5.43e-12) + (0.45x4.57e-12)]x1 + [(0.8x5.43e-12) + (0.55x4.57e-12)]x1 = 1e-11 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x5.43e-12) + (0.22x4.57e-12)]x1 + [(0.3x5.43e-12) + (0.78x4.57e-12)]x1 = 1e-11 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 2e-10 = 2e-12 - πB(a2) = π(a2).λC(a2) = 0.09 x 2e-10 = 1.8e-11 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 2e-10 = 2e-12 - πC(a2) = π(a2).λB(a2) = 0.09 x 2e-10 = 1.8e-11 -π message B --> D - πD(b1) = π(b1) = 5.43e-12 = 5.43e-12 - πD(b2) = π(b2) = 4.57e-12 = 4.57e-12 -π message C --> D - πD(c1) = π(c1) = 1.32e-12 = 1.32e-12 - πD(c2) = π(c2) = 8.68e-12 = 8.68e-12 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 2e-10 x 2e-10 = 4e-20 - λ(a2) = λB(a2).λC(a2) = 2e-10 x 2e-10 = 4e-20 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 2e-12) + (0.6 x 1.8e-11) = 1.086e-11 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 2e-12) + (0.4 x 1.8e-11) = 9.14e-12 - λ(b1) = λD(b1) = 1e-11 = 1e-11 - λ(b2) = λD(b2) = 1e-11 = 1e-11 - belief change = 0 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 2e-12) + (0.12 x 1.8e-11) = 2.64e-12 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 2e-12) + (0.88 x 1.8e-11) = 1.736e-11 - λ(c1) = λD(c1) = 1e-11 = 1e-11 - λ(c2) = λD(c2) = 1e-11 = 1e-11 - belief change = 2.775557562e-17 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 5.43e-12 x 1.32e-12) + (0.7 x 5.43e-12 x 8.68e-12) + (0.45 x 4.57e-12 x 1.32e-12) + (0.22 x 4.57e-12 x 8.68e-12) = 4.5867652e-23 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 5.43e-12 x 1.32e-12) + (0.3 x 5.43e-12 x 8.68e-12) + (0.55 x 4.57e-12 x 1.32e-12) + (0.78 x 4.57e-12 x 8.68e-12) = 5.4132348e-23 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 43 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 4e-20 0.1 - a2 0.09 4e-20 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 2e-12 2e-10 - a2 1.8e-11 2e-10 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 2e-12 2e-10 - a2 1.8e-11 2e-10 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 1.086e-11 1e-11 0.543 - b2 9.14e-12 1e-11 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 5.43e-12 1e-11 - b2 4.57e-12 1e-11 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 2.64e-12 1e-11 0.132 - c2 1.736e-11 1e-11 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 1.32e-12 1e-11 - c2 8.68e-12 1e-11 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 4.5867652e-23 1 0.45867652 - d2 5.4132348e-23 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x1e-11 + [(0.97)]x1e-11 = 1e-11 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x1e-11 + [(0.4)]x1e-11 = 1e-11 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x1e-11 + [(0.76)]x1e-11 = 1e-11 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x1e-11 + [(0.88)]x1e-11 = 1e-11 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x1.32e-12) + (0.7x8.68e-12)]x1 + [(0.8x1.32e-12) + (0.3x8.68e-12)]x1 = 1e-11 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x1.32e-12) + (0.22x8.68e-12)]x1 + [(0.55x1.32e-12) + (0.78x8.68e-12)]x1 = 1e-11 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x5.43e-12) + (0.45x4.57e-12)]x1 + [(0.8x5.43e-12) + (0.55x4.57e-12)]x1 = 1e-11 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x5.43e-12) + (0.22x4.57e-12)]x1 + [(0.3x5.43e-12) + (0.78x4.57e-12)]x1 = 1e-11 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 2e-10 = 2e-12 - πB(a2) = π(a2).λC(a2) = 0.09 x 2e-10 = 1.8e-11 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 2e-10 = 2e-12 - πC(a2) = π(a2).λB(a2) = 0.09 x 2e-10 = 1.8e-11 -π message B --> D - πD(b1) = π(b1) = 1.086e-11 = 1.086e-11 - πD(b2) = π(b2) = 9.14e-12 = 9.14e-12 -π message C --> D - πD(c1) = π(c1) = 2.64e-12 = 2.64e-12 - πD(c2) = π(c2) = 1.736e-11 = 1.736e-11 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 1e-11 x 1e-11 = 1e-22 - λ(a2) = λB(a2).λC(a2) = 1e-11 x 1e-11 = 1e-22 - belief change = 1.110223025e-16 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 2e-12) + (0.6 x 1.8e-11) = 1.086e-11 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 2e-12) + (0.4 x 1.8e-11) = 9.14e-12 - λ(b1) = λD(b1) = 1e-11 = 1e-11 - λ(b2) = λD(b2) = 1e-11 = 1e-11 - belief change = 0 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 2e-12) + (0.12 x 1.8e-11) = 2.64e-12 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 2e-12) + (0.88 x 1.8e-11) = 1.736e-11 - λ(c1) = λD(c1) = 1e-11 = 1e-11 - λ(c2) = λD(c2) = 1e-11 = 1e-11 - belief change = 0 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 1.086e-11 x 2.64e-12) + (0.7 x 1.086e-11 x 1.736e-11) + (0.45 x 9.14e-12 x 2.64e-12) + (0.22 x 9.14e-12 x 1.736e-11) = 1.83470608e-22 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 1.086e-11 x 2.64e-12) + (0.3 x 1.086e-11 x 1.736e-11) + (0.55 x 9.14e-12 x 2.64e-12) + (0.78 x 9.14e-12 x 1.736e-11) = 2.16529392e-22 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 44 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 1e-22 0.1 - a2 0.09 1e-22 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 2e-12 1e-11 - a2 1.8e-11 1e-11 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 2e-12 1e-11 - a2 1.8e-11 1e-11 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 1.086e-11 1e-11 0.543 - b2 9.14e-12 1e-11 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 1.086e-11 1e-11 - b2 9.14e-12 1e-11 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 2.64e-12 1e-11 0.132 - c2 1.736e-11 1e-11 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 2.64e-12 1e-11 - c2 1.736e-11 1e-11 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 1.83470608e-22 1 0.45867652 - d2 2.16529392e-22 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x1e-11 + [(0.97)]x1e-11 = 1e-11 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x1e-11 + [(0.4)]x1e-11 = 1e-11 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x1e-11 + [(0.76)]x1e-11 = 1e-11 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x1e-11 + [(0.88)]x1e-11 = 1e-11 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x2.64e-12) + (0.7x1.736e-11)]x1 + [(0.8x2.64e-12) + (0.3x1.736e-11)]x1 = 2e-11 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x2.64e-12) + (0.22x1.736e-11)]x1 + [(0.55x2.64e-12) + (0.78x1.736e-11)]x1 = 2e-11 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x1.086e-11) + (0.45x9.14e-12)]x1 + [(0.8x1.086e-11) + (0.55x9.14e-12)]x1 = 2e-11 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x1.086e-11) + (0.22x9.14e-12)]x1 + [(0.3x1.086e-11) + (0.78x9.14e-12)]x1 = 2e-11 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 1e-11 = 1e-13 - πB(a2) = π(a2).λC(a2) = 0.09 x 1e-11 = 9e-13 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 1e-11 = 1e-13 - πC(a2) = π(a2).λB(a2) = 0.09 x 1e-11 = 9e-13 -π message B --> D - πD(b1) = π(b1) = 1.086e-11 = 1.086e-11 - πD(b2) = π(b2) = 9.14e-12 = 9.14e-12 -π message C --> D - πD(c1) = π(c1) = 2.64e-12 = 2.64e-12 - πD(c2) = π(c2) = 1.736e-11 = 1.736e-11 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 1e-11 x 1e-11 = 1e-22 - λ(a2) = λB(a2).λC(a2) = 1e-11 x 1e-11 = 1e-22 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 1e-13) + (0.6 x 9e-13) = 5.43e-13 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 1e-13) + (0.4 x 9e-13) = 4.57e-13 - λ(b1) = λD(b1) = 2e-11 = 2e-11 - λ(b2) = λD(b2) = 2e-11 = 2e-11 - belief change = 5.551115123e-17 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 1e-13) + (0.12 x 9e-13) = 1.32e-13 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 1e-13) + (0.88 x 9e-13) = 8.68e-13 - λ(c1) = λD(c1) = 2e-11 = 2e-11 - λ(c2) = λD(c2) = 2e-11 = 2e-11 - belief change = 0 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 1.086e-11 x 2.64e-12) + (0.7 x 1.086e-11 x 1.736e-11) + (0.45 x 9.14e-12 x 2.64e-12) + (0.22 x 9.14e-12 x 1.736e-11) = 1.83470608e-22 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 1.086e-11 x 2.64e-12) + (0.3 x 1.086e-11 x 1.736e-11) + (0.55 x 9.14e-12 x 2.64e-12) + (0.78 x 9.14e-12 x 1.736e-11) = 2.16529392e-22 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 45 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 1e-22 0.1 - a2 0.09 1e-22 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 1e-13 1e-11 - a2 9e-13 1e-11 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 1e-13 1e-11 - a2 9e-13 1e-11 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 5.43e-13 2e-11 0.543 - b2 4.57e-13 2e-11 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 1.086e-11 2e-11 - b2 9.14e-12 2e-11 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 1.32e-13 2e-11 0.132 - c2 8.68e-13 2e-11 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 2.64e-12 2e-11 - c2 1.736e-11 2e-11 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 1.83470608e-22 1 0.45867652 - d2 2.16529392e-22 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x2e-11 + [(0.97)]x2e-11 = 2e-11 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x2e-11 + [(0.4)]x2e-11 = 2e-11 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x2e-11 + [(0.76)]x2e-11 = 2e-11 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x2e-11 + [(0.88)]x2e-11 = 2e-11 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x2.64e-12) + (0.7x1.736e-11)]x1 + [(0.8x2.64e-12) + (0.3x1.736e-11)]x1 = 2e-11 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x2.64e-12) + (0.22x1.736e-11)]x1 + [(0.55x2.64e-12) + (0.78x1.736e-11)]x1 = 2e-11 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x1.086e-11) + (0.45x9.14e-12)]x1 + [(0.8x1.086e-11) + (0.55x9.14e-12)]x1 = 2e-11 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x1.086e-11) + (0.22x9.14e-12)]x1 + [(0.3x1.086e-11) + (0.78x9.14e-12)]x1 = 2e-11 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 1e-11 = 1e-13 - πB(a2) = π(a2).λC(a2) = 0.09 x 1e-11 = 9e-13 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 1e-11 = 1e-13 - πC(a2) = π(a2).λB(a2) = 0.09 x 1e-11 = 9e-13 -π message B --> D - πD(b1) = π(b1) = 5.43e-13 = 5.43e-13 - πD(b2) = π(b2) = 4.57e-13 = 4.57e-13 -π message C --> D - πD(c1) = π(c1) = 1.32e-13 = 1.32e-13 - πD(c2) = π(c2) = 8.68e-13 = 8.68e-13 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 2e-11 x 2e-11 = 4e-22 - λ(a2) = λB(a2).λC(a2) = 2e-11 x 2e-11 = 4e-22 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 1e-13) + (0.6 x 9e-13) = 5.43e-13 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 1e-13) + (0.4 x 9e-13) = 4.57e-13 - λ(b1) = λD(b1) = 2e-11 = 2e-11 - λ(b2) = λD(b2) = 2e-11 = 2e-11 - belief change = 0 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 1e-13) + (0.12 x 9e-13) = 1.32e-13 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 1e-13) + (0.88 x 9e-13) = 8.68e-13 - λ(c1) = λD(c1) = 2e-11 = 2e-11 - λ(c2) = λD(c2) = 2e-11 = 2e-11 - belief change = 0 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 5.43e-13 x 1.32e-13) + (0.7 x 5.43e-13 x 8.68e-13) + (0.45 x 4.57e-13 x 1.32e-13) + (0.22 x 4.57e-13 x 8.68e-13) = 4.5867652e-25 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 5.43e-13 x 1.32e-13) + (0.3 x 5.43e-13 x 8.68e-13) + (0.55 x 4.57e-13 x 1.32e-13) + (0.78 x 4.57e-13 x 8.68e-13) = 5.4132348e-25 - λ(d1) = 1 - λ(d2) = 1 - belief change = 1.665334537e-16 - - -******************************************************************************** -Iteration 46 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 4e-22 0.1 - a2 0.09 4e-22 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 1e-13 2e-11 - a2 9e-13 2e-11 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 1e-13 2e-11 - a2 9e-13 2e-11 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 5.43e-13 2e-11 0.543 - b2 4.57e-13 2e-11 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 5.43e-13 2e-11 - b2 4.57e-13 2e-11 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 1.32e-13 2e-11 0.132 - c2 8.68e-13 2e-11 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 1.32e-13 2e-11 - c2 8.68e-13 2e-11 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 4.5867652e-25 1 0.45867652 - d2 5.4132348e-25 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x2e-11 + [(0.97)]x2e-11 = 2e-11 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x2e-11 + [(0.4)]x2e-11 = 2e-11 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x2e-11 + [(0.76)]x2e-11 = 2e-11 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x2e-11 + [(0.88)]x2e-11 = 2e-11 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x1.32e-13) + (0.7x8.68e-13)]x1 + [(0.8x1.32e-13) + (0.3x8.68e-13)]x1 = 1e-12 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x1.32e-13) + (0.22x8.68e-13)]x1 + [(0.55x1.32e-13) + (0.78x8.68e-13)]x1 = 1e-12 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x5.43e-13) + (0.45x4.57e-13)]x1 + [(0.8x5.43e-13) + (0.55x4.57e-13)]x1 = 1e-12 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x5.43e-13) + (0.22x4.57e-13)]x1 + [(0.3x5.43e-13) + (0.78x4.57e-13)]x1 = 1e-12 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 2e-11 = 2e-13 - πB(a2) = π(a2).λC(a2) = 0.09 x 2e-11 = 1.8e-12 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 2e-11 = 2e-13 - πC(a2) = π(a2).λB(a2) = 0.09 x 2e-11 = 1.8e-12 -π message B --> D - πD(b1) = π(b1) = 5.43e-13 = 5.43e-13 - πD(b2) = π(b2) = 4.57e-13 = 4.57e-13 -π message C --> D - πD(c1) = π(c1) = 1.32e-13 = 1.32e-13 - πD(c2) = π(c2) = 8.68e-13 = 8.68e-13 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 2e-11 x 2e-11 = 4e-22 - λ(a2) = λB(a2).λC(a2) = 2e-11 x 2e-11 = 4e-22 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 2e-13) + (0.6 x 1.8e-12) = 1.086e-12 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 2e-13) + (0.4 x 1.8e-12) = 9.14e-13 - λ(b1) = λD(b1) = 1e-12 = 1e-12 - λ(b2) = λD(b2) = 1e-12 = 1e-12 - belief change = 2.775557562e-16 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 2e-13) + (0.12 x 1.8e-12) = 2.64e-13 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 2e-13) + (0.88 x 1.8e-12) = 1.736e-12 - λ(c1) = λD(c1) = 1e-12 = 1e-12 - λ(c2) = λD(c2) = 1e-12 = 1e-12 - belief change = 2.775557562e-17 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 5.43e-13 x 1.32e-13) + (0.7 x 5.43e-13 x 8.68e-13) + (0.45 x 4.57e-13 x 1.32e-13) + (0.22 x 4.57e-13 x 8.68e-13) = 4.5867652e-25 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 5.43e-13 x 1.32e-13) + (0.3 x 5.43e-13 x 8.68e-13) + (0.55 x 4.57e-13 x 1.32e-13) + (0.78 x 4.57e-13 x 8.68e-13) = 5.4132348e-25 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 47 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 4e-22 0.1 - a2 0.09 4e-22 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 2e-13 2e-11 - a2 1.8e-12 2e-11 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 2e-13 2e-11 - a2 1.8e-12 2e-11 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 1.086e-12 1e-12 0.543 - b2 9.14e-13 1e-12 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 5.43e-13 1e-12 - b2 4.57e-13 1e-12 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 2.64e-13 1e-12 0.132 - c2 1.736e-12 1e-12 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 1.32e-13 1e-12 - c2 8.68e-13 1e-12 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 4.5867652e-25 1 0.45867652 - d2 5.4132348e-25 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x1e-12 + [(0.97)]x1e-12 = 1e-12 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x1e-12 + [(0.4)]x1e-12 = 1e-12 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x1e-12 + [(0.76)]x1e-12 = 1e-12 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x1e-12 + [(0.88)]x1e-12 = 1e-12 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x1.32e-13) + (0.7x8.68e-13)]x1 + [(0.8x1.32e-13) + (0.3x8.68e-13)]x1 = 1e-12 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x1.32e-13) + (0.22x8.68e-13)]x1 + [(0.55x1.32e-13) + (0.78x8.68e-13)]x1 = 1e-12 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x5.43e-13) + (0.45x4.57e-13)]x1 + [(0.8x5.43e-13) + (0.55x4.57e-13)]x1 = 1e-12 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x5.43e-13) + (0.22x4.57e-13)]x1 + [(0.3x5.43e-13) + (0.78x4.57e-13)]x1 = 1e-12 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 2e-11 = 2e-13 - πB(a2) = π(a2).λC(a2) = 0.09 x 2e-11 = 1.8e-12 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 2e-11 = 2e-13 - πC(a2) = π(a2).λB(a2) = 0.09 x 2e-11 = 1.8e-12 -π message B --> D - πD(b1) = π(b1) = 1.086e-12 = 1.086e-12 - πD(b2) = π(b2) = 9.14e-13 = 9.14e-13 -π message C --> D - πD(c1) = π(c1) = 2.64e-13 = 2.64e-13 - πD(c2) = π(c2) = 1.736e-12 = 1.736e-12 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 1e-12 x 1e-12 = 1e-24 - λ(a2) = λB(a2).λC(a2) = 1e-12 x 1e-12 = 1e-24 - belief change = 1.110223025e-16 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 2e-13) + (0.6 x 1.8e-12) = 1.086e-12 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 2e-13) + (0.4 x 1.8e-12) = 9.14e-13 - λ(b1) = λD(b1) = 1e-12 = 1e-12 - λ(b2) = λD(b2) = 1e-12 = 1e-12 - belief change = 0 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 2e-13) + (0.12 x 1.8e-12) = 2.64e-13 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 2e-13) + (0.88 x 1.8e-12) = 1.736e-12 - λ(c1) = λD(c1) = 1e-12 = 1e-12 - λ(c2) = λD(c2) = 1e-12 = 1e-12 - belief change = 0 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 1.086e-12 x 2.64e-13) + (0.7 x 1.086e-12 x 1.736e-12) + (0.45 x 9.14e-13 x 2.64e-13) + (0.22 x 9.14e-13 x 1.736e-12) = 1.83470608e-24 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 1.086e-12 x 2.64e-13) + (0.3 x 1.086e-12 x 1.736e-12) + (0.55 x 9.14e-13 x 2.64e-13) + (0.78 x 9.14e-13 x 1.736e-12) = 2.16529392e-24 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 48 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 1e-24 0.1 - a2 0.09 1e-24 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 2e-13 1e-12 - a2 1.8e-12 1e-12 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 2e-13 1e-12 - a2 1.8e-12 1e-12 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 1.086e-12 1e-12 0.543 - b2 9.14e-13 1e-12 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 1.086e-12 1e-12 - b2 9.14e-13 1e-12 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 2.64e-13 1e-12 0.132 - c2 1.736e-12 1e-12 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 2.64e-13 1e-12 - c2 1.736e-12 1e-12 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 1.83470608e-24 1 0.45867652 - d2 2.16529392e-24 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x1e-12 + [(0.97)]x1e-12 = 1e-12 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x1e-12 + [(0.4)]x1e-12 = 1e-12 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x1e-12 + [(0.76)]x1e-12 = 1e-12 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x1e-12 + [(0.88)]x1e-12 = 1e-12 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x2.64e-13) + (0.7x1.736e-12)]x1 + [(0.8x2.64e-13) + (0.3x1.736e-12)]x1 = 2e-12 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x2.64e-13) + (0.22x1.736e-12)]x1 + [(0.55x2.64e-13) + (0.78x1.736e-12)]x1 = 2e-12 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x1.086e-12) + (0.45x9.14e-13)]x1 + [(0.8x1.086e-12) + (0.55x9.14e-13)]x1 = 2e-12 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x1.086e-12) + (0.22x9.14e-13)]x1 + [(0.3x1.086e-12) + (0.78x9.14e-13)]x1 = 2e-12 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 1e-12 = 1e-14 - πB(a2) = π(a2).λC(a2) = 0.09 x 1e-12 = 9e-14 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 1e-12 = 1e-14 - πC(a2) = π(a2).λB(a2) = 0.09 x 1e-12 = 9e-14 -π message B --> D - πD(b1) = π(b1) = 1.086e-12 = 1.086e-12 - πD(b2) = π(b2) = 9.14e-13 = 9.14e-13 -π message C --> D - πD(c1) = π(c1) = 2.64e-13 = 2.64e-13 - πD(c2) = π(c2) = 1.736e-12 = 1.736e-12 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 1e-12 x 1e-12 = 1e-24 - λ(a2) = λB(a2).λC(a2) = 1e-12 x 1e-12 = 1e-24 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 1e-14) + (0.6 x 9e-14) = 5.43e-14 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 1e-14) + (0.4 x 9e-14) = 4.57e-14 - λ(b1) = λD(b1) = 2e-12 = 2e-12 - λ(b2) = λD(b2) = 2e-12 = 2e-12 - belief change = 0 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 1e-14) + (0.12 x 9e-14) = 1.32e-14 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 1e-14) + (0.88 x 9e-14) = 8.68e-14 - λ(c1) = λD(c1) = 2e-12 = 2e-12 - λ(c2) = λD(c2) = 2e-12 = 2e-12 - belief change = 1.387778781e-16 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 1.086e-12 x 2.64e-13) + (0.7 x 1.086e-12 x 1.736e-12) + (0.45 x 9.14e-13 x 2.64e-13) + (0.22 x 9.14e-13 x 1.736e-12) = 1.83470608e-24 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 1.086e-12 x 2.64e-13) + (0.3 x 1.086e-12 x 1.736e-12) + (0.55 x 9.14e-13 x 2.64e-13) + (0.78 x 9.14e-13 x 1.736e-12) = 2.16529392e-24 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 49 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 1e-24 0.1 - a2 0.09 1e-24 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 1e-14 1e-12 - a2 9e-14 1e-12 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 1e-14 1e-12 - a2 9e-14 1e-12 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 5.43e-14 2e-12 0.543 - b2 4.57e-14 2e-12 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 1.086e-12 2e-12 - b2 9.14e-13 2e-12 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 1.32e-14 2e-12 0.132 - c2 8.68e-14 2e-12 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 2.64e-13 2e-12 - c2 1.736e-12 2e-12 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 1.83470608e-24 1 0.45867652 - d2 2.16529392e-24 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x2e-12 + [(0.97)]x2e-12 = 2e-12 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x2e-12 + [(0.4)]x2e-12 = 2e-12 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x2e-12 + [(0.76)]x2e-12 = 2e-12 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x2e-12 + [(0.88)]x2e-12 = 2e-12 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x2.64e-13) + (0.7x1.736e-12)]x1 + [(0.8x2.64e-13) + (0.3x1.736e-12)]x1 = 2e-12 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x2.64e-13) + (0.22x1.736e-12)]x1 + [(0.55x2.64e-13) + (0.78x1.736e-12)]x1 = 2e-12 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x1.086e-12) + (0.45x9.14e-13)]x1 + [(0.8x1.086e-12) + (0.55x9.14e-13)]x1 = 2e-12 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x1.086e-12) + (0.22x9.14e-13)]x1 + [(0.3x1.086e-12) + (0.78x9.14e-13)]x1 = 2e-12 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 1e-12 = 1e-14 - πB(a2) = π(a2).λC(a2) = 0.09 x 1e-12 = 9e-14 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 1e-12 = 1e-14 - πC(a2) = π(a2).λB(a2) = 0.09 x 1e-12 = 9e-14 -π message B --> D - πD(b1) = π(b1) = 5.43e-14 = 5.43e-14 - πD(b2) = π(b2) = 4.57e-14 = 4.57e-14 -π message C --> D - πD(c1) = π(c1) = 1.32e-14 = 1.32e-14 - πD(c2) = π(c2) = 8.68e-14 = 8.68e-14 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 2e-12 x 2e-12 = 4e-24 - λ(a2) = λB(a2).λC(a2) = 2e-12 x 2e-12 = 4e-24 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 1e-14) + (0.6 x 9e-14) = 5.43e-14 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 1e-14) + (0.4 x 9e-14) = 4.57e-14 - λ(b1) = λD(b1) = 2e-12 = 2e-12 - λ(b2) = λD(b2) = 2e-12 = 2e-12 - belief change = 0 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 1e-14) + (0.12 x 9e-14) = 1.32e-14 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 1e-14) + (0.88 x 9e-14) = 8.68e-14 - λ(c1) = λD(c1) = 2e-12 = 2e-12 - λ(c2) = λD(c2) = 2e-12 = 2e-12 - belief change = 0 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 5.43e-14 x 1.32e-14) + (0.7 x 5.43e-14 x 8.68e-14) + (0.45 x 4.57e-14 x 1.32e-14) + (0.22 x 4.57e-14 x 8.68e-14) = 4.5867652e-27 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 5.43e-14 x 1.32e-14) + (0.3 x 5.43e-14 x 8.68e-14) + (0.55 x 4.57e-14 x 1.32e-14) + (0.78 x 4.57e-14 x 8.68e-14) = 5.4132348e-27 - λ(d1) = 1 - λ(d2) = 1 - belief change = 1.110223025e-16 - - -******************************************************************************** -Iteration 50 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 4e-24 0.1 - a2 0.09 4e-24 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 1e-14 2e-12 - a2 9e-14 2e-12 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 1e-14 2e-12 - a2 9e-14 2e-12 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 5.43e-14 2e-12 0.543 - b2 4.57e-14 2e-12 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 5.43e-14 2e-12 - b2 4.57e-14 2e-12 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 1.32e-14 2e-12 0.132 - c2 8.68e-14 2e-12 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 1.32e-14 2e-12 - c2 8.68e-14 2e-12 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 4.5867652e-27 1 0.45867652 - d2 5.4132348e-27 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x2e-12 + [(0.97)]x2e-12 = 2e-12 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x2e-12 + [(0.4)]x2e-12 = 2e-12 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x2e-12 + [(0.76)]x2e-12 = 2e-12 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x2e-12 + [(0.88)]x2e-12 = 2e-12 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x1.32e-14) + (0.7x8.68e-14)]x1 + [(0.8x1.32e-14) + (0.3x8.68e-14)]x1 = 1e-13 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x1.32e-14) + (0.22x8.68e-14)]x1 + [(0.55x1.32e-14) + (0.78x8.68e-14)]x1 = 1e-13 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x5.43e-14) + (0.45x4.57e-14)]x1 + [(0.8x5.43e-14) + (0.55x4.57e-14)]x1 = 1e-13 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x5.43e-14) + (0.22x4.57e-14)]x1 + [(0.3x5.43e-14) + (0.78x4.57e-14)]x1 = 1e-13 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 2e-12 = 2e-14 - πB(a2) = π(a2).λC(a2) = 0.09 x 2e-12 = 1.8e-13 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 2e-12 = 2e-14 - πC(a2) = π(a2).λB(a2) = 0.09 x 2e-12 = 1.8e-13 -π message B --> D - πD(b1) = π(b1) = 5.43e-14 = 5.43e-14 - πD(b2) = π(b2) = 4.57e-14 = 4.57e-14 -π message C --> D - πD(c1) = π(c1) = 1.32e-14 = 1.32e-14 - πD(c2) = π(c2) = 8.68e-14 = 8.68e-14 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 2e-12 x 2e-12 = 4e-24 - λ(a2) = λB(a2).λC(a2) = 2e-12 x 2e-12 = 4e-24 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 2e-14) + (0.6 x 1.8e-13) = 1.086e-13 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 2e-14) + (0.4 x 1.8e-13) = 9.14e-14 - λ(b1) = λD(b1) = 1e-13 = 1e-13 - λ(b2) = λD(b2) = 1e-13 = 1e-13 - belief change = 1.665334537e-16 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 2e-14) + (0.12 x 1.8e-13) = 2.64e-14 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 2e-14) + (0.88 x 1.8e-13) = 1.736e-13 - λ(c1) = λD(c1) = 1e-13 = 1e-13 - λ(c2) = λD(c2) = 1e-13 = 1e-13 - belief change = 1.110223025e-16 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 5.43e-14 x 1.32e-14) + (0.7 x 5.43e-14 x 8.68e-14) + (0.45 x 4.57e-14 x 1.32e-14) + (0.22 x 4.57e-14 x 8.68e-14) = 4.5867652e-27 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 5.43e-14 x 1.32e-14) + (0.3 x 5.43e-14 x 8.68e-14) + (0.55 x 4.57e-14 x 1.32e-14) + (0.78 x 4.57e-14 x 8.68e-14) = 5.4132348e-27 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 51 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 4e-24 0.1 - a2 0.09 4e-24 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 2e-14 2e-12 - a2 1.8e-13 2e-12 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 2e-14 2e-12 - a2 1.8e-13 2e-12 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 1.086e-13 1e-13 0.543 - b2 9.14e-14 1e-13 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 5.43e-14 1e-13 - b2 4.57e-14 1e-13 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 2.64e-14 1e-13 0.132 - c2 1.736e-13 1e-13 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 1.32e-14 1e-13 - c2 8.68e-14 1e-13 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 4.5867652e-27 1 0.45867652 - d2 5.4132348e-27 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x1e-13 + [(0.97)]x1e-13 = 1e-13 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x1e-13 + [(0.4)]x1e-13 = 1e-13 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x1e-13 + [(0.76)]x1e-13 = 1e-13 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x1e-13 + [(0.88)]x1e-13 = 1e-13 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x1.32e-14) + (0.7x8.68e-14)]x1 + [(0.8x1.32e-14) + (0.3x8.68e-14)]x1 = 1e-13 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x1.32e-14) + (0.22x8.68e-14)]x1 + [(0.55x1.32e-14) + (0.78x8.68e-14)]x1 = 1e-13 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x5.43e-14) + (0.45x4.57e-14)]x1 + [(0.8x5.43e-14) + (0.55x4.57e-14)]x1 = 1e-13 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x5.43e-14) + (0.22x4.57e-14)]x1 + [(0.3x5.43e-14) + (0.78x4.57e-14)]x1 = 1e-13 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 2e-12 = 2e-14 - πB(a2) = π(a2).λC(a2) = 0.09 x 2e-12 = 1.8e-13 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 2e-12 = 2e-14 - πC(a2) = π(a2).λB(a2) = 0.09 x 2e-12 = 1.8e-13 -π message B --> D - πD(b1) = π(b1) = 1.086e-13 = 1.086e-13 - πD(b2) = π(b2) = 9.14e-14 = 9.14e-14 -π message C --> D - πD(c1) = π(c1) = 2.64e-14 = 2.64e-14 - πD(c2) = π(c2) = 1.736e-13 = 1.736e-13 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 1e-13 x 1e-13 = 1e-26 - λ(a2) = λB(a2).λC(a2) = 1e-13 x 1e-13 = 1e-26 - belief change = 1.387778781e-16 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 2e-14) + (0.6 x 1.8e-13) = 1.086e-13 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 2e-14) + (0.4 x 1.8e-13) = 9.14e-14 - λ(b1) = λD(b1) = 1e-13 = 1e-13 - λ(b2) = λD(b2) = 1e-13 = 1e-13 - belief change = 0 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 2e-14) + (0.12 x 1.8e-13) = 2.64e-14 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 2e-14) + (0.88 x 1.8e-13) = 1.736e-13 - λ(c1) = λD(c1) = 1e-13 = 1e-13 - λ(c2) = λD(c2) = 1e-13 = 1e-13 - belief change = 0 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 1.086e-13 x 2.64e-14) + (0.7 x 1.086e-13 x 1.736e-13) + (0.45 x 9.14e-14 x 2.64e-14) + (0.22 x 9.14e-14 x 1.736e-13) = 1.83470608e-26 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 1.086e-13 x 2.64e-14) + (0.3 x 1.086e-13 x 1.736e-13) + (0.55 x 9.14e-14 x 2.64e-14) + (0.78 x 9.14e-14 x 1.736e-13) = 2.16529392e-26 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 52 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 1e-26 0.1 - a2 0.09 1e-26 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 2e-14 1e-13 - a2 1.8e-13 1e-13 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 2e-14 1e-13 - a2 1.8e-13 1e-13 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 1.086e-13 1e-13 0.543 - b2 9.14e-14 1e-13 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 1.086e-13 1e-13 - b2 9.14e-14 1e-13 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 2.64e-14 1e-13 0.132 - c2 1.736e-13 1e-13 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 2.64e-14 1e-13 - c2 1.736e-13 1e-13 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 1.83470608e-26 1 0.45867652 - d2 2.16529392e-26 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x1e-13 + [(0.97)]x1e-13 = 1e-13 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x1e-13 + [(0.4)]x1e-13 = 1e-13 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x1e-13 + [(0.76)]x1e-13 = 1e-13 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x1e-13 + [(0.88)]x1e-13 = 1e-13 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x2.64e-14) + (0.7x1.736e-13)]x1 + [(0.8x2.64e-14) + (0.3x1.736e-13)]x1 = 2e-13 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x2.64e-14) + (0.22x1.736e-13)]x1 + [(0.55x2.64e-14) + (0.78x1.736e-13)]x1 = 2e-13 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x1.086e-13) + (0.45x9.14e-14)]x1 + [(0.8x1.086e-13) + (0.55x9.14e-14)]x1 = 2e-13 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x1.086e-13) + (0.22x9.14e-14)]x1 + [(0.3x1.086e-13) + (0.78x9.14e-14)]x1 = 2e-13 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 1e-13 = 1e-15 - πB(a2) = π(a2).λC(a2) = 0.09 x 1e-13 = 9e-15 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 1e-13 = 1e-15 - πC(a2) = π(a2).λB(a2) = 0.09 x 1e-13 = 9e-15 -π message B --> D - πD(b1) = π(b1) = 1.086e-13 = 1.086e-13 - πD(b2) = π(b2) = 9.14e-14 = 9.14e-14 -π message C --> D - πD(c1) = π(c1) = 2.64e-14 = 2.64e-14 - πD(c2) = π(c2) = 1.736e-13 = 1.736e-13 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 1e-13 x 1e-13 = 1e-26 - λ(a2) = λB(a2).λC(a2) = 1e-13 x 1e-13 = 1e-26 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 1e-15) + (0.6 x 9e-15) = 5.43e-15 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 1e-15) + (0.4 x 9e-15) = 4.57e-15 - λ(b1) = λD(b1) = 2e-13 = 2e-13 - λ(b2) = λD(b2) = 2e-13 = 2e-13 - belief change = 1.665334537e-16 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 1e-15) + (0.12 x 9e-15) = 1.32e-15 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 1e-15) + (0.88 x 9e-15) = 8.68e-15 - λ(c1) = λD(c1) = 2e-13 = 2e-13 - λ(c2) = λD(c2) = 2e-13 = 2e-13 - belief change = 1.387778781e-16 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 1.086e-13 x 2.64e-14) + (0.7 x 1.086e-13 x 1.736e-13) + (0.45 x 9.14e-14 x 2.64e-14) + (0.22 x 9.14e-14 x 1.736e-13) = 1.83470608e-26 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 1.086e-13 x 2.64e-14) + (0.3 x 1.086e-13 x 1.736e-13) + (0.55 x 9.14e-14 x 2.64e-14) + (0.78 x 9.14e-14 x 1.736e-13) = 2.16529392e-26 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 53 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 1e-26 0.1 - a2 0.09 1e-26 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 1e-15 1e-13 - a2 9e-15 1e-13 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 1e-15 1e-13 - a2 9e-15 1e-13 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 5.43e-15 2e-13 0.543 - b2 4.57e-15 2e-13 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 1.086e-13 2e-13 - b2 9.14e-14 2e-13 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 1.32e-15 2e-13 0.132 - c2 8.68e-15 2e-13 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 2.64e-14 2e-13 - c2 1.736e-13 2e-13 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 1.83470608e-26 1 0.45867652 - d2 2.16529392e-26 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x2e-13 + [(0.97)]x2e-13 = 2e-13 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x2e-13 + [(0.4)]x2e-13 = 2e-13 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x2e-13 + [(0.76)]x2e-13 = 2e-13 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x2e-13 + [(0.88)]x2e-13 = 2e-13 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x2.64e-14) + (0.7x1.736e-13)]x1 + [(0.8x2.64e-14) + (0.3x1.736e-13)]x1 = 2e-13 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x2.64e-14) + (0.22x1.736e-13)]x1 + [(0.55x2.64e-14) + (0.78x1.736e-13)]x1 = 2e-13 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x1.086e-13) + (0.45x9.14e-14)]x1 + [(0.8x1.086e-13) + (0.55x9.14e-14)]x1 = 2e-13 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x1.086e-13) + (0.22x9.14e-14)]x1 + [(0.3x1.086e-13) + (0.78x9.14e-14)]x1 = 2e-13 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 1e-13 = 1e-15 - πB(a2) = π(a2).λC(a2) = 0.09 x 1e-13 = 9e-15 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 1e-13 = 1e-15 - πC(a2) = π(a2).λB(a2) = 0.09 x 1e-13 = 9e-15 -π message B --> D - πD(b1) = π(b1) = 5.43e-15 = 5.43e-15 - πD(b2) = π(b2) = 4.57e-15 = 4.57e-15 -π message C --> D - πD(c1) = π(c1) = 1.32e-15 = 1.32e-15 - πD(c2) = π(c2) = 8.68e-15 = 8.68e-15 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 2e-13 x 2e-13 = 4e-26 - λ(a2) = λB(a2).λC(a2) = 2e-13 x 2e-13 = 4e-26 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 1e-15) + (0.6 x 9e-15) = 5.43e-15 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 1e-15) + (0.4 x 9e-15) = 4.57e-15 - λ(b1) = λD(b1) = 2e-13 = 2e-13 - λ(b2) = λD(b2) = 2e-13 = 2e-13 - belief change = 0 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 1e-15) + (0.12 x 9e-15) = 1.32e-15 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 1e-15) + (0.88 x 9e-15) = 8.68e-15 - λ(c1) = λD(c1) = 2e-13 = 2e-13 - λ(c2) = λD(c2) = 2e-13 = 2e-13 - belief change = 0 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 5.43e-15 x 1.32e-15) + (0.7 x 5.43e-15 x 8.68e-15) + (0.45 x 4.57e-15 x 1.32e-15) + (0.22 x 4.57e-15 x 8.68e-15) = 4.5867652e-29 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 5.43e-15 x 1.32e-15) + (0.3 x 5.43e-15 x 8.68e-15) + (0.55 x 4.57e-15 x 1.32e-15) + (0.78 x 4.57e-15 x 8.68e-15) = 5.4132348e-29 - λ(d1) = 1 - λ(d2) = 1 - belief change = 1.110223025e-16 - - -******************************************************************************** -Iteration 54 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 4e-26 0.1 - a2 0.09 4e-26 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 1e-15 2e-13 - a2 9e-15 2e-13 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 1e-15 2e-13 - a2 9e-15 2e-13 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 5.43e-15 2e-13 0.543 - b2 4.57e-15 2e-13 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 5.43e-15 2e-13 - b2 4.57e-15 2e-13 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 1.32e-15 2e-13 0.132 - c2 8.68e-15 2e-13 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 1.32e-15 2e-13 - c2 8.68e-15 2e-13 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 4.5867652e-29 1 0.45867652 - d2 5.4132348e-29 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x2e-13 + [(0.97)]x2e-13 = 2e-13 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x2e-13 + [(0.4)]x2e-13 = 2e-13 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x2e-13 + [(0.76)]x2e-13 = 2e-13 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x2e-13 + [(0.88)]x2e-13 = 2e-13 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x1.32e-15) + (0.7x8.68e-15)]x1 + [(0.8x1.32e-15) + (0.3x8.68e-15)]x1 = 1e-14 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x1.32e-15) + (0.22x8.68e-15)]x1 + [(0.55x1.32e-15) + (0.78x8.68e-15)]x1 = 1e-14 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x5.43e-15) + (0.45x4.57e-15)]x1 + [(0.8x5.43e-15) + (0.55x4.57e-15)]x1 = 1e-14 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x5.43e-15) + (0.22x4.57e-15)]x1 + [(0.3x5.43e-15) + (0.78x4.57e-15)]x1 = 1e-14 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 2e-13 = 2e-15 - πB(a2) = π(a2).λC(a2) = 0.09 x 2e-13 = 1.8e-14 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 2e-13 = 2e-15 - πC(a2) = π(a2).λB(a2) = 0.09 x 2e-13 = 1.8e-14 -π message B --> D - πD(b1) = π(b1) = 5.43e-15 = 5.43e-15 - πD(b2) = π(b2) = 4.57e-15 = 4.57e-15 -π message C --> D - πD(c1) = π(c1) = 1.32e-15 = 1.32e-15 - πD(c2) = π(c2) = 8.68e-15 = 8.68e-15 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 2e-13 x 2e-13 = 4e-26 - λ(a2) = λB(a2).λC(a2) = 2e-13 x 2e-13 = 4e-26 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 2e-15) + (0.6 x 1.8e-14) = 1.086e-14 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 2e-15) + (0.4 x 1.8e-14) = 9.14e-15 - λ(b1) = λD(b1) = 1e-14 = 1e-14 - λ(b2) = λD(b2) = 1e-14 = 1e-14 - belief change = 3.330669074e-16 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 2e-15) + (0.12 x 1.8e-14) = 2.64e-15 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 2e-15) + (0.88 x 1.8e-14) = 1.736e-14 - λ(c1) = λD(c1) = 1e-14 = 1e-14 - λ(c2) = λD(c2) = 1e-14 = 1e-14 - belief change = 1.110223025e-16 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 5.43e-15 x 1.32e-15) + (0.7 x 5.43e-15 x 8.68e-15) + (0.45 x 4.57e-15 x 1.32e-15) + (0.22 x 4.57e-15 x 8.68e-15) = 4.5867652e-29 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 5.43e-15 x 1.32e-15) + (0.3 x 5.43e-15 x 8.68e-15) + (0.55 x 4.57e-15 x 1.32e-15) + (0.78 x 4.57e-15 x 8.68e-15) = 5.4132348e-29 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 55 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 4e-26 0.1 - a2 0.09 4e-26 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 2e-15 2e-13 - a2 1.8e-14 2e-13 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 2e-15 2e-13 - a2 1.8e-14 2e-13 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 1.086e-14 1e-14 0.543 - b2 9.14e-15 1e-14 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 5.43e-15 1e-14 - b2 4.57e-15 1e-14 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 2.64e-15 1e-14 0.132 - c2 1.736e-14 1e-14 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 1.32e-15 1e-14 - c2 8.68e-15 1e-14 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 4.5867652e-29 1 0.45867652 - d2 5.4132348e-29 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x1e-14 + [(0.97)]x1e-14 = 1e-14 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x1e-14 + [(0.4)]x1e-14 = 1e-14 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x1e-14 + [(0.76)]x1e-14 = 1e-14 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x1e-14 + [(0.88)]x1e-14 = 1e-14 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x1.32e-15) + (0.7x8.68e-15)]x1 + [(0.8x1.32e-15) + (0.3x8.68e-15)]x1 = 1e-14 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x1.32e-15) + (0.22x8.68e-15)]x1 + [(0.55x1.32e-15) + (0.78x8.68e-15)]x1 = 1e-14 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x5.43e-15) + (0.45x4.57e-15)]x1 + [(0.8x5.43e-15) + (0.55x4.57e-15)]x1 = 1e-14 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x5.43e-15) + (0.22x4.57e-15)]x1 + [(0.3x5.43e-15) + (0.78x4.57e-15)]x1 = 1e-14 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 2e-13 = 2e-15 - πB(a2) = π(a2).λC(a2) = 0.09 x 2e-13 = 1.8e-14 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 2e-13 = 2e-15 - πC(a2) = π(a2).λB(a2) = 0.09 x 2e-13 = 1.8e-14 -π message B --> D - πD(b1) = π(b1) = 1.086e-14 = 1.086e-14 - πD(b2) = π(b2) = 9.14e-15 = 9.14e-15 -π message C --> D - πD(c1) = π(c1) = 2.64e-15 = 2.64e-15 - πD(c2) = π(c2) = 1.736e-14 = 1.736e-14 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 1e-14 x 1e-14 = 1e-28 - λ(a2) = λB(a2).λC(a2) = 1e-14 x 1e-14 = 1e-28 - belief change = 1.526556659e-16 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 2e-15) + (0.6 x 1.8e-14) = 1.086e-14 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 2e-15) + (0.4 x 1.8e-14) = 9.14e-15 - λ(b1) = λD(b1) = 1e-14 = 1e-14 - λ(b2) = λD(b2) = 1e-14 = 1e-14 - belief change = 0 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 2e-15) + (0.12 x 1.8e-14) = 2.64e-15 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 2e-15) + (0.88 x 1.8e-14) = 1.736e-14 - λ(c1) = λD(c1) = 1e-14 = 1e-14 - λ(c2) = λD(c2) = 1e-14 = 1e-14 - belief change = 0 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 1.086e-14 x 2.64e-15) + (0.7 x 1.086e-14 x 1.736e-14) + (0.45 x 9.14e-15 x 2.64e-15) + (0.22 x 9.14e-15 x 1.736e-14) = 1.83470608e-28 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 1.086e-14 x 2.64e-15) + (0.3 x 1.086e-14 x 1.736e-14) + (0.55 x 9.14e-15 x 2.64e-15) + (0.78 x 9.14e-15 x 1.736e-14) = 2.16529392e-28 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 56 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 1e-28 0.1 - a2 0.09 1e-28 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 2e-15 1e-14 - a2 1.8e-14 1e-14 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 2e-15 1e-14 - a2 1.8e-14 1e-14 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 1.086e-14 1e-14 0.543 - b2 9.14e-15 1e-14 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 1.086e-14 1e-14 - b2 9.14e-15 1e-14 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 2.64e-15 1e-14 0.132 - c2 1.736e-14 1e-14 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 2.64e-15 1e-14 - c2 1.736e-14 1e-14 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 1.83470608e-28 1 0.45867652 - d2 2.16529392e-28 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x1e-14 + [(0.97)]x1e-14 = 1e-14 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x1e-14 + [(0.4)]x1e-14 = 1e-14 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x1e-14 + [(0.76)]x1e-14 = 1e-14 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x1e-14 + [(0.88)]x1e-14 = 1e-14 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x2.64e-15) + (0.7x1.736e-14)]x1 + [(0.8x2.64e-15) + (0.3x1.736e-14)]x1 = 2e-14 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x2.64e-15) + (0.22x1.736e-14)]x1 + [(0.55x2.64e-15) + (0.78x1.736e-14)]x1 = 2e-14 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x1.086e-14) + (0.45x9.14e-15)]x1 + [(0.8x1.086e-14) + (0.55x9.14e-15)]x1 = 2e-14 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x1.086e-14) + (0.22x9.14e-15)]x1 + [(0.3x1.086e-14) + (0.78x9.14e-15)]x1 = 2e-14 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 1e-14 = 1e-16 - πB(a2) = π(a2).λC(a2) = 0.09 x 1e-14 = 9e-16 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 1e-14 = 1e-16 - πC(a2) = π(a2).λB(a2) = 0.09 x 1e-14 = 9e-16 -π message B --> D - πD(b1) = π(b1) = 1.086e-14 = 1.086e-14 - πD(b2) = π(b2) = 9.14e-15 = 9.14e-15 -π message C --> D - πD(c1) = π(c1) = 2.64e-15 = 2.64e-15 - πD(c2) = π(c2) = 1.736e-14 = 1.736e-14 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 1e-14 x 1e-14 = 1e-28 - λ(a2) = λB(a2).λC(a2) = 1e-14 x 1e-14 = 1e-28 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 1e-16) + (0.6 x 9e-16) = 5.43e-16 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 1e-16) + (0.4 x 9e-16) = 4.57e-16 - λ(b1) = λD(b1) = 2e-14 = 2e-14 - λ(b2) = λD(b2) = 2e-14 = 2e-14 - belief change = 1.110223025e-16 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 1e-16) + (0.12 x 9e-16) = 1.32e-16 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 1e-16) + (0.88 x 9e-16) = 8.68e-16 - λ(c1) = λD(c1) = 2e-14 = 2e-14 - λ(c2) = λD(c2) = 2e-14 = 2e-14 - belief change = 0 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 1.086e-14 x 2.64e-15) + (0.7 x 1.086e-14 x 1.736e-14) + (0.45 x 9.14e-15 x 2.64e-15) + (0.22 x 9.14e-15 x 1.736e-14) = 1.83470608e-28 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 1.086e-14 x 2.64e-15) + (0.3 x 1.086e-14 x 1.736e-14) + (0.55 x 9.14e-15 x 2.64e-15) + (0.78 x 9.14e-15 x 1.736e-14) = 2.16529392e-28 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 57 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 1e-28 0.1 - a2 0.09 1e-28 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 1e-16 1e-14 - a2 9e-16 1e-14 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 1e-16 1e-14 - a2 9e-16 1e-14 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 5.43e-16 2e-14 0.543 - b2 4.57e-16 2e-14 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 1.086e-14 2e-14 - b2 9.14e-15 2e-14 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 1.32e-16 2e-14 0.132 - c2 8.68e-16 2e-14 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 2.64e-15 2e-14 - c2 1.736e-14 2e-14 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 1.83470608e-28 1 0.45867652 - d2 2.16529392e-28 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x2e-14 + [(0.97)]x2e-14 = 2e-14 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x2e-14 + [(0.4)]x2e-14 = 2e-14 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x2e-14 + [(0.76)]x2e-14 = 2e-14 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x2e-14 + [(0.88)]x2e-14 = 2e-14 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x2.64e-15) + (0.7x1.736e-14)]x1 + [(0.8x2.64e-15) + (0.3x1.736e-14)]x1 = 2e-14 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x2.64e-15) + (0.22x1.736e-14)]x1 + [(0.55x2.64e-15) + (0.78x1.736e-14)]x1 = 2e-14 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x1.086e-14) + (0.45x9.14e-15)]x1 + [(0.8x1.086e-14) + (0.55x9.14e-15)]x1 = 2e-14 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x1.086e-14) + (0.22x9.14e-15)]x1 + [(0.3x1.086e-14) + (0.78x9.14e-15)]x1 = 2e-14 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 1e-14 = 1e-16 - πB(a2) = π(a2).λC(a2) = 0.09 x 1e-14 = 9e-16 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 1e-14 = 1e-16 - πC(a2) = π(a2).λB(a2) = 0.09 x 1e-14 = 9e-16 -π message B --> D - πD(b1) = π(b1) = 5.43e-16 = 5.43e-16 - πD(b2) = π(b2) = 4.57e-16 = 4.57e-16 -π message C --> D - πD(c1) = π(c1) = 1.32e-16 = 1.32e-16 - πD(c2) = π(c2) = 8.68e-16 = 8.68e-16 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 2e-14 x 2e-14 = 4e-28 - λ(a2) = λB(a2).λC(a2) = 2e-14 x 2e-14 = 4e-28 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 1e-16) + (0.6 x 9e-16) = 5.43e-16 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 1e-16) + (0.4 x 9e-16) = 4.57e-16 - λ(b1) = λD(b1) = 2e-14 = 2e-14 - λ(b2) = λD(b2) = 2e-14 = 2e-14 - belief change = 0 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 1e-16) + (0.12 x 9e-16) = 1.32e-16 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 1e-16) + (0.88 x 9e-16) = 8.68e-16 - λ(c1) = λD(c1) = 2e-14 = 2e-14 - λ(c2) = λD(c2) = 2e-14 = 2e-14 - belief change = 0 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 5.43e-16 x 1.32e-16) + (0.7 x 5.43e-16 x 8.68e-16) + (0.45 x 4.57e-16 x 1.32e-16) + (0.22 x 4.57e-16 x 8.68e-16) = 4.5867652e-31 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 5.43e-16 x 1.32e-16) + (0.3 x 5.43e-16 x 8.68e-16) + (0.55 x 4.57e-16 x 1.32e-16) + (0.78 x 4.57e-16 x 8.68e-16) = 5.4132348e-31 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 58 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 4e-28 0.1 - a2 0.09 4e-28 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 1e-16 2e-14 - a2 9e-16 2e-14 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 1e-16 2e-14 - a2 9e-16 2e-14 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 5.43e-16 2e-14 0.543 - b2 4.57e-16 2e-14 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 5.43e-16 2e-14 - b2 4.57e-16 2e-14 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 1.32e-16 2e-14 0.132 - c2 8.68e-16 2e-14 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 1.32e-16 2e-14 - c2 8.68e-16 2e-14 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 4.5867652e-31 1 0.45867652 - d2 5.4132348e-31 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x2e-14 + [(0.97)]x2e-14 = 2e-14 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x2e-14 + [(0.4)]x2e-14 = 2e-14 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x2e-14 + [(0.76)]x2e-14 = 2e-14 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x2e-14 + [(0.88)]x2e-14 = 2e-14 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x1.32e-16) + (0.7x8.68e-16)]x1 + [(0.8x1.32e-16) + (0.3x8.68e-16)]x1 = 1e-15 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x1.32e-16) + (0.22x8.68e-16)]x1 + [(0.55x1.32e-16) + (0.78x8.68e-16)]x1 = 1e-15 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x5.43e-16) + (0.45x4.57e-16)]x1 + [(0.8x5.43e-16) + (0.55x4.57e-16)]x1 = 1e-15 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x5.43e-16) + (0.22x4.57e-16)]x1 + [(0.3x5.43e-16) + (0.78x4.57e-16)]x1 = 1e-15 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 2e-14 = 2e-16 - πB(a2) = π(a2).λC(a2) = 0.09 x 2e-14 = 1.8e-15 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 2e-14 = 2e-16 - πC(a2) = π(a2).λB(a2) = 0.09 x 2e-14 = 1.8e-15 -π message B --> D - πD(b1) = π(b1) = 5.43e-16 = 5.43e-16 - πD(b2) = π(b2) = 4.57e-16 = 4.57e-16 -π message C --> D - πD(c1) = π(c1) = 1.32e-16 = 1.32e-16 - πD(c2) = π(c2) = 8.68e-16 = 8.68e-16 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 2e-14 x 2e-14 = 4e-28 - λ(a2) = λB(a2).λC(a2) = 2e-14 x 2e-14 = 4e-28 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 2e-16) + (0.6 x 1.8e-15) = 1.086e-15 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 2e-16) + (0.4 x 1.8e-15) = 9.14e-16 - λ(b1) = λD(b1) = 1e-15 = 1e-15 - λ(b2) = λD(b2) = 1e-15 = 1e-15 - belief change = 5.551115123e-17 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 2e-16) + (0.12 x 1.8e-15) = 2.64e-16 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 2e-16) + (0.88 x 1.8e-15) = 1.736e-15 - λ(c1) = λD(c1) = 1e-15 = 1e-15 - λ(c2) = λD(c2) = 1e-15 = 1e-15 - belief change = 1.387778781e-16 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 5.43e-16 x 1.32e-16) + (0.7 x 5.43e-16 x 8.68e-16) + (0.45 x 4.57e-16 x 1.32e-16) + (0.22 x 4.57e-16 x 8.68e-16) = 4.5867652e-31 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 5.43e-16 x 1.32e-16) + (0.3 x 5.43e-16 x 8.68e-16) + (0.55 x 4.57e-16 x 1.32e-16) + (0.78 x 4.57e-16 x 8.68e-16) = 5.4132348e-31 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 59 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 4e-28 0.1 - a2 0.09 4e-28 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 2e-16 2e-14 - a2 1.8e-15 2e-14 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 2e-16 2e-14 - a2 1.8e-15 2e-14 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 1.086e-15 1e-15 0.543 - b2 9.14e-16 1e-15 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 5.43e-16 1e-15 - b2 4.57e-16 1e-15 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 2.64e-16 1e-15 0.132 - c2 1.736e-15 1e-15 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 1.32e-16 1e-15 - c2 8.68e-16 1e-15 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 4.5867652e-31 1 0.45867652 - d2 5.4132348e-31 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x1e-15 + [(0.97)]x1e-15 = 1e-15 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x1e-15 + [(0.4)]x1e-15 = 1e-15 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x1e-15 + [(0.76)]x1e-15 = 1e-15 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x1e-15 + [(0.88)]x1e-15 = 1e-15 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x1.32e-16) + (0.7x8.68e-16)]x1 + [(0.8x1.32e-16) + (0.3x8.68e-16)]x1 = 1e-15 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x1.32e-16) + (0.22x8.68e-16)]x1 + [(0.55x1.32e-16) + (0.78x8.68e-16)]x1 = 1e-15 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x5.43e-16) + (0.45x4.57e-16)]x1 + [(0.8x5.43e-16) + (0.55x4.57e-16)]x1 = 1e-15 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x5.43e-16) + (0.22x4.57e-16)]x1 + [(0.3x5.43e-16) + (0.78x4.57e-16)]x1 = 1e-15 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 2e-14 = 2e-16 - πB(a2) = π(a2).λC(a2) = 0.09 x 2e-14 = 1.8e-15 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 2e-14 = 2e-16 - πC(a2) = π(a2).λB(a2) = 0.09 x 2e-14 = 1.8e-15 -π message B --> D - πD(b1) = π(b1) = 1.086e-15 = 1.086e-15 - πD(b2) = π(b2) = 9.14e-16 = 9.14e-16 -π message C --> D - πD(c1) = π(c1) = 2.64e-16 = 2.64e-16 - πD(c2) = π(c2) = 1.736e-15 = 1.736e-15 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 1e-15 x 1e-15 = 1e-30 - λ(a2) = λB(a2).λC(a2) = 1e-15 x 1e-15 = 1e-30 - belief change = 1.387778781e-17 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 2e-16) + (0.6 x 1.8e-15) = 1.086e-15 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 2e-16) + (0.4 x 1.8e-15) = 9.14e-16 - λ(b1) = λD(b1) = 1e-15 = 1e-15 - λ(b2) = λD(b2) = 1e-15 = 1e-15 - belief change = 0 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 2e-16) + (0.12 x 1.8e-15) = 2.64e-16 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 2e-16) + (0.88 x 1.8e-15) = 1.736e-15 - λ(c1) = λD(c1) = 1e-15 = 1e-15 - λ(c2) = λD(c2) = 1e-15 = 1e-15 - belief change = 0 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 1.086e-15 x 2.64e-16) + (0.7 x 1.086e-15 x 1.736e-15) + (0.45 x 9.14e-16 x 2.64e-16) + (0.22 x 9.14e-16 x 1.736e-15) = 1.83470608e-30 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 1.086e-15 x 2.64e-16) + (0.3 x 1.086e-15 x 1.736e-15) + (0.55 x 9.14e-16 x 2.64e-16) + (0.78 x 9.14e-16 x 1.736e-15) = 2.16529392e-30 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 60 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 1e-30 0.1 - a2 0.09 1e-30 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 2e-16 1e-15 - a2 1.8e-15 1e-15 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 2e-16 1e-15 - a2 1.8e-15 1e-15 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 1.086e-15 1e-15 0.543 - b2 9.14e-16 1e-15 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 1.086e-15 1e-15 - b2 9.14e-16 1e-15 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 2.64e-16 1e-15 0.132 - c2 1.736e-15 1e-15 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 2.64e-16 1e-15 - c2 1.736e-15 1e-15 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 1.83470608e-30 1 0.45867652 - d2 2.16529392e-30 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x1e-15 + [(0.97)]x1e-15 = 1e-15 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x1e-15 + [(0.4)]x1e-15 = 1e-15 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x1e-15 + [(0.76)]x1e-15 = 1e-15 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x1e-15 + [(0.88)]x1e-15 = 1e-15 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x2.64e-16) + (0.7x1.736e-15)]x1 + [(0.8x2.64e-16) + (0.3x1.736e-15)]x1 = 2e-15 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x2.64e-16) + (0.22x1.736e-15)]x1 + [(0.55x2.64e-16) + (0.78x1.736e-15)]x1 = 2e-15 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x1.086e-15) + (0.45x9.14e-16)]x1 + [(0.8x1.086e-15) + (0.55x9.14e-16)]x1 = 2e-15 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x1.086e-15) + (0.22x9.14e-16)]x1 + [(0.3x1.086e-15) + (0.78x9.14e-16)]x1 = 2e-15 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 1e-15 = 1e-17 - πB(a2) = π(a2).λC(a2) = 0.09 x 1e-15 = 9e-17 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 1e-15 = 1e-17 - πC(a2) = π(a2).λB(a2) = 0.09 x 1e-15 = 9e-17 -π message B --> D - πD(b1) = π(b1) = 1.086e-15 = 1.086e-15 - πD(b2) = π(b2) = 9.14e-16 = 9.14e-16 -π message C --> D - πD(c1) = π(c1) = 2.64e-16 = 2.64e-16 - πD(c2) = π(c2) = 1.736e-15 = 1.736e-15 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 1e-15 x 1e-15 = 1e-30 - λ(a2) = λB(a2).λC(a2) = 1e-15 x 1e-15 = 1e-30 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 1e-17) + (0.6 x 9e-17) = 5.43e-17 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 1e-17) + (0.4 x 9e-17) = 4.57e-17 - λ(b1) = λD(b1) = 2e-15 = 2e-15 - λ(b2) = λD(b2) = 2e-15 = 2e-15 - belief change = 0 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 1e-17) + (0.12 x 9e-17) = 1.32e-17 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 1e-17) + (0.88 x 9e-17) = 8.68e-17 - λ(c1) = λD(c1) = 2e-15 = 2e-15 - λ(c2) = λD(c2) = 2e-15 = 2e-15 - belief change = 2.498001805e-16 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 1.086e-15 x 2.64e-16) + (0.7 x 1.086e-15 x 1.736e-15) + (0.45 x 9.14e-16 x 2.64e-16) + (0.22 x 9.14e-16 x 1.736e-15) = 1.83470608e-30 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 1.086e-15 x 2.64e-16) + (0.3 x 1.086e-15 x 1.736e-15) + (0.55 x 9.14e-16 x 2.64e-16) + (0.78 x 9.14e-16 x 1.736e-15) = 2.16529392e-30 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 61 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 1e-30 0.1 - a2 0.09 1e-30 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 1e-17 1e-15 - a2 9e-17 1e-15 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 1e-17 1e-15 - a2 9e-17 1e-15 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 5.43e-17 2e-15 0.543 - b2 4.57e-17 2e-15 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 1.086e-15 2e-15 - b2 9.14e-16 2e-15 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 1.32e-17 2e-15 0.132 - c2 8.68e-17 2e-15 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 2.64e-16 2e-15 - c2 1.736e-15 2e-15 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 1.83470608e-30 1 0.45867652 - d2 2.16529392e-30 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x2e-15 + [(0.97)]x2e-15 = 2e-15 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x2e-15 + [(0.4)]x2e-15 = 2e-15 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x2e-15 + [(0.76)]x2e-15 = 2e-15 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x2e-15 + [(0.88)]x2e-15 = 2e-15 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x2.64e-16) + (0.7x1.736e-15)]x1 + [(0.8x2.64e-16) + (0.3x1.736e-15)]x1 = 2e-15 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x2.64e-16) + (0.22x1.736e-15)]x1 + [(0.55x2.64e-16) + (0.78x1.736e-15)]x1 = 2e-15 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x1.086e-15) + (0.45x9.14e-16)]x1 + [(0.8x1.086e-15) + (0.55x9.14e-16)]x1 = 2e-15 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x1.086e-15) + (0.22x9.14e-16)]x1 + [(0.3x1.086e-15) + (0.78x9.14e-16)]x1 = 2e-15 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 1e-15 = 1e-17 - πB(a2) = π(a2).λC(a2) = 0.09 x 1e-15 = 9e-17 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 1e-15 = 1e-17 - πC(a2) = π(a2).λB(a2) = 0.09 x 1e-15 = 9e-17 -π message B --> D - πD(b1) = π(b1) = 5.43e-17 = 5.43e-17 - πD(b2) = π(b2) = 4.57e-17 = 4.57e-17 -π message C --> D - πD(c1) = π(c1) = 1.32e-17 = 1.32e-17 - πD(c2) = π(c2) = 8.68e-17 = 8.68e-17 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 2e-15 x 2e-15 = 4e-30 - λ(a2) = λB(a2).λC(a2) = 2e-15 x 2e-15 = 4e-30 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 1e-17) + (0.6 x 9e-17) = 5.43e-17 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 1e-17) + (0.4 x 9e-17) = 4.57e-17 - λ(b1) = λD(b1) = 2e-15 = 2e-15 - λ(b2) = λD(b2) = 2e-15 = 2e-15 - belief change = 0 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 1e-17) + (0.12 x 9e-17) = 1.32e-17 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 1e-17) + (0.88 x 9e-17) = 8.68e-17 - λ(c1) = λD(c1) = 2e-15 = 2e-15 - λ(c2) = λD(c2) = 2e-15 = 2e-15 - belief change = 0 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 5.43e-17 x 1.32e-17) + (0.7 x 5.43e-17 x 8.68e-17) + (0.45 x 4.57e-17 x 1.32e-17) + (0.22 x 4.57e-17 x 8.68e-17) = 4.5867652e-33 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 5.43e-17 x 1.32e-17) + (0.3 x 5.43e-17 x 8.68e-17) + (0.55 x 4.57e-17 x 1.32e-17) + (0.78 x 4.57e-17 x 8.68e-17) = 5.4132348e-33 - λ(d1) = 1 - λ(d2) = 1 - belief change = 2.220446049e-16 - - -******************************************************************************** -Iteration 62 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 4e-30 0.1 - a2 0.09 4e-30 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 1e-17 2e-15 - a2 9e-17 2e-15 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 1e-17 2e-15 - a2 9e-17 2e-15 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 5.43e-17 2e-15 0.543 - b2 4.57e-17 2e-15 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 5.43e-17 2e-15 - b2 4.57e-17 2e-15 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 1.32e-17 2e-15 0.132 - c2 8.68e-17 2e-15 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 1.32e-17 2e-15 - c2 8.68e-17 2e-15 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 4.5867652e-33 1 0.45867652 - d2 5.4132348e-33 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x2e-15 + [(0.97)]x2e-15 = 2e-15 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x2e-15 + [(0.4)]x2e-15 = 2e-15 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x2e-15 + [(0.76)]x2e-15 = 2e-15 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x2e-15 + [(0.88)]x2e-15 = 2e-15 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x1.32e-17) + (0.7x8.68e-17)]x1 + [(0.8x1.32e-17) + (0.3x8.68e-17)]x1 = 1e-16 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x1.32e-17) + (0.22x8.68e-17)]x1 + [(0.55x1.32e-17) + (0.78x8.68e-17)]x1 = 1e-16 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x5.43e-17) + (0.45x4.57e-17)]x1 + [(0.8x5.43e-17) + (0.55x4.57e-17)]x1 = 1e-16 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x5.43e-17) + (0.22x4.57e-17)]x1 + [(0.3x5.43e-17) + (0.78x4.57e-17)]x1 = 1e-16 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 2e-15 = 2e-17 - πB(a2) = π(a2).λC(a2) = 0.09 x 2e-15 = 1.8e-16 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 2e-15 = 2e-17 - πC(a2) = π(a2).λB(a2) = 0.09 x 2e-15 = 1.8e-16 -π message B --> D - πD(b1) = π(b1) = 5.43e-17 = 5.43e-17 - πD(b2) = π(b2) = 4.57e-17 = 4.57e-17 -π message C --> D - πD(c1) = π(c1) = 1.32e-17 = 1.32e-17 - πD(c2) = π(c2) = 8.68e-17 = 8.68e-17 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 2e-15 x 2e-15 = 4e-30 - λ(a2) = λB(a2).λC(a2) = 2e-15 x 2e-15 = 4e-30 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 2e-17) + (0.6 x 1.8e-16) = 1.086e-16 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 2e-17) + (0.4 x 1.8e-16) = 9.14e-17 - λ(b1) = λD(b1) = 1e-16 = 1e-16 - λ(b2) = λD(b2) = 1e-16 = 1e-16 - belief change = 0 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 2e-17) + (0.12 x 1.8e-16) = 2.64e-17 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 2e-17) + (0.88 x 1.8e-16) = 1.736e-16 - λ(c1) = λD(c1) = 1e-16 = 1e-16 - λ(c2) = λD(c2) = 1e-16 = 1e-16 - belief change = 1.110223025e-16 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 5.43e-17 x 1.32e-17) + (0.7 x 5.43e-17 x 8.68e-17) + (0.45 x 4.57e-17 x 1.32e-17) + (0.22 x 4.57e-17 x 8.68e-17) = 4.5867652e-33 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 5.43e-17 x 1.32e-17) + (0.3 x 5.43e-17 x 8.68e-17) + (0.55 x 4.57e-17 x 1.32e-17) + (0.78 x 4.57e-17 x 8.68e-17) = 5.4132348e-33 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 63 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 4e-30 0.1 - a2 0.09 4e-30 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 2e-17 2e-15 - a2 1.8e-16 2e-15 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 2e-17 2e-15 - a2 1.8e-16 2e-15 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 1.086e-16 1e-16 0.543 - b2 9.14e-17 1e-16 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 5.43e-17 1e-16 - b2 4.57e-17 1e-16 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 2.64e-17 1e-16 0.132 - c2 1.736e-16 1e-16 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 1.32e-17 1e-16 - c2 8.68e-17 1e-16 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 4.5867652e-33 1 0.45867652 - d2 5.4132348e-33 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x1e-16 + [(0.97)]x1e-16 = 1e-16 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x1e-16 + [(0.4)]x1e-16 = 1e-16 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x1e-16 + [(0.76)]x1e-16 = 1e-16 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x1e-16 + [(0.88)]x1e-16 = 1e-16 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x1.32e-17) + (0.7x8.68e-17)]x1 + [(0.8x1.32e-17) + (0.3x8.68e-17)]x1 = 1e-16 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x1.32e-17) + (0.22x8.68e-17)]x1 + [(0.55x1.32e-17) + (0.78x8.68e-17)]x1 = 1e-16 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x5.43e-17) + (0.45x4.57e-17)]x1 + [(0.8x5.43e-17) + (0.55x4.57e-17)]x1 = 1e-16 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x5.43e-17) + (0.22x4.57e-17)]x1 + [(0.3x5.43e-17) + (0.78x4.57e-17)]x1 = 1e-16 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 2e-15 = 2e-17 - πB(a2) = π(a2).λC(a2) = 0.09 x 2e-15 = 1.8e-16 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 2e-15 = 2e-17 - πC(a2) = π(a2).λB(a2) = 0.09 x 2e-15 = 1.8e-16 -π message B --> D - πD(b1) = π(b1) = 1.086e-16 = 1.086e-16 - πD(b2) = π(b2) = 9.14e-17 = 9.14e-17 -π message C --> D - πD(c1) = π(c1) = 2.64e-17 = 2.64e-17 - πD(c2) = π(c2) = 1.736e-16 = 1.736e-16 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 1e-16 x 1e-16 = 1e-32 - λ(a2) = λB(a2).λC(a2) = 1e-16 x 1e-16 = 1e-32 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 2e-17) + (0.6 x 1.8e-16) = 1.086e-16 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 2e-17) + (0.4 x 1.8e-16) = 9.14e-17 - λ(b1) = λD(b1) = 1e-16 = 1e-16 - λ(b2) = λD(b2) = 1e-16 = 1e-16 - belief change = 0 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 2e-17) + (0.12 x 1.8e-16) = 2.64e-17 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 2e-17) + (0.88 x 1.8e-16) = 1.736e-16 - λ(c1) = λD(c1) = 1e-16 = 1e-16 - λ(c2) = λD(c2) = 1e-16 = 1e-16 - belief change = 0 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 1.086e-16 x 2.64e-17) + (0.7 x 1.086e-16 x 1.736e-16) + (0.45 x 9.14e-17 x 2.64e-17) + (0.22 x 9.14e-17 x 1.736e-16) = 1.83470608e-32 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 1.086e-16 x 2.64e-17) + (0.3 x 1.086e-16 x 1.736e-16) + (0.55 x 9.14e-17 x 2.64e-17) + (0.78 x 9.14e-17 x 1.736e-16) = 2.16529392e-32 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 64 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 1e-32 0.1 - a2 0.09 1e-32 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 2e-17 1e-16 - a2 1.8e-16 1e-16 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 2e-17 1e-16 - a2 1.8e-16 1e-16 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 1.086e-16 1e-16 0.543 - b2 9.14e-17 1e-16 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 1.086e-16 1e-16 - b2 9.14e-17 1e-16 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 2.64e-17 1e-16 0.132 - c2 1.736e-16 1e-16 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 2.64e-17 1e-16 - c2 1.736e-16 1e-16 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 1.83470608e-32 1 0.45867652 - d2 2.16529392e-32 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x1e-16 + [(0.97)]x1e-16 = 1e-16 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x1e-16 + [(0.4)]x1e-16 = 1e-16 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x1e-16 + [(0.76)]x1e-16 = 1e-16 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x1e-16 + [(0.88)]x1e-16 = 1e-16 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x2.64e-17) + (0.7x1.736e-16)]x1 + [(0.8x2.64e-17) + (0.3x1.736e-16)]x1 = 2e-16 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x2.64e-17) + (0.22x1.736e-16)]x1 + [(0.55x2.64e-17) + (0.78x1.736e-16)]x1 = 2e-16 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x1.086e-16) + (0.45x9.14e-17)]x1 + [(0.8x1.086e-16) + (0.55x9.14e-17)]x1 = 2e-16 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x1.086e-16) + (0.22x9.14e-17)]x1 + [(0.3x1.086e-16) + (0.78x9.14e-17)]x1 = 2e-16 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 1e-16 = 1e-18 - πB(a2) = π(a2).λC(a2) = 0.09 x 1e-16 = 9e-18 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 1e-16 = 1e-18 - πC(a2) = π(a2).λB(a2) = 0.09 x 1e-16 = 9e-18 -π message B --> D - πD(b1) = π(b1) = 1.086e-16 = 1.086e-16 - πD(b2) = π(b2) = 9.14e-17 = 9.14e-17 -π message C --> D - πD(c1) = π(c1) = 2.64e-17 = 2.64e-17 - πD(c2) = π(c2) = 1.736e-16 = 1.736e-16 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 1e-16 x 1e-16 = 1e-32 - λ(a2) = λB(a2).λC(a2) = 1e-16 x 1e-16 = 1e-32 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 1e-18) + (0.6 x 9e-18) = 5.43e-18 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 1e-18) + (0.4 x 9e-18) = 4.57e-18 - λ(b1) = λD(b1) = 2e-16 = 2e-16 - λ(b2) = λD(b2) = 2e-16 = 2e-16 - belief change = 1.665334537e-16 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 1e-18) + (0.12 x 9e-18) = 1.32e-18 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 1e-18) + (0.88 x 9e-18) = 8.68e-18 - λ(c1) = λD(c1) = 2e-16 = 2e-16 - λ(c2) = λD(c2) = 2e-16 = 2e-16 - belief change = 1.110223025e-16 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 1.086e-16 x 2.64e-17) + (0.7 x 1.086e-16 x 1.736e-16) + (0.45 x 9.14e-17 x 2.64e-17) + (0.22 x 9.14e-17 x 1.736e-16) = 1.83470608e-32 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 1.086e-16 x 2.64e-17) + (0.3 x 1.086e-16 x 1.736e-16) + (0.55 x 9.14e-17 x 2.64e-17) + (0.78 x 9.14e-17 x 1.736e-16) = 2.16529392e-32 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 65 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 1e-32 0.1 - a2 0.09 1e-32 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 1e-18 1e-16 - a2 9e-18 1e-16 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 1e-18 1e-16 - a2 9e-18 1e-16 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 5.43e-18 2e-16 0.543 - b2 4.57e-18 2e-16 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 1.086e-16 2e-16 - b2 9.14e-17 2e-16 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 1.32e-18 2e-16 0.132 - c2 8.68e-18 2e-16 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 2.64e-17 2e-16 - c2 1.736e-16 2e-16 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 1.83470608e-32 1 0.45867652 - d2 2.16529392e-32 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x2e-16 + [(0.97)]x2e-16 = 2e-16 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x2e-16 + [(0.4)]x2e-16 = 2e-16 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x2e-16 + [(0.76)]x2e-16 = 2e-16 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x2e-16 + [(0.88)]x2e-16 = 2e-16 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x2.64e-17) + (0.7x1.736e-16)]x1 + [(0.8x2.64e-17) + (0.3x1.736e-16)]x1 = 2e-16 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x2.64e-17) + (0.22x1.736e-16)]x1 + [(0.55x2.64e-17) + (0.78x1.736e-16)]x1 = 2e-16 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x1.086e-16) + (0.45x9.14e-17)]x1 + [(0.8x1.086e-16) + (0.55x9.14e-17)]x1 = 2e-16 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x1.086e-16) + (0.22x9.14e-17)]x1 + [(0.3x1.086e-16) + (0.78x9.14e-17)]x1 = 2e-16 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 1e-16 = 1e-18 - πB(a2) = π(a2).λC(a2) = 0.09 x 1e-16 = 9e-18 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 1e-16 = 1e-18 - πC(a2) = π(a2).λB(a2) = 0.09 x 1e-16 = 9e-18 -π message B --> D - πD(b1) = π(b1) = 5.43e-18 = 5.43e-18 - πD(b2) = π(b2) = 4.57e-18 = 4.57e-18 -π message C --> D - πD(c1) = π(c1) = 1.32e-18 = 1.32e-18 - πD(c2) = π(c2) = 8.68e-18 = 8.68e-18 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 2e-16 x 2e-16 = 4e-32 - λ(a2) = λB(a2).λC(a2) = 2e-16 x 2e-16 = 4e-32 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 1e-18) + (0.6 x 9e-18) = 5.43e-18 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 1e-18) + (0.4 x 9e-18) = 4.57e-18 - λ(b1) = λD(b1) = 2e-16 = 2e-16 - λ(b2) = λD(b2) = 2e-16 = 2e-16 - belief change = 0 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 1e-18) + (0.12 x 9e-18) = 1.32e-18 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 1e-18) + (0.88 x 9e-18) = 8.68e-18 - λ(c1) = λD(c1) = 2e-16 = 2e-16 - λ(c2) = λD(c2) = 2e-16 = 2e-16 - belief change = 0 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 5.43e-18 x 1.32e-18) + (0.7 x 5.43e-18 x 8.68e-18) + (0.45 x 4.57e-18 x 1.32e-18) + (0.22 x 4.57e-18 x 8.68e-18) = 4.5867652e-35 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 5.43e-18 x 1.32e-18) + (0.3 x 5.43e-18 x 8.68e-18) + (0.55 x 4.57e-18 x 1.32e-18) + (0.78 x 4.57e-18 x 8.68e-18) = 5.4132348e-35 - λ(d1) = 1 - λ(d2) = 1 - belief change = 5.551115123e-17 - - -******************************************************************************** -Iteration 66 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 4e-32 0.1 - a2 0.09 4e-32 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 1e-18 2e-16 - a2 9e-18 2e-16 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 1e-18 2e-16 - a2 9e-18 2e-16 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 5.43e-18 2e-16 0.543 - b2 4.57e-18 2e-16 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 5.43e-18 2e-16 - b2 4.57e-18 2e-16 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 1.32e-18 2e-16 0.132 - c2 8.68e-18 2e-16 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 1.32e-18 2e-16 - c2 8.68e-18 2e-16 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 4.5867652e-35 1 0.45867652 - d2 5.4132348e-35 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x2e-16 + [(0.97)]x2e-16 = 2e-16 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x2e-16 + [(0.4)]x2e-16 = 2e-16 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x2e-16 + [(0.76)]x2e-16 = 2e-16 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x2e-16 + [(0.88)]x2e-16 = 2e-16 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x1.32e-18) + (0.7x8.68e-18)]x1 + [(0.8x1.32e-18) + (0.3x8.68e-18)]x1 = 1e-17 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x1.32e-18) + (0.22x8.68e-18)]x1 + [(0.55x1.32e-18) + (0.78x8.68e-18)]x1 = 1e-17 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x5.43e-18) + (0.45x4.57e-18)]x1 + [(0.8x5.43e-18) + (0.55x4.57e-18)]x1 = 1e-17 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x5.43e-18) + (0.22x4.57e-18)]x1 + [(0.3x5.43e-18) + (0.78x4.57e-18)]x1 = 1e-17 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 2e-16 = 2e-18 - πB(a2) = π(a2).λC(a2) = 0.09 x 2e-16 = 1.8e-17 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 2e-16 = 2e-18 - πC(a2) = π(a2).λB(a2) = 0.09 x 2e-16 = 1.8e-17 -π message B --> D - πD(b1) = π(b1) = 5.43e-18 = 5.43e-18 - πD(b2) = π(b2) = 4.57e-18 = 4.57e-18 -π message C --> D - πD(c1) = π(c1) = 1.32e-18 = 1.32e-18 - πD(c2) = π(c2) = 8.68e-18 = 8.68e-18 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 2e-16 x 2e-16 = 4e-32 - λ(a2) = λB(a2).λC(a2) = 2e-16 x 2e-16 = 4e-32 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 2e-18) + (0.6 x 1.8e-17) = 1.086e-17 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 2e-18) + (0.4 x 1.8e-17) = 9.14e-18 - λ(b1) = λD(b1) = 1e-17 = 1e-17 - λ(b2) = λD(b2) = 1e-17 = 1e-17 - belief change = 1.665334537e-16 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 2e-18) + (0.12 x 1.8e-17) = 2.64e-18 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 2e-18) + (0.88 x 1.8e-17) = 1.736e-17 - λ(c1) = λD(c1) = 1e-17 = 1e-17 - λ(c2) = λD(c2) = 1e-17 = 1e-17 - belief change = 1.387778781e-16 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 5.43e-18 x 1.32e-18) + (0.7 x 5.43e-18 x 8.68e-18) + (0.45 x 4.57e-18 x 1.32e-18) + (0.22 x 4.57e-18 x 8.68e-18) = 4.5867652e-35 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 5.43e-18 x 1.32e-18) + (0.3 x 5.43e-18 x 8.68e-18) + (0.55 x 4.57e-18 x 1.32e-18) + (0.78 x 4.57e-18 x 8.68e-18) = 5.4132348e-35 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 67 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 4e-32 0.1 - a2 0.09 4e-32 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 2e-18 2e-16 - a2 1.8e-17 2e-16 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 2e-18 2e-16 - a2 1.8e-17 2e-16 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 1.086e-17 1e-17 0.543 - b2 9.14e-18 1e-17 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 5.43e-18 1e-17 - b2 4.57e-18 1e-17 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 2.64e-18 1e-17 0.132 - c2 1.736e-17 1e-17 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 1.32e-18 1e-17 - c2 8.68e-18 1e-17 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 4.5867652e-35 1 0.45867652 - d2 5.4132348e-35 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x1e-17 + [(0.97)]x1e-17 = 1e-17 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x1e-17 + [(0.4)]x1e-17 = 1e-17 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x1e-17 + [(0.76)]x1e-17 = 1e-17 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x1e-17 + [(0.88)]x1e-17 = 1e-17 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x1.32e-18) + (0.7x8.68e-18)]x1 + [(0.8x1.32e-18) + (0.3x8.68e-18)]x1 = 1e-17 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x1.32e-18) + (0.22x8.68e-18)]x1 + [(0.55x1.32e-18) + (0.78x8.68e-18)]x1 = 1e-17 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x5.43e-18) + (0.45x4.57e-18)]x1 + [(0.8x5.43e-18) + (0.55x4.57e-18)]x1 = 1e-17 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x5.43e-18) + (0.22x4.57e-18)]x1 + [(0.3x5.43e-18) + (0.78x4.57e-18)]x1 = 1e-17 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 2e-16 = 2e-18 - πB(a2) = π(a2).λC(a2) = 0.09 x 2e-16 = 1.8e-17 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 2e-16 = 2e-18 - πC(a2) = π(a2).λB(a2) = 0.09 x 2e-16 = 1.8e-17 -π message B --> D - πD(b1) = π(b1) = 1.086e-17 = 1.086e-17 - πD(b2) = π(b2) = 9.14e-18 = 9.14e-18 -π message C --> D - πD(c1) = π(c1) = 2.64e-18 = 2.64e-18 - πD(c2) = π(c2) = 1.736e-17 = 1.736e-17 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 1e-17 x 1e-17 = 1e-34 - λ(a2) = λB(a2).λC(a2) = 1e-17 x 1e-17 = 1e-34 - belief change = 2.775557562e-17 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 2e-18) + (0.6 x 1.8e-17) = 1.086e-17 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 2e-18) + (0.4 x 1.8e-17) = 9.14e-18 - λ(b1) = λD(b1) = 1e-17 = 1e-17 - λ(b2) = λD(b2) = 1e-17 = 1e-17 - belief change = 0 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 2e-18) + (0.12 x 1.8e-17) = 2.64e-18 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 2e-18) + (0.88 x 1.8e-17) = 1.736e-17 - λ(c1) = λD(c1) = 1e-17 = 1e-17 - λ(c2) = λD(c2) = 1e-17 = 1e-17 - belief change = 0 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 1.086e-17 x 2.64e-18) + (0.7 x 1.086e-17 x 1.736e-17) + (0.45 x 9.14e-18 x 2.64e-18) + (0.22 x 9.14e-18 x 1.736e-17) = 1.83470608e-34 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 1.086e-17 x 2.64e-18) + (0.3 x 1.086e-17 x 1.736e-17) + (0.55 x 9.14e-18 x 2.64e-18) + (0.78 x 9.14e-18 x 1.736e-17) = 2.16529392e-34 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 68 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 1e-34 0.1 - a2 0.09 1e-34 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 2e-18 1e-17 - a2 1.8e-17 1e-17 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 2e-18 1e-17 - a2 1.8e-17 1e-17 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 1.086e-17 1e-17 0.543 - b2 9.14e-18 1e-17 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 1.086e-17 1e-17 - b2 9.14e-18 1e-17 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 2.64e-18 1e-17 0.132 - c2 1.736e-17 1e-17 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 2.64e-18 1e-17 - c2 1.736e-17 1e-17 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 1.83470608e-34 1 0.45867652 - d2 2.16529392e-34 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x1e-17 + [(0.97)]x1e-17 = 1e-17 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x1e-17 + [(0.4)]x1e-17 = 1e-17 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x1e-17 + [(0.76)]x1e-17 = 1e-17 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x1e-17 + [(0.88)]x1e-17 = 1e-17 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x2.64e-18) + (0.7x1.736e-17)]x1 + [(0.8x2.64e-18) + (0.3x1.736e-17)]x1 = 2e-17 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x2.64e-18) + (0.22x1.736e-17)]x1 + [(0.55x2.64e-18) + (0.78x1.736e-17)]x1 = 2e-17 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x1.086e-17) + (0.45x9.14e-18)]x1 + [(0.8x1.086e-17) + (0.55x9.14e-18)]x1 = 2e-17 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x1.086e-17) + (0.22x9.14e-18)]x1 + [(0.3x1.086e-17) + (0.78x9.14e-18)]x1 = 2e-17 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 1e-17 = 1e-19 - πB(a2) = π(a2).λC(a2) = 0.09 x 1e-17 = 9e-19 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 1e-17 = 1e-19 - πC(a2) = π(a2).λB(a2) = 0.09 x 1e-17 = 9e-19 -π message B --> D - πD(b1) = π(b1) = 1.086e-17 = 1.086e-17 - πD(b2) = π(b2) = 9.14e-18 = 9.14e-18 -π message C --> D - πD(c1) = π(c1) = 2.64e-18 = 2.64e-18 - πD(c2) = π(c2) = 1.736e-17 = 1.736e-17 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 1e-17 x 1e-17 = 1e-34 - λ(a2) = λB(a2).λC(a2) = 1e-17 x 1e-17 = 1e-34 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 1e-19) + (0.6 x 9e-19) = 5.43e-19 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 1e-19) + (0.4 x 9e-19) = 4.57e-19 - λ(b1) = λD(b1) = 2e-17 = 2e-17 - λ(b2) = λD(b2) = 2e-17 = 2e-17 - belief change = 5.551115123e-17 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 1e-19) + (0.12 x 9e-19) = 1.32e-19 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 1e-19) + (0.88 x 9e-19) = 8.68e-19 - λ(c1) = λD(c1) = 2e-17 = 2e-17 - λ(c2) = λD(c2) = 2e-17 = 2e-17 - belief change = 1.110223025e-16 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 1.086e-17 x 2.64e-18) + (0.7 x 1.086e-17 x 1.736e-17) + (0.45 x 9.14e-18 x 2.64e-18) + (0.22 x 9.14e-18 x 1.736e-17) = 1.83470608e-34 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 1.086e-17 x 2.64e-18) + (0.3 x 1.086e-17 x 1.736e-17) + (0.55 x 9.14e-18 x 2.64e-18) + (0.78 x 9.14e-18 x 1.736e-17) = 2.16529392e-34 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 69 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 1e-34 0.1 - a2 0.09 1e-34 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 1e-19 1e-17 - a2 9e-19 1e-17 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 1e-19 1e-17 - a2 9e-19 1e-17 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 5.43e-19 2e-17 0.543 - b2 4.57e-19 2e-17 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 1.086e-17 2e-17 - b2 9.14e-18 2e-17 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 1.32e-19 2e-17 0.132 - c2 8.68e-19 2e-17 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 2.64e-18 2e-17 - c2 1.736e-17 2e-17 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 1.83470608e-34 1 0.45867652 - d2 2.16529392e-34 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x2e-17 + [(0.97)]x2e-17 = 2e-17 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x2e-17 + [(0.4)]x2e-17 = 2e-17 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x2e-17 + [(0.76)]x2e-17 = 2e-17 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x2e-17 + [(0.88)]x2e-17 = 2e-17 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x2.64e-18) + (0.7x1.736e-17)]x1 + [(0.8x2.64e-18) + (0.3x1.736e-17)]x1 = 2e-17 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x2.64e-18) + (0.22x1.736e-17)]x1 + [(0.55x2.64e-18) + (0.78x1.736e-17)]x1 = 2e-17 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x1.086e-17) + (0.45x9.14e-18)]x1 + [(0.8x1.086e-17) + (0.55x9.14e-18)]x1 = 2e-17 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x1.086e-17) + (0.22x9.14e-18)]x1 + [(0.3x1.086e-17) + (0.78x9.14e-18)]x1 = 2e-17 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 1e-17 = 1e-19 - πB(a2) = π(a2).λC(a2) = 0.09 x 1e-17 = 9e-19 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 1e-17 = 1e-19 - πC(a2) = π(a2).λB(a2) = 0.09 x 1e-17 = 9e-19 -π message B --> D - πD(b1) = π(b1) = 5.43e-19 = 5.43e-19 - πD(b2) = π(b2) = 4.57e-19 = 4.57e-19 -π message C --> D - πD(c1) = π(c1) = 1.32e-19 = 1.32e-19 - πD(c2) = π(c2) = 8.68e-19 = 8.68e-19 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 2e-17 x 2e-17 = 4e-34 - λ(a2) = λB(a2).λC(a2) = 2e-17 x 2e-17 = 4e-34 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 1e-19) + (0.6 x 9e-19) = 5.43e-19 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 1e-19) + (0.4 x 9e-19) = 4.57e-19 - λ(b1) = λD(b1) = 2e-17 = 2e-17 - λ(b2) = λD(b2) = 2e-17 = 2e-17 - belief change = 0 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 1e-19) + (0.12 x 9e-19) = 1.32e-19 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 1e-19) + (0.88 x 9e-19) = 8.68e-19 - λ(c1) = λD(c1) = 2e-17 = 2e-17 - λ(c2) = λD(c2) = 2e-17 = 2e-17 - belief change = 0 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 5.43e-19 x 1.32e-19) + (0.7 x 5.43e-19 x 8.68e-19) + (0.45 x 4.57e-19 x 1.32e-19) + (0.22 x 4.57e-19 x 8.68e-19) = 4.5867652e-37 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 5.43e-19 x 1.32e-19) + (0.3 x 5.43e-19 x 8.68e-19) + (0.55 x 4.57e-19 x 1.32e-19) + (0.78 x 4.57e-19 x 8.68e-19) = 5.4132348e-37 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 70 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 4e-34 0.1 - a2 0.09 4e-34 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 1e-19 2e-17 - a2 9e-19 2e-17 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 1e-19 2e-17 - a2 9e-19 2e-17 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 5.43e-19 2e-17 0.543 - b2 4.57e-19 2e-17 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 5.43e-19 2e-17 - b2 4.57e-19 2e-17 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 1.32e-19 2e-17 0.132 - c2 8.68e-19 2e-17 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 1.32e-19 2e-17 - c2 8.68e-19 2e-17 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 4.5867652e-37 1 0.45867652 - d2 5.4132348e-37 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x2e-17 + [(0.97)]x2e-17 = 2e-17 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x2e-17 + [(0.4)]x2e-17 = 2e-17 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x2e-17 + [(0.76)]x2e-17 = 2e-17 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x2e-17 + [(0.88)]x2e-17 = 2e-17 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x1.32e-19) + (0.7x8.68e-19)]x1 + [(0.8x1.32e-19) + (0.3x8.68e-19)]x1 = 1e-18 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x1.32e-19) + (0.22x8.68e-19)]x1 + [(0.55x1.32e-19) + (0.78x8.68e-19)]x1 = 1e-18 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x5.43e-19) + (0.45x4.57e-19)]x1 + [(0.8x5.43e-19) + (0.55x4.57e-19)]x1 = 1e-18 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x5.43e-19) + (0.22x4.57e-19)]x1 + [(0.3x5.43e-19) + (0.78x4.57e-19)]x1 = 1e-18 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 2e-17 = 2e-19 - πB(a2) = π(a2).λC(a2) = 0.09 x 2e-17 = 1.8e-18 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 2e-17 = 2e-19 - πC(a2) = π(a2).λB(a2) = 0.09 x 2e-17 = 1.8e-18 -π message B --> D - πD(b1) = π(b1) = 5.43e-19 = 5.43e-19 - πD(b2) = π(b2) = 4.57e-19 = 4.57e-19 -π message C --> D - πD(c1) = π(c1) = 1.32e-19 = 1.32e-19 - πD(c2) = π(c2) = 8.68e-19 = 8.68e-19 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 2e-17 x 2e-17 = 4e-34 - λ(a2) = λB(a2).λC(a2) = 2e-17 x 2e-17 = 4e-34 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 2e-19) + (0.6 x 1.8e-18) = 1.086e-18 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 2e-19) + (0.4 x 1.8e-18) = 9.14e-19 - λ(b1) = λD(b1) = 1e-18 = 1e-18 - λ(b2) = λD(b2) = 1e-18 = 1e-18 - belief change = 5.551115123e-17 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 2e-19) + (0.12 x 1.8e-18) = 2.64e-19 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 2e-19) + (0.88 x 1.8e-18) = 1.736e-18 - λ(c1) = λD(c1) = 1e-18 = 1e-18 - λ(c2) = λD(c2) = 1e-18 = 1e-18 - belief change = 2.775557562e-17 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 5.43e-19 x 1.32e-19) + (0.7 x 5.43e-19 x 8.68e-19) + (0.45 x 4.57e-19 x 1.32e-19) + (0.22 x 4.57e-19 x 8.68e-19) = 4.5867652e-37 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 5.43e-19 x 1.32e-19) + (0.3 x 5.43e-19 x 8.68e-19) + (0.55 x 4.57e-19 x 1.32e-19) + (0.78 x 4.57e-19 x 8.68e-19) = 5.4132348e-37 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 71 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 4e-34 0.1 - a2 0.09 4e-34 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 2e-19 2e-17 - a2 1.8e-18 2e-17 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 2e-19 2e-17 - a2 1.8e-18 2e-17 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 1.086e-18 1e-18 0.543 - b2 9.14e-19 1e-18 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 5.43e-19 1e-18 - b2 4.57e-19 1e-18 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 2.64e-19 1e-18 0.132 - c2 1.736e-18 1e-18 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 1.32e-19 1e-18 - c2 8.68e-19 1e-18 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 4.5867652e-37 1 0.45867652 - d2 5.4132348e-37 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x1e-18 + [(0.97)]x1e-18 = 1e-18 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x1e-18 + [(0.4)]x1e-18 = 1e-18 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x1e-18 + [(0.76)]x1e-18 = 1e-18 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x1e-18 + [(0.88)]x1e-18 = 1e-18 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x1.32e-19) + (0.7x8.68e-19)]x1 + [(0.8x1.32e-19) + (0.3x8.68e-19)]x1 = 1e-18 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x1.32e-19) + (0.22x8.68e-19)]x1 + [(0.55x1.32e-19) + (0.78x8.68e-19)]x1 = 1e-18 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x5.43e-19) + (0.45x4.57e-19)]x1 + [(0.8x5.43e-19) + (0.55x4.57e-19)]x1 = 1e-18 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x5.43e-19) + (0.22x4.57e-19)]x1 + [(0.3x5.43e-19) + (0.78x4.57e-19)]x1 = 1e-18 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 2e-17 = 2e-19 - πB(a2) = π(a2).λC(a2) = 0.09 x 2e-17 = 1.8e-18 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 2e-17 = 2e-19 - πC(a2) = π(a2).λB(a2) = 0.09 x 2e-17 = 1.8e-18 -π message B --> D - πD(b1) = π(b1) = 1.086e-18 = 1.086e-18 - πD(b2) = π(b2) = 9.14e-19 = 9.14e-19 -π message C --> D - πD(c1) = π(c1) = 2.64e-19 = 2.64e-19 - πD(c2) = π(c2) = 1.736e-18 = 1.736e-18 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 1e-18 x 1e-18 = 1e-36 - λ(a2) = λB(a2).λC(a2) = 1e-18 x 1e-18 = 1e-36 - belief change = 1.110223025e-16 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 2e-19) + (0.6 x 1.8e-18) = 1.086e-18 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 2e-19) + (0.4 x 1.8e-18) = 9.14e-19 - λ(b1) = λD(b1) = 1e-18 = 1e-18 - λ(b2) = λD(b2) = 1e-18 = 1e-18 - belief change = 0 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 2e-19) + (0.12 x 1.8e-18) = 2.64e-19 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 2e-19) + (0.88 x 1.8e-18) = 1.736e-18 - λ(c1) = λD(c1) = 1e-18 = 1e-18 - λ(c2) = λD(c2) = 1e-18 = 1e-18 - belief change = 0 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 1.086e-18 x 2.64e-19) + (0.7 x 1.086e-18 x 1.736e-18) + (0.45 x 9.14e-19 x 2.64e-19) + (0.22 x 9.14e-19 x 1.736e-18) = 1.83470608e-36 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 1.086e-18 x 2.64e-19) + (0.3 x 1.086e-18 x 1.736e-18) + (0.55 x 9.14e-19 x 2.64e-19) + (0.78 x 9.14e-19 x 1.736e-18) = 2.16529392e-36 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 72 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 1e-36 0.1 - a2 0.09 1e-36 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 2e-19 1e-18 - a2 1.8e-18 1e-18 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 2e-19 1e-18 - a2 1.8e-18 1e-18 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 1.086e-18 1e-18 0.543 - b2 9.14e-19 1e-18 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 1.086e-18 1e-18 - b2 9.14e-19 1e-18 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 2.64e-19 1e-18 0.132 - c2 1.736e-18 1e-18 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 2.64e-19 1e-18 - c2 1.736e-18 1e-18 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 1.83470608e-36 1 0.45867652 - d2 2.16529392e-36 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x1e-18 + [(0.97)]x1e-18 = 1e-18 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x1e-18 + [(0.4)]x1e-18 = 1e-18 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x1e-18 + [(0.76)]x1e-18 = 1e-18 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x1e-18 + [(0.88)]x1e-18 = 1e-18 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x2.64e-19) + (0.7x1.736e-18)]x1 + [(0.8x2.64e-19) + (0.3x1.736e-18)]x1 = 2e-18 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x2.64e-19) + (0.22x1.736e-18)]x1 + [(0.55x2.64e-19) + (0.78x1.736e-18)]x1 = 2e-18 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x1.086e-18) + (0.45x9.14e-19)]x1 + [(0.8x1.086e-18) + (0.55x9.14e-19)]x1 = 2e-18 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x1.086e-18) + (0.22x9.14e-19)]x1 + [(0.3x1.086e-18) + (0.78x9.14e-19)]x1 = 2e-18 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 1e-18 = 1e-20 - πB(a2) = π(a2).λC(a2) = 0.09 x 1e-18 = 9e-20 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 1e-18 = 1e-20 - πC(a2) = π(a2).λB(a2) = 0.09 x 1e-18 = 9e-20 -π message B --> D - πD(b1) = π(b1) = 1.086e-18 = 1.086e-18 - πD(b2) = π(b2) = 9.14e-19 = 9.14e-19 -π message C --> D - πD(c1) = π(c1) = 2.64e-19 = 2.64e-19 - πD(c2) = π(c2) = 1.736e-18 = 1.736e-18 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 1e-18 x 1e-18 = 1e-36 - λ(a2) = λB(a2).λC(a2) = 1e-18 x 1e-18 = 1e-36 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 1e-20) + (0.6 x 9e-20) = 5.43e-20 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 1e-20) + (0.4 x 9e-20) = 4.57e-20 - λ(b1) = λD(b1) = 2e-18 = 2e-18 - λ(b2) = λD(b2) = 2e-18 = 2e-18 - belief change = 1.110223025e-16 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 1e-20) + (0.12 x 9e-20) = 1.32e-20 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 1e-20) + (0.88 x 9e-20) = 8.68e-20 - λ(c1) = λD(c1) = 2e-18 = 2e-18 - λ(c2) = λD(c2) = 2e-18 = 2e-18 - belief change = 1.387778781e-16 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 1.086e-18 x 2.64e-19) + (0.7 x 1.086e-18 x 1.736e-18) + (0.45 x 9.14e-19 x 2.64e-19) + (0.22 x 9.14e-19 x 1.736e-18) = 1.83470608e-36 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 1.086e-18 x 2.64e-19) + (0.3 x 1.086e-18 x 1.736e-18) + (0.55 x 9.14e-19 x 2.64e-19) + (0.78 x 9.14e-19 x 1.736e-18) = 2.16529392e-36 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 73 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 1e-36 0.1 - a2 0.09 1e-36 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 1e-20 1e-18 - a2 9e-20 1e-18 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 1e-20 1e-18 - a2 9e-20 1e-18 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 5.43e-20 2e-18 0.543 - b2 4.57e-20 2e-18 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 1.086e-18 2e-18 - b2 9.14e-19 2e-18 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 1.32e-20 2e-18 0.132 - c2 8.68e-20 2e-18 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 2.64e-19 2e-18 - c2 1.736e-18 2e-18 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 1.83470608e-36 1 0.45867652 - d2 2.16529392e-36 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x2e-18 + [(0.97)]x2e-18 = 2e-18 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x2e-18 + [(0.4)]x2e-18 = 2e-18 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x2e-18 + [(0.76)]x2e-18 = 2e-18 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x2e-18 + [(0.88)]x2e-18 = 2e-18 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x2.64e-19) + (0.7x1.736e-18)]x1 + [(0.8x2.64e-19) + (0.3x1.736e-18)]x1 = 2e-18 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x2.64e-19) + (0.22x1.736e-18)]x1 + [(0.55x2.64e-19) + (0.78x1.736e-18)]x1 = 2e-18 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x1.086e-18) + (0.45x9.14e-19)]x1 + [(0.8x1.086e-18) + (0.55x9.14e-19)]x1 = 2e-18 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x1.086e-18) + (0.22x9.14e-19)]x1 + [(0.3x1.086e-18) + (0.78x9.14e-19)]x1 = 2e-18 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 1e-18 = 1e-20 - πB(a2) = π(a2).λC(a2) = 0.09 x 1e-18 = 9e-20 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 1e-18 = 1e-20 - πC(a2) = π(a2).λB(a2) = 0.09 x 1e-18 = 9e-20 -π message B --> D - πD(b1) = π(b1) = 5.43e-20 = 5.43e-20 - πD(b2) = π(b2) = 4.57e-20 = 4.57e-20 -π message C --> D - πD(c1) = π(c1) = 1.32e-20 = 1.32e-20 - πD(c2) = π(c2) = 8.68e-20 = 8.68e-20 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 2e-18 x 2e-18 = 4e-36 - λ(a2) = λB(a2).λC(a2) = 2e-18 x 2e-18 = 4e-36 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 1e-20) + (0.6 x 9e-20) = 5.43e-20 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 1e-20) + (0.4 x 9e-20) = 4.57e-20 - λ(b1) = λD(b1) = 2e-18 = 2e-18 - λ(b2) = λD(b2) = 2e-18 = 2e-18 - belief change = 0 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 1e-20) + (0.12 x 9e-20) = 1.32e-20 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 1e-20) + (0.88 x 9e-20) = 8.68e-20 - λ(c1) = λD(c1) = 2e-18 = 2e-18 - λ(c2) = λD(c2) = 2e-18 = 2e-18 - belief change = 0 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 5.43e-20 x 1.32e-20) + (0.7 x 5.43e-20 x 8.68e-20) + (0.45 x 4.57e-20 x 1.32e-20) + (0.22 x 4.57e-20 x 8.68e-20) = 4.5867652e-39 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 5.43e-20 x 1.32e-20) + (0.3 x 5.43e-20 x 8.68e-20) + (0.55 x 4.57e-20 x 1.32e-20) + (0.78 x 4.57e-20 x 8.68e-20) = 5.4132348e-39 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 74 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 4e-36 0.1 - a2 0.09 4e-36 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 1e-20 2e-18 - a2 9e-20 2e-18 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 1e-20 2e-18 - a2 9e-20 2e-18 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 5.43e-20 2e-18 0.543 - b2 4.57e-20 2e-18 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 5.43e-20 2e-18 - b2 4.57e-20 2e-18 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 1.32e-20 2e-18 0.132 - c2 8.68e-20 2e-18 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 1.32e-20 2e-18 - c2 8.68e-20 2e-18 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 4.5867652e-39 1 0.45867652 - d2 5.4132348e-39 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x2e-18 + [(0.97)]x2e-18 = 2e-18 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x2e-18 + [(0.4)]x2e-18 = 2e-18 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x2e-18 + [(0.76)]x2e-18 = 2e-18 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x2e-18 + [(0.88)]x2e-18 = 2e-18 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x1.32e-20) + (0.7x8.68e-20)]x1 + [(0.8x1.32e-20) + (0.3x8.68e-20)]x1 = 1e-19 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x1.32e-20) + (0.22x8.68e-20)]x1 + [(0.55x1.32e-20) + (0.78x8.68e-20)]x1 = 1e-19 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x5.43e-20) + (0.45x4.57e-20)]x1 + [(0.8x5.43e-20) + (0.55x4.57e-20)]x1 = 1e-19 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x5.43e-20) + (0.22x4.57e-20)]x1 + [(0.3x5.43e-20) + (0.78x4.57e-20)]x1 = 1e-19 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 2e-18 = 2e-20 - πB(a2) = π(a2).λC(a2) = 0.09 x 2e-18 = 1.8e-19 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 2e-18 = 2e-20 - πC(a2) = π(a2).λB(a2) = 0.09 x 2e-18 = 1.8e-19 -π message B --> D - πD(b1) = π(b1) = 5.43e-20 = 5.43e-20 - πD(b2) = π(b2) = 4.57e-20 = 4.57e-20 -π message C --> D - πD(c1) = π(c1) = 1.32e-20 = 1.32e-20 - πD(c2) = π(c2) = 8.68e-20 = 8.68e-20 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 2e-18 x 2e-18 = 4e-36 - λ(a2) = λB(a2).λC(a2) = 2e-18 x 2e-18 = 4e-36 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 2e-20) + (0.6 x 1.8e-19) = 1.086e-19 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 2e-20) + (0.4 x 1.8e-19) = 9.14e-20 - λ(b1) = λD(b1) = 1e-19 = 1e-19 - λ(b2) = λD(b2) = 1e-19 = 1e-19 - belief change = 5.551115123e-17 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 2e-20) + (0.12 x 1.8e-19) = 2.64e-20 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 2e-20) + (0.88 x 1.8e-19) = 1.736e-19 - λ(c1) = λD(c1) = 1e-19 = 1e-19 - λ(c2) = λD(c2) = 1e-19 = 1e-19 - belief change = 0 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 5.43e-20 x 1.32e-20) + (0.7 x 5.43e-20 x 8.68e-20) + (0.45 x 4.57e-20 x 1.32e-20) + (0.22 x 4.57e-20 x 8.68e-20) = 4.5867652e-39 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 5.43e-20 x 1.32e-20) + (0.3 x 5.43e-20 x 8.68e-20) + (0.55 x 4.57e-20 x 1.32e-20) + (0.78 x 4.57e-20 x 8.68e-20) = 5.4132348e-39 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 75 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 4e-36 0.1 - a2 0.09 4e-36 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 2e-20 2e-18 - a2 1.8e-19 2e-18 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 2e-20 2e-18 - a2 1.8e-19 2e-18 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 1.086e-19 1e-19 0.543 - b2 9.14e-20 1e-19 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 5.43e-20 1e-19 - b2 4.57e-20 1e-19 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 2.64e-20 1e-19 0.132 - c2 1.736e-19 1e-19 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 1.32e-20 1e-19 - c2 8.68e-20 1e-19 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 4.5867652e-39 1 0.45867652 - d2 5.4132348e-39 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x1e-19 + [(0.97)]x1e-19 = 1e-19 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x1e-19 + [(0.4)]x1e-19 = 1e-19 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x1e-19 + [(0.76)]x1e-19 = 1e-19 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x1e-19 + [(0.88)]x1e-19 = 1e-19 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x1.32e-20) + (0.7x8.68e-20)]x1 + [(0.8x1.32e-20) + (0.3x8.68e-20)]x1 = 1e-19 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x1.32e-20) + (0.22x8.68e-20)]x1 + [(0.55x1.32e-20) + (0.78x8.68e-20)]x1 = 1e-19 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x5.43e-20) + (0.45x4.57e-20)]x1 + [(0.8x5.43e-20) + (0.55x4.57e-20)]x1 = 1e-19 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x5.43e-20) + (0.22x4.57e-20)]x1 + [(0.3x5.43e-20) + (0.78x4.57e-20)]x1 = 1e-19 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 2e-18 = 2e-20 - πB(a2) = π(a2).λC(a2) = 0.09 x 2e-18 = 1.8e-19 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 2e-18 = 2e-20 - πC(a2) = π(a2).λB(a2) = 0.09 x 2e-18 = 1.8e-19 -π message B --> D - πD(b1) = π(b1) = 1.086e-19 = 1.086e-19 - πD(b2) = π(b2) = 9.14e-20 = 9.14e-20 -π message C --> D - πD(c1) = π(c1) = 2.64e-20 = 2.64e-20 - πD(c2) = π(c2) = 1.736e-19 = 1.736e-19 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 1e-19 x 1e-19 = 1e-38 - λ(a2) = λB(a2).λC(a2) = 1e-19 x 1e-19 = 1e-38 - belief change = 1.249000903e-16 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 2e-20) + (0.6 x 1.8e-19) = 1.086e-19 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 2e-20) + (0.4 x 1.8e-19) = 9.14e-20 - λ(b1) = λD(b1) = 1e-19 = 1e-19 - λ(b2) = λD(b2) = 1e-19 = 1e-19 - belief change = 0 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 2e-20) + (0.12 x 1.8e-19) = 2.64e-20 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 2e-20) + (0.88 x 1.8e-19) = 1.736e-19 - λ(c1) = λD(c1) = 1e-19 = 1e-19 - λ(c2) = λD(c2) = 1e-19 = 1e-19 - belief change = 0 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 1.086e-19 x 2.64e-20) + (0.7 x 1.086e-19 x 1.736e-19) + (0.45 x 9.14e-20 x 2.64e-20) + (0.22 x 9.14e-20 x 1.736e-19) = 1.83470608e-38 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 1.086e-19 x 2.64e-20) + (0.3 x 1.086e-19 x 1.736e-19) + (0.55 x 9.14e-20 x 2.64e-20) + (0.78 x 9.14e-20 x 1.736e-19) = 2.16529392e-38 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 76 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 1e-38 0.1 - a2 0.09 1e-38 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 2e-20 1e-19 - a2 1.8e-19 1e-19 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 2e-20 1e-19 - a2 1.8e-19 1e-19 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 1.086e-19 1e-19 0.543 - b2 9.14e-20 1e-19 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 1.086e-19 1e-19 - b2 9.14e-20 1e-19 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 2.64e-20 1e-19 0.132 - c2 1.736e-19 1e-19 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 2.64e-20 1e-19 - c2 1.736e-19 1e-19 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 1.83470608e-38 1 0.45867652 - d2 2.16529392e-38 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x1e-19 + [(0.97)]x1e-19 = 1e-19 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x1e-19 + [(0.4)]x1e-19 = 1e-19 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x1e-19 + [(0.76)]x1e-19 = 1e-19 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x1e-19 + [(0.88)]x1e-19 = 1e-19 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x2.64e-20) + (0.7x1.736e-19)]x1 + [(0.8x2.64e-20) + (0.3x1.736e-19)]x1 = 2e-19 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x2.64e-20) + (0.22x1.736e-19)]x1 + [(0.55x2.64e-20) + (0.78x1.736e-19)]x1 = 2e-19 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x1.086e-19) + (0.45x9.14e-20)]x1 + [(0.8x1.086e-19) + (0.55x9.14e-20)]x1 = 2e-19 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x1.086e-19) + (0.22x9.14e-20)]x1 + [(0.3x1.086e-19) + (0.78x9.14e-20)]x1 = 2e-19 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 1e-19 = 1e-21 - πB(a2) = π(a2).λC(a2) = 0.09 x 1e-19 = 9e-21 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 1e-19 = 1e-21 - πC(a2) = π(a2).λB(a2) = 0.09 x 1e-19 = 9e-21 -π message B --> D - πD(b1) = π(b1) = 1.086e-19 = 1.086e-19 - πD(b2) = π(b2) = 9.14e-20 = 9.14e-20 -π message C --> D - πD(c1) = π(c1) = 2.64e-20 = 2.64e-20 - πD(c2) = π(c2) = 1.736e-19 = 1.736e-19 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 1e-19 x 1e-19 = 1e-38 - λ(a2) = λB(a2).λC(a2) = 1e-19 x 1e-19 = 1e-38 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 1e-21) + (0.6 x 9e-21) = 5.43e-21 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 1e-21) + (0.4 x 9e-21) = 4.57e-21 - λ(b1) = λD(b1) = 2e-19 = 2e-19 - λ(b2) = λD(b2) = 2e-19 = 2e-19 - belief change = 5.551115123e-17 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 1e-21) + (0.12 x 9e-21) = 1.32e-21 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 1e-21) + (0.88 x 9e-21) = 8.68e-21 - λ(c1) = λD(c1) = 2e-19 = 2e-19 - λ(c2) = λD(c2) = 2e-19 = 2e-19 - belief change = 1.387778781e-16 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 1.086e-19 x 2.64e-20) + (0.7 x 1.086e-19 x 1.736e-19) + (0.45 x 9.14e-20 x 2.64e-20) + (0.22 x 9.14e-20 x 1.736e-19) = 1.83470608e-38 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 1.086e-19 x 2.64e-20) + (0.3 x 1.086e-19 x 1.736e-19) + (0.55 x 9.14e-20 x 2.64e-20) + (0.78 x 9.14e-20 x 1.736e-19) = 2.16529392e-38 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 77 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 1e-38 0.1 - a2 0.09 1e-38 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 1e-21 1e-19 - a2 9e-21 1e-19 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 1e-21 1e-19 - a2 9e-21 1e-19 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 5.43e-21 2e-19 0.543 - b2 4.57e-21 2e-19 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 1.086e-19 2e-19 - b2 9.14e-20 2e-19 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 1.32e-21 2e-19 0.132 - c2 8.68e-21 2e-19 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 2.64e-20 2e-19 - c2 1.736e-19 2e-19 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 1.83470608e-38 1 0.45867652 - d2 2.16529392e-38 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x2e-19 + [(0.97)]x2e-19 = 2e-19 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x2e-19 + [(0.4)]x2e-19 = 2e-19 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x2e-19 + [(0.76)]x2e-19 = 2e-19 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x2e-19 + [(0.88)]x2e-19 = 2e-19 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x2.64e-20) + (0.7x1.736e-19)]x1 + [(0.8x2.64e-20) + (0.3x1.736e-19)]x1 = 2e-19 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x2.64e-20) + (0.22x1.736e-19)]x1 + [(0.55x2.64e-20) + (0.78x1.736e-19)]x1 = 2e-19 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x1.086e-19) + (0.45x9.14e-20)]x1 + [(0.8x1.086e-19) + (0.55x9.14e-20)]x1 = 2e-19 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x1.086e-19) + (0.22x9.14e-20)]x1 + [(0.3x1.086e-19) + (0.78x9.14e-20)]x1 = 2e-19 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 1e-19 = 1e-21 - πB(a2) = π(a2).λC(a2) = 0.09 x 1e-19 = 9e-21 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 1e-19 = 1e-21 - πC(a2) = π(a2).λB(a2) = 0.09 x 1e-19 = 9e-21 -π message B --> D - πD(b1) = π(b1) = 5.43e-21 = 5.43e-21 - πD(b2) = π(b2) = 4.57e-21 = 4.57e-21 -π message C --> D - πD(c1) = π(c1) = 1.32e-21 = 1.32e-21 - πD(c2) = π(c2) = 8.68e-21 = 8.68e-21 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 2e-19 x 2e-19 = 4e-38 - λ(a2) = λB(a2).λC(a2) = 2e-19 x 2e-19 = 4e-38 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 1e-21) + (0.6 x 9e-21) = 5.43e-21 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 1e-21) + (0.4 x 9e-21) = 4.57e-21 - λ(b1) = λD(b1) = 2e-19 = 2e-19 - λ(b2) = λD(b2) = 2e-19 = 2e-19 - belief change = 0 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 1e-21) + (0.12 x 9e-21) = 1.32e-21 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 1e-21) + (0.88 x 9e-21) = 8.68e-21 - λ(c1) = λD(c1) = 2e-19 = 2e-19 - λ(c2) = λD(c2) = 2e-19 = 2e-19 - belief change = 0 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 5.43e-21 x 1.32e-21) + (0.7 x 5.43e-21 x 8.68e-21) + (0.45 x 4.57e-21 x 1.32e-21) + (0.22 x 4.57e-21 x 8.68e-21) = 4.5867652e-41 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 5.43e-21 x 1.32e-21) + (0.3 x 5.43e-21 x 8.68e-21) + (0.55 x 4.57e-21 x 1.32e-21) + (0.78 x 4.57e-21 x 8.68e-21) = 5.4132348e-41 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 78 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 4e-38 0.1 - a2 0.09 4e-38 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 1e-21 2e-19 - a2 9e-21 2e-19 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 1e-21 2e-19 - a2 9e-21 2e-19 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 5.43e-21 2e-19 0.543 - b2 4.57e-21 2e-19 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 5.43e-21 2e-19 - b2 4.57e-21 2e-19 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 1.32e-21 2e-19 0.132 - c2 8.68e-21 2e-19 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 1.32e-21 2e-19 - c2 8.68e-21 2e-19 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 4.5867652e-41 1 0.45867652 - d2 5.4132348e-41 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x2e-19 + [(0.97)]x2e-19 = 2e-19 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x2e-19 + [(0.4)]x2e-19 = 2e-19 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x2e-19 + [(0.76)]x2e-19 = 2e-19 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x2e-19 + [(0.88)]x2e-19 = 2e-19 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x1.32e-21) + (0.7x8.68e-21)]x1 + [(0.8x1.32e-21) + (0.3x8.68e-21)]x1 = 1e-20 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x1.32e-21) + (0.22x8.68e-21)]x1 + [(0.55x1.32e-21) + (0.78x8.68e-21)]x1 = 1e-20 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x5.43e-21) + (0.45x4.57e-21)]x1 + [(0.8x5.43e-21) + (0.55x4.57e-21)]x1 = 1e-20 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x5.43e-21) + (0.22x4.57e-21)]x1 + [(0.3x5.43e-21) + (0.78x4.57e-21)]x1 = 1e-20 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 2e-19 = 2e-21 - πB(a2) = π(a2).λC(a2) = 0.09 x 2e-19 = 1.8e-20 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 2e-19 = 2e-21 - πC(a2) = π(a2).λB(a2) = 0.09 x 2e-19 = 1.8e-20 -π message B --> D - πD(b1) = π(b1) = 5.43e-21 = 5.43e-21 - πD(b2) = π(b2) = 4.57e-21 = 4.57e-21 -π message C --> D - πD(c1) = π(c1) = 1.32e-21 = 1.32e-21 - πD(c2) = π(c2) = 8.68e-21 = 8.68e-21 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 2e-19 x 2e-19 = 4e-38 - λ(a2) = λB(a2).λC(a2) = 2e-19 x 2e-19 = 4e-38 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 2e-21) + (0.6 x 1.8e-20) = 1.086e-20 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 2e-21) + (0.4 x 1.8e-20) = 9.14e-21 - λ(b1) = λD(b1) = 1e-20 = 1e-20 - λ(b2) = λD(b2) = 1e-20 = 1e-20 - belief change = 5.551115123e-17 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 2e-21) + (0.12 x 1.8e-20) = 2.64e-21 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 2e-21) + (0.88 x 1.8e-20) = 1.736e-20 - λ(c1) = λD(c1) = 1e-20 = 1e-20 - λ(c2) = λD(c2) = 1e-20 = 1e-20 - belief change = 1.110223025e-16 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 5.43e-21 x 1.32e-21) + (0.7 x 5.43e-21 x 8.68e-21) + (0.45 x 4.57e-21 x 1.32e-21) + (0.22 x 4.57e-21 x 8.68e-21) = 4.5867652e-41 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 5.43e-21 x 1.32e-21) + (0.3 x 5.43e-21 x 8.68e-21) + (0.55 x 4.57e-21 x 1.32e-21) + (0.78 x 4.57e-21 x 8.68e-21) = 5.4132348e-41 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 79 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 4e-38 0.1 - a2 0.09 4e-38 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 2e-21 2e-19 - a2 1.8e-20 2e-19 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 2e-21 2e-19 - a2 1.8e-20 2e-19 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 1.086e-20 1e-20 0.543 - b2 9.14e-21 1e-20 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 5.43e-21 1e-20 - b2 4.57e-21 1e-20 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 2.64e-21 1e-20 0.132 - c2 1.736e-20 1e-20 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 1.32e-21 1e-20 - c2 8.68e-21 1e-20 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 4.5867652e-41 1 0.45867652 - d2 5.4132348e-41 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x1e-20 + [(0.97)]x1e-20 = 1e-20 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x1e-20 + [(0.4)]x1e-20 = 1e-20 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x1e-20 + [(0.76)]x1e-20 = 1e-20 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x1e-20 + [(0.88)]x1e-20 = 1e-20 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x1.32e-21) + (0.7x8.68e-21)]x1 + [(0.8x1.32e-21) + (0.3x8.68e-21)]x1 = 1e-20 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x1.32e-21) + (0.22x8.68e-21)]x1 + [(0.55x1.32e-21) + (0.78x8.68e-21)]x1 = 1e-20 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x5.43e-21) + (0.45x4.57e-21)]x1 + [(0.8x5.43e-21) + (0.55x4.57e-21)]x1 = 1e-20 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x5.43e-21) + (0.22x4.57e-21)]x1 + [(0.3x5.43e-21) + (0.78x4.57e-21)]x1 = 1e-20 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 2e-19 = 2e-21 - πB(a2) = π(a2).λC(a2) = 0.09 x 2e-19 = 1.8e-20 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 2e-19 = 2e-21 - πC(a2) = π(a2).λB(a2) = 0.09 x 2e-19 = 1.8e-20 -π message B --> D - πD(b1) = π(b1) = 1.086e-20 = 1.086e-20 - πD(b2) = π(b2) = 9.14e-21 = 9.14e-21 -π message C --> D - πD(c1) = π(c1) = 2.64e-21 = 2.64e-21 - πD(c2) = π(c2) = 1.736e-20 = 1.736e-20 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 1e-20 x 1e-20 = 1e-40 - λ(a2) = λB(a2).λC(a2) = 1e-20 x 1e-20 = 1e-40 - belief change = 1.249000903e-16 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 2e-21) + (0.6 x 1.8e-20) = 1.086e-20 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 2e-21) + (0.4 x 1.8e-20) = 9.14e-21 - λ(b1) = λD(b1) = 1e-20 = 1e-20 - λ(b2) = λD(b2) = 1e-20 = 1e-20 - belief change = 0 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 2e-21) + (0.12 x 1.8e-20) = 2.64e-21 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 2e-21) + (0.88 x 1.8e-20) = 1.736e-20 - λ(c1) = λD(c1) = 1e-20 = 1e-20 - λ(c2) = λD(c2) = 1e-20 = 1e-20 - belief change = 0 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 1.086e-20 x 2.64e-21) + (0.7 x 1.086e-20 x 1.736e-20) + (0.45 x 9.14e-21 x 2.64e-21) + (0.22 x 9.14e-21 x 1.736e-20) = 1.83470608e-40 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 1.086e-20 x 2.64e-21) + (0.3 x 1.086e-20 x 1.736e-20) + (0.55 x 9.14e-21 x 2.64e-21) + (0.78 x 9.14e-21 x 1.736e-20) = 2.16529392e-40 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 80 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 1e-40 0.1 - a2 0.09 1e-40 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 2e-21 1e-20 - a2 1.8e-20 1e-20 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 2e-21 1e-20 - a2 1.8e-20 1e-20 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 1.086e-20 1e-20 0.543 - b2 9.14e-21 1e-20 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 1.086e-20 1e-20 - b2 9.14e-21 1e-20 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 2.64e-21 1e-20 0.132 - c2 1.736e-20 1e-20 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 2.64e-21 1e-20 - c2 1.736e-20 1e-20 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 1.83470608e-40 1 0.45867652 - d2 2.16529392e-40 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x1e-20 + [(0.97)]x1e-20 = 1e-20 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x1e-20 + [(0.4)]x1e-20 = 1e-20 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x1e-20 + [(0.76)]x1e-20 = 1e-20 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x1e-20 + [(0.88)]x1e-20 = 1e-20 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x2.64e-21) + (0.7x1.736e-20)]x1 + [(0.8x2.64e-21) + (0.3x1.736e-20)]x1 = 2e-20 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x2.64e-21) + (0.22x1.736e-20)]x1 + [(0.55x2.64e-21) + (0.78x1.736e-20)]x1 = 2e-20 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x1.086e-20) + (0.45x9.14e-21)]x1 + [(0.8x1.086e-20) + (0.55x9.14e-21)]x1 = 2e-20 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x1.086e-20) + (0.22x9.14e-21)]x1 + [(0.3x1.086e-20) + (0.78x9.14e-21)]x1 = 2e-20 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 1e-20 = 1e-22 - πB(a2) = π(a2).λC(a2) = 0.09 x 1e-20 = 9e-22 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 1e-20 = 1e-22 - πC(a2) = π(a2).λB(a2) = 0.09 x 1e-20 = 9e-22 -π message B --> D - πD(b1) = π(b1) = 1.086e-20 = 1.086e-20 - πD(b2) = π(b2) = 9.14e-21 = 9.14e-21 -π message C --> D - πD(c1) = π(c1) = 2.64e-21 = 2.64e-21 - πD(c2) = π(c2) = 1.736e-20 = 1.736e-20 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 1e-20 x 1e-20 = 1e-40 - λ(a2) = λB(a2).λC(a2) = 1e-20 x 1e-20 = 1e-40 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 1e-22) + (0.6 x 9e-22) = 5.43e-22 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 1e-22) + (0.4 x 9e-22) = 4.57e-22 - λ(b1) = λD(b1) = 2e-20 = 2e-20 - λ(b2) = λD(b2) = 2e-20 = 2e-20 - belief change = 5.551115123e-17 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 1e-22) + (0.12 x 9e-22) = 1.32e-22 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 1e-22) + (0.88 x 9e-22) = 8.68e-22 - λ(c1) = λD(c1) = 2e-20 = 2e-20 - λ(c2) = λD(c2) = 2e-20 = 2e-20 - belief change = 2.775557562e-17 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 1.086e-20 x 2.64e-21) + (0.7 x 1.086e-20 x 1.736e-20) + (0.45 x 9.14e-21 x 2.64e-21) + (0.22 x 9.14e-21 x 1.736e-20) = 1.83470608e-40 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 1.086e-20 x 2.64e-21) + (0.3 x 1.086e-20 x 1.736e-20) + (0.55 x 9.14e-21 x 2.64e-21) + (0.78 x 9.14e-21 x 1.736e-20) = 2.16529392e-40 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 81 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 1e-40 0.1 - a2 0.09 1e-40 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 1e-22 1e-20 - a2 9e-22 1e-20 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 1e-22 1e-20 - a2 9e-22 1e-20 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 5.43e-22 2e-20 0.543 - b2 4.57e-22 2e-20 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 1.086e-20 2e-20 - b2 9.14e-21 2e-20 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 1.32e-22 2e-20 0.132 - c2 8.68e-22 2e-20 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 2.64e-21 2e-20 - c2 1.736e-20 2e-20 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 1.83470608e-40 1 0.45867652 - d2 2.16529392e-40 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x2e-20 + [(0.97)]x2e-20 = 2e-20 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x2e-20 + [(0.4)]x2e-20 = 2e-20 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x2e-20 + [(0.76)]x2e-20 = 2e-20 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x2e-20 + [(0.88)]x2e-20 = 2e-20 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x2.64e-21) + (0.7x1.736e-20)]x1 + [(0.8x2.64e-21) + (0.3x1.736e-20)]x1 = 2e-20 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x2.64e-21) + (0.22x1.736e-20)]x1 + [(0.55x2.64e-21) + (0.78x1.736e-20)]x1 = 2e-20 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x1.086e-20) + (0.45x9.14e-21)]x1 + [(0.8x1.086e-20) + (0.55x9.14e-21)]x1 = 2e-20 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x1.086e-20) + (0.22x9.14e-21)]x1 + [(0.3x1.086e-20) + (0.78x9.14e-21)]x1 = 2e-20 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 1e-20 = 1e-22 - πB(a2) = π(a2).λC(a2) = 0.09 x 1e-20 = 9e-22 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 1e-20 = 1e-22 - πC(a2) = π(a2).λB(a2) = 0.09 x 1e-20 = 9e-22 -π message B --> D - πD(b1) = π(b1) = 5.43e-22 = 5.43e-22 - πD(b2) = π(b2) = 4.57e-22 = 4.57e-22 -π message C --> D - πD(c1) = π(c1) = 1.32e-22 = 1.32e-22 - πD(c2) = π(c2) = 8.68e-22 = 8.68e-22 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 2e-20 x 2e-20 = 4e-40 - λ(a2) = λB(a2).λC(a2) = 2e-20 x 2e-20 = 4e-40 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 1e-22) + (0.6 x 9e-22) = 5.43e-22 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 1e-22) + (0.4 x 9e-22) = 4.57e-22 - λ(b1) = λD(b1) = 2e-20 = 2e-20 - λ(b2) = λD(b2) = 2e-20 = 2e-20 - belief change = 0 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 1e-22) + (0.12 x 9e-22) = 1.32e-22 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 1e-22) + (0.88 x 9e-22) = 8.68e-22 - λ(c1) = λD(c1) = 2e-20 = 2e-20 - λ(c2) = λD(c2) = 2e-20 = 2e-20 - belief change = 0 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 5.43e-22 x 1.32e-22) + (0.7 x 5.43e-22 x 8.68e-22) + (0.45 x 4.57e-22 x 1.32e-22) + (0.22 x 4.57e-22 x 8.68e-22) = 4.5867652e-43 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 5.43e-22 x 1.32e-22) + (0.3 x 5.43e-22 x 8.68e-22) + (0.55 x 4.57e-22 x 1.32e-22) + (0.78 x 4.57e-22 x 8.68e-22) = 5.4132348e-43 - λ(d1) = 1 - λ(d2) = 1 - belief change = 1.665334537e-16 - - -******************************************************************************** -Iteration 82 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 4e-40 0.1 - a2 0.09 4e-40 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 1e-22 2e-20 - a2 9e-22 2e-20 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 1e-22 2e-20 - a2 9e-22 2e-20 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 5.43e-22 2e-20 0.543 - b2 4.57e-22 2e-20 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 5.43e-22 2e-20 - b2 4.57e-22 2e-20 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 1.32e-22 2e-20 0.132 - c2 8.68e-22 2e-20 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 1.32e-22 2e-20 - c2 8.68e-22 2e-20 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 4.5867652e-43 1 0.45867652 - d2 5.4132348e-43 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x2e-20 + [(0.97)]x2e-20 = 2e-20 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x2e-20 + [(0.4)]x2e-20 = 2e-20 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x2e-20 + [(0.76)]x2e-20 = 2e-20 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x2e-20 + [(0.88)]x2e-20 = 2e-20 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x1.32e-22) + (0.7x8.68e-22)]x1 + [(0.8x1.32e-22) + (0.3x8.68e-22)]x1 = 1e-21 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x1.32e-22) + (0.22x8.68e-22)]x1 + [(0.55x1.32e-22) + (0.78x8.68e-22)]x1 = 1e-21 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x5.43e-22) + (0.45x4.57e-22)]x1 + [(0.8x5.43e-22) + (0.55x4.57e-22)]x1 = 1e-21 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x5.43e-22) + (0.22x4.57e-22)]x1 + [(0.3x5.43e-22) + (0.78x4.57e-22)]x1 = 1e-21 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 2e-20 = 2e-22 - πB(a2) = π(a2).λC(a2) = 0.09 x 2e-20 = 1.8e-21 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 2e-20 = 2e-22 - πC(a2) = π(a2).λB(a2) = 0.09 x 2e-20 = 1.8e-21 -π message B --> D - πD(b1) = π(b1) = 5.43e-22 = 5.43e-22 - πD(b2) = π(b2) = 4.57e-22 = 4.57e-22 -π message C --> D - πD(c1) = π(c1) = 1.32e-22 = 1.32e-22 - πD(c2) = π(c2) = 8.68e-22 = 8.68e-22 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 2e-20 x 2e-20 = 4e-40 - λ(a2) = λB(a2).λC(a2) = 2e-20 x 2e-20 = 4e-40 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 2e-22) + (0.6 x 1.8e-21) = 1.086e-21 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 2e-22) + (0.4 x 1.8e-21) = 9.14e-22 - λ(b1) = λD(b1) = 1e-21 = 1e-21 - λ(b2) = λD(b2) = 1e-21 = 1e-21 - belief change = 1.110223025e-16 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 2e-22) + (0.12 x 1.8e-21) = 2.64e-22 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 2e-22) + (0.88 x 1.8e-21) = 1.736e-21 - λ(c1) = λD(c1) = 1e-21 = 1e-21 - λ(c2) = λD(c2) = 1e-21 = 1e-21 - belief change = 2.775557562e-17 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 5.43e-22 x 1.32e-22) + (0.7 x 5.43e-22 x 8.68e-22) + (0.45 x 4.57e-22 x 1.32e-22) + (0.22 x 4.57e-22 x 8.68e-22) = 4.5867652e-43 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 5.43e-22 x 1.32e-22) + (0.3 x 5.43e-22 x 8.68e-22) + (0.55 x 4.57e-22 x 1.32e-22) + (0.78 x 4.57e-22 x 8.68e-22) = 5.4132348e-43 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 83 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 4e-40 0.1 - a2 0.09 4e-40 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 2e-22 2e-20 - a2 1.8e-21 2e-20 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 2e-22 2e-20 - a2 1.8e-21 2e-20 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 1.086e-21 1e-21 0.543 - b2 9.14e-22 1e-21 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 5.43e-22 1e-21 - b2 4.57e-22 1e-21 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 2.64e-22 1e-21 0.132 - c2 1.736e-21 1e-21 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 1.32e-22 1e-21 - c2 8.68e-22 1e-21 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 4.5867652e-43 1 0.45867652 - d2 5.4132348e-43 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x1e-21 + [(0.97)]x1e-21 = 1e-21 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x1e-21 + [(0.4)]x1e-21 = 1e-21 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x1e-21 + [(0.76)]x1e-21 = 1e-21 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x1e-21 + [(0.88)]x1e-21 = 1e-21 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x1.32e-22) + (0.7x8.68e-22)]x1 + [(0.8x1.32e-22) + (0.3x8.68e-22)]x1 = 1e-21 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x1.32e-22) + (0.22x8.68e-22)]x1 + [(0.55x1.32e-22) + (0.78x8.68e-22)]x1 = 1e-21 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x5.43e-22) + (0.45x4.57e-22)]x1 + [(0.8x5.43e-22) + (0.55x4.57e-22)]x1 = 1e-21 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x5.43e-22) + (0.22x4.57e-22)]x1 + [(0.3x5.43e-22) + (0.78x4.57e-22)]x1 = 1e-21 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 2e-20 = 2e-22 - πB(a2) = π(a2).λC(a2) = 0.09 x 2e-20 = 1.8e-21 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 2e-20 = 2e-22 - πC(a2) = π(a2).λB(a2) = 0.09 x 2e-20 = 1.8e-21 -π message B --> D - πD(b1) = π(b1) = 1.086e-21 = 1.086e-21 - πD(b2) = π(b2) = 9.14e-22 = 9.14e-22 -π message C --> D - πD(c1) = π(c1) = 2.64e-22 = 2.64e-22 - πD(c2) = π(c2) = 1.736e-21 = 1.736e-21 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 1e-21 x 1e-21 = 1e-42 - λ(a2) = λB(a2).λC(a2) = 1e-21 x 1e-21 = 1e-42 - belief change = 1.249000903e-16 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 2e-22) + (0.6 x 1.8e-21) = 1.086e-21 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 2e-22) + (0.4 x 1.8e-21) = 9.14e-22 - λ(b1) = λD(b1) = 1e-21 = 1e-21 - λ(b2) = λD(b2) = 1e-21 = 1e-21 - belief change = 0 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 2e-22) + (0.12 x 1.8e-21) = 2.64e-22 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 2e-22) + (0.88 x 1.8e-21) = 1.736e-21 - λ(c1) = λD(c1) = 1e-21 = 1e-21 - λ(c2) = λD(c2) = 1e-21 = 1e-21 - belief change = 0 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 1.086e-21 x 2.64e-22) + (0.7 x 1.086e-21 x 1.736e-21) + (0.45 x 9.14e-22 x 2.64e-22) + (0.22 x 9.14e-22 x 1.736e-21) = 1.83470608e-42 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 1.086e-21 x 2.64e-22) + (0.3 x 1.086e-21 x 1.736e-21) + (0.55 x 9.14e-22 x 2.64e-22) + (0.78 x 9.14e-22 x 1.736e-21) = 2.16529392e-42 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 84 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 1e-42 0.1 - a2 0.09 1e-42 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 2e-22 1e-21 - a2 1.8e-21 1e-21 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 2e-22 1e-21 - a2 1.8e-21 1e-21 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 1.086e-21 1e-21 0.543 - b2 9.14e-22 1e-21 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 1.086e-21 1e-21 - b2 9.14e-22 1e-21 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 2.64e-22 1e-21 0.132 - c2 1.736e-21 1e-21 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 2.64e-22 1e-21 - c2 1.736e-21 1e-21 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 1.83470608e-42 1 0.45867652 - d2 2.16529392e-42 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x1e-21 + [(0.97)]x1e-21 = 1e-21 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x1e-21 + [(0.4)]x1e-21 = 1e-21 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x1e-21 + [(0.76)]x1e-21 = 1e-21 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x1e-21 + [(0.88)]x1e-21 = 1e-21 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x2.64e-22) + (0.7x1.736e-21)]x1 + [(0.8x2.64e-22) + (0.3x1.736e-21)]x1 = 2e-21 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x2.64e-22) + (0.22x1.736e-21)]x1 + [(0.55x2.64e-22) + (0.78x1.736e-21)]x1 = 2e-21 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x1.086e-21) + (0.45x9.14e-22)]x1 + [(0.8x1.086e-21) + (0.55x9.14e-22)]x1 = 2e-21 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x1.086e-21) + (0.22x9.14e-22)]x1 + [(0.3x1.086e-21) + (0.78x9.14e-22)]x1 = 2e-21 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 1e-21 = 1e-23 - πB(a2) = π(a2).λC(a2) = 0.09 x 1e-21 = 9e-23 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 1e-21 = 1e-23 - πC(a2) = π(a2).λB(a2) = 0.09 x 1e-21 = 9e-23 -π message B --> D - πD(b1) = π(b1) = 1.086e-21 = 1.086e-21 - πD(b2) = π(b2) = 9.14e-22 = 9.14e-22 -π message C --> D - πD(c1) = π(c1) = 2.64e-22 = 2.64e-22 - πD(c2) = π(c2) = 1.736e-21 = 1.736e-21 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 1e-21 x 1e-21 = 1e-42 - λ(a2) = λB(a2).λC(a2) = 1e-21 x 1e-21 = 1e-42 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 1e-23) + (0.6 x 9e-23) = 5.43e-23 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 1e-23) + (0.4 x 9e-23) = 4.57e-23 - λ(b1) = λD(b1) = 2e-21 = 2e-21 - λ(b2) = λD(b2) = 2e-21 = 2e-21 - belief change = 2.220446049e-16 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 1e-23) + (0.12 x 9e-23) = 1.32e-23 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 1e-23) + (0.88 x 9e-23) = 8.68e-23 - λ(c1) = λD(c1) = 2e-21 = 2e-21 - λ(c2) = λD(c2) = 2e-21 = 2e-21 - belief change = 0 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 1.086e-21 x 2.64e-22) + (0.7 x 1.086e-21 x 1.736e-21) + (0.45 x 9.14e-22 x 2.64e-22) + (0.22 x 9.14e-22 x 1.736e-21) = 1.83470608e-42 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 1.086e-21 x 2.64e-22) + (0.3 x 1.086e-21 x 1.736e-21) + (0.55 x 9.14e-22 x 2.64e-22) + (0.78 x 9.14e-22 x 1.736e-21) = 2.16529392e-42 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 85 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 1e-42 0.1 - a2 0.09 1e-42 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 1e-23 1e-21 - a2 9e-23 1e-21 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 1e-23 1e-21 - a2 9e-23 1e-21 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 5.43e-23 2e-21 0.543 - b2 4.57e-23 2e-21 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 1.086e-21 2e-21 - b2 9.14e-22 2e-21 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 1.32e-23 2e-21 0.132 - c2 8.68e-23 2e-21 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 2.64e-22 2e-21 - c2 1.736e-21 2e-21 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 1.83470608e-42 1 0.45867652 - d2 2.16529392e-42 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x2e-21 + [(0.97)]x2e-21 = 2e-21 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x2e-21 + [(0.4)]x2e-21 = 2e-21 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x2e-21 + [(0.76)]x2e-21 = 2e-21 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x2e-21 + [(0.88)]x2e-21 = 2e-21 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x2.64e-22) + (0.7x1.736e-21)]x1 + [(0.8x2.64e-22) + (0.3x1.736e-21)]x1 = 2e-21 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x2.64e-22) + (0.22x1.736e-21)]x1 + [(0.55x2.64e-22) + (0.78x1.736e-21)]x1 = 2e-21 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x1.086e-21) + (0.45x9.14e-22)]x1 + [(0.8x1.086e-21) + (0.55x9.14e-22)]x1 = 2e-21 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x1.086e-21) + (0.22x9.14e-22)]x1 + [(0.3x1.086e-21) + (0.78x9.14e-22)]x1 = 2e-21 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 1e-21 = 1e-23 - πB(a2) = π(a2).λC(a2) = 0.09 x 1e-21 = 9e-23 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 1e-21 = 1e-23 - πC(a2) = π(a2).λB(a2) = 0.09 x 1e-21 = 9e-23 -π message B --> D - πD(b1) = π(b1) = 5.43e-23 = 5.43e-23 - πD(b2) = π(b2) = 4.57e-23 = 4.57e-23 -π message C --> D - πD(c1) = π(c1) = 1.32e-23 = 1.32e-23 - πD(c2) = π(c2) = 8.68e-23 = 8.68e-23 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 2e-21 x 2e-21 = 4e-42 - λ(a2) = λB(a2).λC(a2) = 2e-21 x 2e-21 = 4e-42 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 1e-23) + (0.6 x 9e-23) = 5.43e-23 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 1e-23) + (0.4 x 9e-23) = 4.57e-23 - λ(b1) = λD(b1) = 2e-21 = 2e-21 - λ(b2) = λD(b2) = 2e-21 = 2e-21 - belief change = 0 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 1e-23) + (0.12 x 9e-23) = 1.32e-23 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 1e-23) + (0.88 x 9e-23) = 8.68e-23 - λ(c1) = λD(c1) = 2e-21 = 2e-21 - λ(c2) = λD(c2) = 2e-21 = 2e-21 - belief change = 0 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 5.43e-23 x 1.32e-23) + (0.7 x 5.43e-23 x 8.68e-23) + (0.45 x 4.57e-23 x 1.32e-23) + (0.22 x 4.57e-23 x 8.68e-23) = 4.5867652e-45 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 5.43e-23 x 1.32e-23) + (0.3 x 5.43e-23 x 8.68e-23) + (0.55 x 4.57e-23 x 1.32e-23) + (0.78 x 4.57e-23 x 8.68e-23) = 5.4132348e-45 - λ(d1) = 1 - λ(d2) = 1 - belief change = 2.220446049e-16 - - -******************************************************************************** -Iteration 86 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 4e-42 0.1 - a2 0.09 4e-42 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 1e-23 2e-21 - a2 9e-23 2e-21 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 1e-23 2e-21 - a2 9e-23 2e-21 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 5.43e-23 2e-21 0.543 - b2 4.57e-23 2e-21 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 5.43e-23 2e-21 - b2 4.57e-23 2e-21 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 1.32e-23 2e-21 0.132 - c2 8.68e-23 2e-21 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 1.32e-23 2e-21 - c2 8.68e-23 2e-21 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 4.5867652e-45 1 0.45867652 - d2 5.4132348e-45 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x2e-21 + [(0.97)]x2e-21 = 2e-21 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x2e-21 + [(0.4)]x2e-21 = 2e-21 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x2e-21 + [(0.76)]x2e-21 = 2e-21 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x2e-21 + [(0.88)]x2e-21 = 2e-21 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x1.32e-23) + (0.7x8.68e-23)]x1 + [(0.8x1.32e-23) + (0.3x8.68e-23)]x1 = 1e-22 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x1.32e-23) + (0.22x8.68e-23)]x1 + [(0.55x1.32e-23) + (0.78x8.68e-23)]x1 = 1e-22 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x5.43e-23) + (0.45x4.57e-23)]x1 + [(0.8x5.43e-23) + (0.55x4.57e-23)]x1 = 1e-22 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x5.43e-23) + (0.22x4.57e-23)]x1 + [(0.3x5.43e-23) + (0.78x4.57e-23)]x1 = 1e-22 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 2e-21 = 2e-23 - πB(a2) = π(a2).λC(a2) = 0.09 x 2e-21 = 1.8e-22 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 2e-21 = 2e-23 - πC(a2) = π(a2).λB(a2) = 0.09 x 2e-21 = 1.8e-22 -π message B --> D - πD(b1) = π(b1) = 5.43e-23 = 5.43e-23 - πD(b2) = π(b2) = 4.57e-23 = 4.57e-23 -π message C --> D - πD(c1) = π(c1) = 1.32e-23 = 1.32e-23 - πD(c2) = π(c2) = 8.68e-23 = 8.68e-23 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 2e-21 x 2e-21 = 4e-42 - λ(a2) = λB(a2).λC(a2) = 2e-21 x 2e-21 = 4e-42 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 2e-23) + (0.6 x 1.8e-22) = 1.086e-22 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 2e-23) + (0.4 x 1.8e-22) = 9.14e-23 - λ(b1) = λD(b1) = 1e-22 = 1e-22 - λ(b2) = λD(b2) = 1e-22 = 1e-22 - belief change = 1.110223025e-16 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 2e-23) + (0.12 x 1.8e-22) = 2.64e-23 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 2e-23) + (0.88 x 1.8e-22) = 1.736e-22 - λ(c1) = λD(c1) = 1e-22 = 1e-22 - λ(c2) = λD(c2) = 1e-22 = 1e-22 - belief change = 0 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 5.43e-23 x 1.32e-23) + (0.7 x 5.43e-23 x 8.68e-23) + (0.45 x 4.57e-23 x 1.32e-23) + (0.22 x 4.57e-23 x 8.68e-23) = 4.5867652e-45 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 5.43e-23 x 1.32e-23) + (0.3 x 5.43e-23 x 8.68e-23) + (0.55 x 4.57e-23 x 1.32e-23) + (0.78 x 4.57e-23 x 8.68e-23) = 5.4132348e-45 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 87 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 4e-42 0.1 - a2 0.09 4e-42 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 2e-23 2e-21 - a2 1.8e-22 2e-21 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 2e-23 2e-21 - a2 1.8e-22 2e-21 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 1.086e-22 1e-22 0.543 - b2 9.14e-23 1e-22 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 5.43e-23 1e-22 - b2 4.57e-23 1e-22 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 2.64e-23 1e-22 0.132 - c2 1.736e-22 1e-22 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 1.32e-23 1e-22 - c2 8.68e-23 1e-22 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 4.5867652e-45 1 0.45867652 - d2 5.4132348e-45 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x1e-22 + [(0.97)]x1e-22 = 1e-22 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x1e-22 + [(0.4)]x1e-22 = 1e-22 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x1e-22 + [(0.76)]x1e-22 = 1e-22 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x1e-22 + [(0.88)]x1e-22 = 1e-22 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x1.32e-23) + (0.7x8.68e-23)]x1 + [(0.8x1.32e-23) + (0.3x8.68e-23)]x1 = 1e-22 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x1.32e-23) + (0.22x8.68e-23)]x1 + [(0.55x1.32e-23) + (0.78x8.68e-23)]x1 = 1e-22 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x5.43e-23) + (0.45x4.57e-23)]x1 + [(0.8x5.43e-23) + (0.55x4.57e-23)]x1 = 1e-22 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x5.43e-23) + (0.22x4.57e-23)]x1 + [(0.3x5.43e-23) + (0.78x4.57e-23)]x1 = 1e-22 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 2e-21 = 2e-23 - πB(a2) = π(a2).λC(a2) = 0.09 x 2e-21 = 1.8e-22 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 2e-21 = 2e-23 - πC(a2) = π(a2).λB(a2) = 0.09 x 2e-21 = 1.8e-22 -π message B --> D - πD(b1) = π(b1) = 1.086e-22 = 1.086e-22 - πD(b2) = π(b2) = 9.14e-23 = 9.14e-23 -π message C --> D - πD(c1) = π(c1) = 2.64e-23 = 2.64e-23 - πD(c2) = π(c2) = 1.736e-22 = 1.736e-22 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 1e-22 x 1e-22 = 1e-44 - λ(a2) = λB(a2).λC(a2) = 1e-22 x 1e-22 = 1e-44 - belief change = 1.387778781e-17 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 2e-23) + (0.6 x 1.8e-22) = 1.086e-22 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 2e-23) + (0.4 x 1.8e-22) = 9.14e-23 - λ(b1) = λD(b1) = 1e-22 = 1e-22 - λ(b2) = λD(b2) = 1e-22 = 1e-22 - belief change = 0 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 2e-23) + (0.12 x 1.8e-22) = 2.64e-23 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 2e-23) + (0.88 x 1.8e-22) = 1.736e-22 - λ(c1) = λD(c1) = 1e-22 = 1e-22 - λ(c2) = λD(c2) = 1e-22 = 1e-22 - belief change = 0 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 1.086e-22 x 2.64e-23) + (0.7 x 1.086e-22 x 1.736e-22) + (0.45 x 9.14e-23 x 2.64e-23) + (0.22 x 9.14e-23 x 1.736e-22) = 1.83470608e-44 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 1.086e-22 x 2.64e-23) + (0.3 x 1.086e-22 x 1.736e-22) + (0.55 x 9.14e-23 x 2.64e-23) + (0.78 x 9.14e-23 x 1.736e-22) = 2.16529392e-44 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 88 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 1e-44 0.1 - a2 0.09 1e-44 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 2e-23 1e-22 - a2 1.8e-22 1e-22 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 2e-23 1e-22 - a2 1.8e-22 1e-22 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 1.086e-22 1e-22 0.543 - b2 9.14e-23 1e-22 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 1.086e-22 1e-22 - b2 9.14e-23 1e-22 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 2.64e-23 1e-22 0.132 - c2 1.736e-22 1e-22 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 2.64e-23 1e-22 - c2 1.736e-22 1e-22 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 1.83470608e-44 1 0.45867652 - d2 2.16529392e-44 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x1e-22 + [(0.97)]x1e-22 = 1e-22 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x1e-22 + [(0.4)]x1e-22 = 1e-22 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x1e-22 + [(0.76)]x1e-22 = 1e-22 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x1e-22 + [(0.88)]x1e-22 = 1e-22 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x2.64e-23) + (0.7x1.736e-22)]x1 + [(0.8x2.64e-23) + (0.3x1.736e-22)]x1 = 2e-22 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x2.64e-23) + (0.22x1.736e-22)]x1 + [(0.55x2.64e-23) + (0.78x1.736e-22)]x1 = 2e-22 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x1.086e-22) + (0.45x9.14e-23)]x1 + [(0.8x1.086e-22) + (0.55x9.14e-23)]x1 = 2e-22 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x1.086e-22) + (0.22x9.14e-23)]x1 + [(0.3x1.086e-22) + (0.78x9.14e-23)]x1 = 2e-22 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 1e-22 = 1e-24 - πB(a2) = π(a2).λC(a2) = 0.09 x 1e-22 = 9e-24 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 1e-22 = 1e-24 - πC(a2) = π(a2).λB(a2) = 0.09 x 1e-22 = 9e-24 -π message B --> D - πD(b1) = π(b1) = 1.086e-22 = 1.086e-22 - πD(b2) = π(b2) = 9.14e-23 = 9.14e-23 -π message C --> D - πD(c1) = π(c1) = 2.64e-23 = 2.64e-23 - πD(c2) = π(c2) = 1.736e-22 = 1.736e-22 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 1e-22 x 1e-22 = 1e-44 - λ(a2) = λB(a2).λC(a2) = 1e-22 x 1e-22 = 1e-44 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 1e-24) + (0.6 x 9e-24) = 5.43e-24 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 1e-24) + (0.4 x 9e-24) = 4.57e-24 - λ(b1) = λD(b1) = 2e-22 = 2e-22 - λ(b2) = λD(b2) = 2e-22 = 2e-22 - belief change = 0 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 1e-24) + (0.12 x 9e-24) = 1.32e-24 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 1e-24) + (0.88 x 9e-24) = 8.68e-24 - λ(c1) = λD(c1) = 2e-22 = 2e-22 - λ(c2) = λD(c2) = 2e-22 = 2e-22 - belief change = 0 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 1.086e-22 x 2.64e-23) + (0.7 x 1.086e-22 x 1.736e-22) + (0.45 x 9.14e-23 x 2.64e-23) + (0.22 x 9.14e-23 x 1.736e-22) = 1.83470608e-44 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 1.086e-22 x 2.64e-23) + (0.3 x 1.086e-22 x 1.736e-22) + (0.55 x 9.14e-23 x 2.64e-23) + (0.78 x 9.14e-23 x 1.736e-22) = 2.16529392e-44 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 89 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 1e-44 0.1 - a2 0.09 1e-44 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 1e-24 1e-22 - a2 9e-24 1e-22 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 1e-24 1e-22 - a2 9e-24 1e-22 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 5.43e-24 2e-22 0.543 - b2 4.57e-24 2e-22 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 1.086e-22 2e-22 - b2 9.14e-23 2e-22 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 1.32e-24 2e-22 0.132 - c2 8.68e-24 2e-22 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 2.64e-23 2e-22 - c2 1.736e-22 2e-22 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 1.83470608e-44 1 0.45867652 - d2 2.16529392e-44 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x2e-22 + [(0.97)]x2e-22 = 2e-22 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x2e-22 + [(0.4)]x2e-22 = 2e-22 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x2e-22 + [(0.76)]x2e-22 = 2e-22 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x2e-22 + [(0.88)]x2e-22 = 2e-22 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x2.64e-23) + (0.7x1.736e-22)]x1 + [(0.8x2.64e-23) + (0.3x1.736e-22)]x1 = 2e-22 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x2.64e-23) + (0.22x1.736e-22)]x1 + [(0.55x2.64e-23) + (0.78x1.736e-22)]x1 = 2e-22 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x1.086e-22) + (0.45x9.14e-23)]x1 + [(0.8x1.086e-22) + (0.55x9.14e-23)]x1 = 2e-22 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x1.086e-22) + (0.22x9.14e-23)]x1 + [(0.3x1.086e-22) + (0.78x9.14e-23)]x1 = 2e-22 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 1e-22 = 1e-24 - πB(a2) = π(a2).λC(a2) = 0.09 x 1e-22 = 9e-24 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 1e-22 = 1e-24 - πC(a2) = π(a2).λB(a2) = 0.09 x 1e-22 = 9e-24 -π message B --> D - πD(b1) = π(b1) = 5.43e-24 = 5.43e-24 - πD(b2) = π(b2) = 4.57e-24 = 4.57e-24 -π message C --> D - πD(c1) = π(c1) = 1.32e-24 = 1.32e-24 - πD(c2) = π(c2) = 8.68e-24 = 8.68e-24 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 2e-22 x 2e-22 = 4e-44 - λ(a2) = λB(a2).λC(a2) = 2e-22 x 2e-22 = 4e-44 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 1e-24) + (0.6 x 9e-24) = 5.43e-24 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 1e-24) + (0.4 x 9e-24) = 4.57e-24 - λ(b1) = λD(b1) = 2e-22 = 2e-22 - λ(b2) = λD(b2) = 2e-22 = 2e-22 - belief change = 0 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 1e-24) + (0.12 x 9e-24) = 1.32e-24 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 1e-24) + (0.88 x 9e-24) = 8.68e-24 - λ(c1) = λD(c1) = 2e-22 = 2e-22 - λ(c2) = λD(c2) = 2e-22 = 2e-22 - belief change = 0 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 5.43e-24 x 1.32e-24) + (0.7 x 5.43e-24 x 8.68e-24) + (0.45 x 4.57e-24 x 1.32e-24) + (0.22 x 4.57e-24 x 8.68e-24) = 4.5867652e-47 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 5.43e-24 x 1.32e-24) + (0.3 x 5.43e-24 x 8.68e-24) + (0.55 x 4.57e-24 x 1.32e-24) + (0.78 x 4.57e-24 x 8.68e-24) = 5.4132348e-47 - λ(d1) = 1 - λ(d2) = 1 - belief change = 1.665334537e-16 - - -******************************************************************************** -Iteration 90 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 4e-44 0.1 - a2 0.09 4e-44 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 1e-24 2e-22 - a2 9e-24 2e-22 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 1e-24 2e-22 - a2 9e-24 2e-22 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 5.43e-24 2e-22 0.543 - b2 4.57e-24 2e-22 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 5.43e-24 2e-22 - b2 4.57e-24 2e-22 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 1.32e-24 2e-22 0.132 - c2 8.68e-24 2e-22 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 1.32e-24 2e-22 - c2 8.68e-24 2e-22 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 4.5867652e-47 1 0.45867652 - d2 5.4132348e-47 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x2e-22 + [(0.97)]x2e-22 = 2e-22 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x2e-22 + [(0.4)]x2e-22 = 2e-22 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x2e-22 + [(0.76)]x2e-22 = 2e-22 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x2e-22 + [(0.88)]x2e-22 = 2e-22 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x1.32e-24) + (0.7x8.68e-24)]x1 + [(0.8x1.32e-24) + (0.3x8.68e-24)]x1 = 1e-23 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x1.32e-24) + (0.22x8.68e-24)]x1 + [(0.55x1.32e-24) + (0.78x8.68e-24)]x1 = 1e-23 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x5.43e-24) + (0.45x4.57e-24)]x1 + [(0.8x5.43e-24) + (0.55x4.57e-24)]x1 = 1e-23 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x5.43e-24) + (0.22x4.57e-24)]x1 + [(0.3x5.43e-24) + (0.78x4.57e-24)]x1 = 1e-23 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 2e-22 = 2e-24 - πB(a2) = π(a2).λC(a2) = 0.09 x 2e-22 = 1.8e-23 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 2e-22 = 2e-24 - πC(a2) = π(a2).λB(a2) = 0.09 x 2e-22 = 1.8e-23 -π message B --> D - πD(b1) = π(b1) = 5.43e-24 = 5.43e-24 - πD(b2) = π(b2) = 4.57e-24 = 4.57e-24 -π message C --> D - πD(c1) = π(c1) = 1.32e-24 = 1.32e-24 - πD(c2) = π(c2) = 8.68e-24 = 8.68e-24 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 2e-22 x 2e-22 = 4e-44 - λ(a2) = λB(a2).λC(a2) = 2e-22 x 2e-22 = 4e-44 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 2e-24) + (0.6 x 1.8e-23) = 1.086e-23 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 2e-24) + (0.4 x 1.8e-23) = 9.14e-24 - λ(b1) = λD(b1) = 1e-23 = 1e-23 - λ(b2) = λD(b2) = 1e-23 = 1e-23 - belief change = 5.551115123e-17 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 2e-24) + (0.12 x 1.8e-23) = 2.64e-24 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 2e-24) + (0.88 x 1.8e-23) = 1.736e-23 - λ(c1) = λD(c1) = 1e-23 = 1e-23 - λ(c2) = λD(c2) = 1e-23 = 1e-23 - belief change = 0 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 5.43e-24 x 1.32e-24) + (0.7 x 5.43e-24 x 8.68e-24) + (0.45 x 4.57e-24 x 1.32e-24) + (0.22 x 4.57e-24 x 8.68e-24) = 4.5867652e-47 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 5.43e-24 x 1.32e-24) + (0.3 x 5.43e-24 x 8.68e-24) + (0.55 x 4.57e-24 x 1.32e-24) + (0.78 x 4.57e-24 x 8.68e-24) = 5.4132348e-47 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 91 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 4e-44 0.1 - a2 0.09 4e-44 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 2e-24 2e-22 - a2 1.8e-23 2e-22 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 2e-24 2e-22 - a2 1.8e-23 2e-22 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 1.086e-23 1e-23 0.543 - b2 9.14e-24 1e-23 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 5.43e-24 1e-23 - b2 4.57e-24 1e-23 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 2.64e-24 1e-23 0.132 - c2 1.736e-23 1e-23 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 1.32e-24 1e-23 - c2 8.68e-24 1e-23 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 4.5867652e-47 1 0.45867652 - d2 5.4132348e-47 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x1e-23 + [(0.97)]x1e-23 = 1e-23 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x1e-23 + [(0.4)]x1e-23 = 1e-23 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x1e-23 + [(0.76)]x1e-23 = 1e-23 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x1e-23 + [(0.88)]x1e-23 = 1e-23 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x1.32e-24) + (0.7x8.68e-24)]x1 + [(0.8x1.32e-24) + (0.3x8.68e-24)]x1 = 1e-23 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x1.32e-24) + (0.22x8.68e-24)]x1 + [(0.55x1.32e-24) + (0.78x8.68e-24)]x1 = 1e-23 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x5.43e-24) + (0.45x4.57e-24)]x1 + [(0.8x5.43e-24) + (0.55x4.57e-24)]x1 = 1e-23 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x5.43e-24) + (0.22x4.57e-24)]x1 + [(0.3x5.43e-24) + (0.78x4.57e-24)]x1 = 1e-23 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 2e-22 = 2e-24 - πB(a2) = π(a2).λC(a2) = 0.09 x 2e-22 = 1.8e-23 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 2e-22 = 2e-24 - πC(a2) = π(a2).λB(a2) = 0.09 x 2e-22 = 1.8e-23 -π message B --> D - πD(b1) = π(b1) = 1.086e-23 = 1.086e-23 - πD(b2) = π(b2) = 9.14e-24 = 9.14e-24 -π message C --> D - πD(c1) = π(c1) = 2.64e-24 = 2.64e-24 - πD(c2) = π(c2) = 1.736e-23 = 1.736e-23 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 1e-23 x 1e-23 = 1e-46 - λ(a2) = λB(a2).λC(a2) = 1e-23 x 1e-23 = 1e-46 - belief change = 1.110223025e-16 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 2e-24) + (0.6 x 1.8e-23) = 1.086e-23 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 2e-24) + (0.4 x 1.8e-23) = 9.14e-24 - λ(b1) = λD(b1) = 1e-23 = 1e-23 - λ(b2) = λD(b2) = 1e-23 = 1e-23 - belief change = 0 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 2e-24) + (0.12 x 1.8e-23) = 2.64e-24 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 2e-24) + (0.88 x 1.8e-23) = 1.736e-23 - λ(c1) = λD(c1) = 1e-23 = 1e-23 - λ(c2) = λD(c2) = 1e-23 = 1e-23 - belief change = 0 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 1.086e-23 x 2.64e-24) + (0.7 x 1.086e-23 x 1.736e-23) + (0.45 x 9.14e-24 x 2.64e-24) + (0.22 x 9.14e-24 x 1.736e-23) = 1.83470608e-46 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 1.086e-23 x 2.64e-24) + (0.3 x 1.086e-23 x 1.736e-23) + (0.55 x 9.14e-24 x 2.64e-24) + (0.78 x 9.14e-24 x 1.736e-23) = 2.16529392e-46 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 92 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 1e-46 0.1 - a2 0.09 1e-46 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 2e-24 1e-23 - a2 1.8e-23 1e-23 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 2e-24 1e-23 - a2 1.8e-23 1e-23 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 1.086e-23 1e-23 0.543 - b2 9.14e-24 1e-23 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 1.086e-23 1e-23 - b2 9.14e-24 1e-23 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 2.64e-24 1e-23 0.132 - c2 1.736e-23 1e-23 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 2.64e-24 1e-23 - c2 1.736e-23 1e-23 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 1.83470608e-46 1 0.45867652 - d2 2.16529392e-46 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x1e-23 + [(0.97)]x1e-23 = 1e-23 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x1e-23 + [(0.4)]x1e-23 = 1e-23 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x1e-23 + [(0.76)]x1e-23 = 1e-23 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x1e-23 + [(0.88)]x1e-23 = 1e-23 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x2.64e-24) + (0.7x1.736e-23)]x1 + [(0.8x2.64e-24) + (0.3x1.736e-23)]x1 = 2e-23 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x2.64e-24) + (0.22x1.736e-23)]x1 + [(0.55x2.64e-24) + (0.78x1.736e-23)]x1 = 2e-23 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x1.086e-23) + (0.45x9.14e-24)]x1 + [(0.8x1.086e-23) + (0.55x9.14e-24)]x1 = 2e-23 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x1.086e-23) + (0.22x9.14e-24)]x1 + [(0.3x1.086e-23) + (0.78x9.14e-24)]x1 = 2e-23 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 1e-23 = 1e-25 - πB(a2) = π(a2).λC(a2) = 0.09 x 1e-23 = 9e-25 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 1e-23 = 1e-25 - πC(a2) = π(a2).λB(a2) = 0.09 x 1e-23 = 9e-25 -π message B --> D - πD(b1) = π(b1) = 1.086e-23 = 1.086e-23 - πD(b2) = π(b2) = 9.14e-24 = 9.14e-24 -π message C --> D - πD(c1) = π(c1) = 2.64e-24 = 2.64e-24 - πD(c2) = π(c2) = 1.736e-23 = 1.736e-23 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 1e-23 x 1e-23 = 1e-46 - λ(a2) = λB(a2).λC(a2) = 1e-23 x 1e-23 = 1e-46 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 1e-25) + (0.6 x 9e-25) = 5.43e-25 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 1e-25) + (0.4 x 9e-25) = 4.57e-25 - λ(b1) = λD(b1) = 2e-23 = 2e-23 - λ(b2) = λD(b2) = 2e-23 = 2e-23 - belief change = 5.551115123e-17 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 1e-25) + (0.12 x 9e-25) = 1.32e-25 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 1e-25) + (0.88 x 9e-25) = 8.68e-25 - λ(c1) = λD(c1) = 2e-23 = 2e-23 - λ(c2) = λD(c2) = 2e-23 = 2e-23 - belief change = 2.775557562e-17 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 1.086e-23 x 2.64e-24) + (0.7 x 1.086e-23 x 1.736e-23) + (0.45 x 9.14e-24 x 2.64e-24) + (0.22 x 9.14e-24 x 1.736e-23) = 1.83470608e-46 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 1.086e-23 x 2.64e-24) + (0.3 x 1.086e-23 x 1.736e-23) + (0.55 x 9.14e-24 x 2.64e-24) + (0.78 x 9.14e-24 x 1.736e-23) = 2.16529392e-46 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 93 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 1e-46 0.1 - a2 0.09 1e-46 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 1e-25 1e-23 - a2 9e-25 1e-23 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 1e-25 1e-23 - a2 9e-25 1e-23 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 5.43e-25 2e-23 0.543 - b2 4.57e-25 2e-23 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 1.086e-23 2e-23 - b2 9.14e-24 2e-23 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 1.32e-25 2e-23 0.132 - c2 8.68e-25 2e-23 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 2.64e-24 2e-23 - c2 1.736e-23 2e-23 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 1.83470608e-46 1 0.45867652 - d2 2.16529392e-46 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x2e-23 + [(0.97)]x2e-23 = 2e-23 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x2e-23 + [(0.4)]x2e-23 = 2e-23 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x2e-23 + [(0.76)]x2e-23 = 2e-23 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x2e-23 + [(0.88)]x2e-23 = 2e-23 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x2.64e-24) + (0.7x1.736e-23)]x1 + [(0.8x2.64e-24) + (0.3x1.736e-23)]x1 = 2e-23 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x2.64e-24) + (0.22x1.736e-23)]x1 + [(0.55x2.64e-24) + (0.78x1.736e-23)]x1 = 2e-23 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x1.086e-23) + (0.45x9.14e-24)]x1 + [(0.8x1.086e-23) + (0.55x9.14e-24)]x1 = 2e-23 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x1.086e-23) + (0.22x9.14e-24)]x1 + [(0.3x1.086e-23) + (0.78x9.14e-24)]x1 = 2e-23 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 1e-23 = 1e-25 - πB(a2) = π(a2).λC(a2) = 0.09 x 1e-23 = 9e-25 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 1e-23 = 1e-25 - πC(a2) = π(a2).λB(a2) = 0.09 x 1e-23 = 9e-25 -π message B --> D - πD(b1) = π(b1) = 5.43e-25 = 5.43e-25 - πD(b2) = π(b2) = 4.57e-25 = 4.57e-25 -π message C --> D - πD(c1) = π(c1) = 1.32e-25 = 1.32e-25 - πD(c2) = π(c2) = 8.68e-25 = 8.68e-25 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 2e-23 x 2e-23 = 4e-46 - λ(a2) = λB(a2).λC(a2) = 2e-23 x 2e-23 = 4e-46 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 1e-25) + (0.6 x 9e-25) = 5.43e-25 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 1e-25) + (0.4 x 9e-25) = 4.57e-25 - λ(b1) = λD(b1) = 2e-23 = 2e-23 - λ(b2) = λD(b2) = 2e-23 = 2e-23 - belief change = 0 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 1e-25) + (0.12 x 9e-25) = 1.32e-25 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 1e-25) + (0.88 x 9e-25) = 8.68e-25 - λ(c1) = λD(c1) = 2e-23 = 2e-23 - λ(c2) = λD(c2) = 2e-23 = 2e-23 - belief change = 0 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 5.43e-25 x 1.32e-25) + (0.7 x 5.43e-25 x 8.68e-25) + (0.45 x 4.57e-25 x 1.32e-25) + (0.22 x 4.57e-25 x 8.68e-25) = 4.5867652e-49 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 5.43e-25 x 1.32e-25) + (0.3 x 5.43e-25 x 8.68e-25) + (0.55 x 4.57e-25 x 1.32e-25) + (0.78 x 4.57e-25 x 8.68e-25) = 5.4132348e-49 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 94 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 4e-46 0.1 - a2 0.09 4e-46 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 1e-25 2e-23 - a2 9e-25 2e-23 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 1e-25 2e-23 - a2 9e-25 2e-23 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 5.43e-25 2e-23 0.543 - b2 4.57e-25 2e-23 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 5.43e-25 2e-23 - b2 4.57e-25 2e-23 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 1.32e-25 2e-23 0.132 - c2 8.68e-25 2e-23 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 1.32e-25 2e-23 - c2 8.68e-25 2e-23 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 4.5867652e-49 1 0.45867652 - d2 5.4132348e-49 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x2e-23 + [(0.97)]x2e-23 = 2e-23 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x2e-23 + [(0.4)]x2e-23 = 2e-23 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x2e-23 + [(0.76)]x2e-23 = 2e-23 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x2e-23 + [(0.88)]x2e-23 = 2e-23 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x1.32e-25) + (0.7x8.68e-25)]x1 + [(0.8x1.32e-25) + (0.3x8.68e-25)]x1 = 1e-24 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x1.32e-25) + (0.22x8.68e-25)]x1 + [(0.55x1.32e-25) + (0.78x8.68e-25)]x1 = 1e-24 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x5.43e-25) + (0.45x4.57e-25)]x1 + [(0.8x5.43e-25) + (0.55x4.57e-25)]x1 = 1e-24 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x5.43e-25) + (0.22x4.57e-25)]x1 + [(0.3x5.43e-25) + (0.78x4.57e-25)]x1 = 1e-24 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 2e-23 = 2e-25 - πB(a2) = π(a2).λC(a2) = 0.09 x 2e-23 = 1.8e-24 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 2e-23 = 2e-25 - πC(a2) = π(a2).λB(a2) = 0.09 x 2e-23 = 1.8e-24 -π message B --> D - πD(b1) = π(b1) = 5.43e-25 = 5.43e-25 - πD(b2) = π(b2) = 4.57e-25 = 4.57e-25 -π message C --> D - πD(c1) = π(c1) = 1.32e-25 = 1.32e-25 - πD(c2) = π(c2) = 8.68e-25 = 8.68e-25 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 2e-23 x 2e-23 = 4e-46 - λ(a2) = λB(a2).λC(a2) = 2e-23 x 2e-23 = 4e-46 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 2e-25) + (0.6 x 1.8e-24) = 1.086e-24 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 2e-25) + (0.4 x 1.8e-24) = 9.14e-25 - λ(b1) = λD(b1) = 1e-24 = 1e-24 - λ(b2) = λD(b2) = 1e-24 = 1e-24 - belief change = 0 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 2e-25) + (0.12 x 1.8e-24) = 2.64e-25 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 2e-25) + (0.88 x 1.8e-24) = 1.736e-24 - λ(c1) = λD(c1) = 1e-24 = 1e-24 - λ(c2) = λD(c2) = 1e-24 = 1e-24 - belief change = 0 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 5.43e-25 x 1.32e-25) + (0.7 x 5.43e-25 x 8.68e-25) + (0.45 x 4.57e-25 x 1.32e-25) + (0.22 x 4.57e-25 x 8.68e-25) = 4.5867652e-49 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 5.43e-25 x 1.32e-25) + (0.3 x 5.43e-25 x 8.68e-25) + (0.55 x 4.57e-25 x 1.32e-25) + (0.78 x 4.57e-25 x 8.68e-25) = 5.4132348e-49 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 95 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 4e-46 0.1 - a2 0.09 4e-46 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 2e-25 2e-23 - a2 1.8e-24 2e-23 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 2e-25 2e-23 - a2 1.8e-24 2e-23 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 1.086e-24 1e-24 0.543 - b2 9.14e-25 1e-24 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 5.43e-25 1e-24 - b2 4.57e-25 1e-24 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 2.64e-25 1e-24 0.132 - c2 1.736e-24 1e-24 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 1.32e-25 1e-24 - c2 8.68e-25 1e-24 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 4.5867652e-49 1 0.45867652 - d2 5.4132348e-49 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x1e-24 + [(0.97)]x1e-24 = 1e-24 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x1e-24 + [(0.4)]x1e-24 = 1e-24 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x1e-24 + [(0.76)]x1e-24 = 1e-24 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x1e-24 + [(0.88)]x1e-24 = 1e-24 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x1.32e-25) + (0.7x8.68e-25)]x1 + [(0.8x1.32e-25) + (0.3x8.68e-25)]x1 = 1e-24 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x1.32e-25) + (0.22x8.68e-25)]x1 + [(0.55x1.32e-25) + (0.78x8.68e-25)]x1 = 1e-24 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x5.43e-25) + (0.45x4.57e-25)]x1 + [(0.8x5.43e-25) + (0.55x4.57e-25)]x1 = 1e-24 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x5.43e-25) + (0.22x4.57e-25)]x1 + [(0.3x5.43e-25) + (0.78x4.57e-25)]x1 = 1e-24 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 2e-23 = 2e-25 - πB(a2) = π(a2).λC(a2) = 0.09 x 2e-23 = 1.8e-24 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 2e-23 = 2e-25 - πC(a2) = π(a2).λB(a2) = 0.09 x 2e-23 = 1.8e-24 -π message B --> D - πD(b1) = π(b1) = 1.086e-24 = 1.086e-24 - πD(b2) = π(b2) = 9.14e-25 = 9.14e-25 -π message C --> D - πD(c1) = π(c1) = 2.64e-25 = 2.64e-25 - πD(c2) = π(c2) = 1.736e-24 = 1.736e-24 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 1e-24 x 1e-24 = 1e-48 - λ(a2) = λB(a2).λC(a2) = 1e-24 x 1e-24 = 1e-48 - belief change = 1.387778781e-16 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 2e-25) + (0.6 x 1.8e-24) = 1.086e-24 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 2e-25) + (0.4 x 1.8e-24) = 9.14e-25 - λ(b1) = λD(b1) = 1e-24 = 1e-24 - λ(b2) = λD(b2) = 1e-24 = 1e-24 - belief change = 0 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 2e-25) + (0.12 x 1.8e-24) = 2.64e-25 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 2e-25) + (0.88 x 1.8e-24) = 1.736e-24 - λ(c1) = λD(c1) = 1e-24 = 1e-24 - λ(c2) = λD(c2) = 1e-24 = 1e-24 - belief change = 0 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 1.086e-24 x 2.64e-25) + (0.7 x 1.086e-24 x 1.736e-24) + (0.45 x 9.14e-25 x 2.64e-25) + (0.22 x 9.14e-25 x 1.736e-24) = 1.83470608e-48 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 1.086e-24 x 2.64e-25) + (0.3 x 1.086e-24 x 1.736e-24) + (0.55 x 9.14e-25 x 2.64e-25) + (0.78 x 9.14e-25 x 1.736e-24) = 2.16529392e-48 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 96 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 1e-48 0.1 - a2 0.09 1e-48 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 2e-25 1e-24 - a2 1.8e-24 1e-24 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 2e-25 1e-24 - a2 1.8e-24 1e-24 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 1.086e-24 1e-24 0.543 - b2 9.14e-25 1e-24 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 1.086e-24 1e-24 - b2 9.14e-25 1e-24 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 2.64e-25 1e-24 0.132 - c2 1.736e-24 1e-24 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 2.64e-25 1e-24 - c2 1.736e-24 1e-24 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 1.83470608e-48 1 0.45867652 - d2 2.16529392e-48 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x1e-24 + [(0.97)]x1e-24 = 1e-24 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x1e-24 + [(0.4)]x1e-24 = 1e-24 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x1e-24 + [(0.76)]x1e-24 = 1e-24 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x1e-24 + [(0.88)]x1e-24 = 1e-24 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x2.64e-25) + (0.7x1.736e-24)]x1 + [(0.8x2.64e-25) + (0.3x1.736e-24)]x1 = 2e-24 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x2.64e-25) + (0.22x1.736e-24)]x1 + [(0.55x2.64e-25) + (0.78x1.736e-24)]x1 = 2e-24 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x1.086e-24) + (0.45x9.14e-25)]x1 + [(0.8x1.086e-24) + (0.55x9.14e-25)]x1 = 2e-24 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x1.086e-24) + (0.22x9.14e-25)]x1 + [(0.3x1.086e-24) + (0.78x9.14e-25)]x1 = 2e-24 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 1e-24 = 1e-26 - πB(a2) = π(a2).λC(a2) = 0.09 x 1e-24 = 9e-26 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 1e-24 = 1e-26 - πC(a2) = π(a2).λB(a2) = 0.09 x 1e-24 = 9e-26 -π message B --> D - πD(b1) = π(b1) = 1.086e-24 = 1.086e-24 - πD(b2) = π(b2) = 9.14e-25 = 9.14e-25 -π message C --> D - πD(c1) = π(c1) = 2.64e-25 = 2.64e-25 - πD(c2) = π(c2) = 1.736e-24 = 1.736e-24 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 1e-24 x 1e-24 = 1e-48 - λ(a2) = λB(a2).λC(a2) = 1e-24 x 1e-24 = 1e-48 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 1e-26) + (0.6 x 9e-26) = 5.43e-26 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 1e-26) + (0.4 x 9e-26) = 4.57e-26 - λ(b1) = λD(b1) = 2e-24 = 2e-24 - λ(b2) = λD(b2) = 2e-24 = 2e-24 - belief change = 1.110223025e-16 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 1e-26) + (0.12 x 9e-26) = 1.32e-26 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 1e-26) + (0.88 x 9e-26) = 8.68e-26 - λ(c1) = λD(c1) = 2e-24 = 2e-24 - λ(c2) = λD(c2) = 2e-24 = 2e-24 - belief change = 2.775557562e-17 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 1.086e-24 x 2.64e-25) + (0.7 x 1.086e-24 x 1.736e-24) + (0.45 x 9.14e-25 x 2.64e-25) + (0.22 x 9.14e-25 x 1.736e-24) = 1.83470608e-48 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 1.086e-24 x 2.64e-25) + (0.3 x 1.086e-24 x 1.736e-24) + (0.55 x 9.14e-25 x 2.64e-25) + (0.78 x 9.14e-25 x 1.736e-24) = 2.16529392e-48 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 97 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 1e-48 0.1 - a2 0.09 1e-48 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 1e-26 1e-24 - a2 9e-26 1e-24 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 1e-26 1e-24 - a2 9e-26 1e-24 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 5.43e-26 2e-24 0.543 - b2 4.57e-26 2e-24 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 1.086e-24 2e-24 - b2 9.14e-25 2e-24 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 1.32e-26 2e-24 0.132 - c2 8.68e-26 2e-24 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 2.64e-25 2e-24 - c2 1.736e-24 2e-24 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 1.83470608e-48 1 0.45867652 - d2 2.16529392e-48 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x2e-24 + [(0.97)]x2e-24 = 2e-24 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x2e-24 + [(0.4)]x2e-24 = 2e-24 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x2e-24 + [(0.76)]x2e-24 = 2e-24 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x2e-24 + [(0.88)]x2e-24 = 2e-24 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x2.64e-25) + (0.7x1.736e-24)]x1 + [(0.8x2.64e-25) + (0.3x1.736e-24)]x1 = 2e-24 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x2.64e-25) + (0.22x1.736e-24)]x1 + [(0.55x2.64e-25) + (0.78x1.736e-24)]x1 = 2e-24 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x1.086e-24) + (0.45x9.14e-25)]x1 + [(0.8x1.086e-24) + (0.55x9.14e-25)]x1 = 2e-24 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x1.086e-24) + (0.22x9.14e-25)]x1 + [(0.3x1.086e-24) + (0.78x9.14e-25)]x1 = 2e-24 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 1e-24 = 1e-26 - πB(a2) = π(a2).λC(a2) = 0.09 x 1e-24 = 9e-26 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 1e-24 = 1e-26 - πC(a2) = π(a2).λB(a2) = 0.09 x 1e-24 = 9e-26 -π message B --> D - πD(b1) = π(b1) = 5.43e-26 = 5.43e-26 - πD(b2) = π(b2) = 4.57e-26 = 4.57e-26 -π message C --> D - πD(c1) = π(c1) = 1.32e-26 = 1.32e-26 - πD(c2) = π(c2) = 8.68e-26 = 8.68e-26 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 2e-24 x 2e-24 = 4e-48 - λ(a2) = λB(a2).λC(a2) = 2e-24 x 2e-24 = 4e-48 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 1e-26) + (0.6 x 9e-26) = 5.43e-26 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 1e-26) + (0.4 x 9e-26) = 4.57e-26 - λ(b1) = λD(b1) = 2e-24 = 2e-24 - λ(b2) = λD(b2) = 2e-24 = 2e-24 - belief change = 0 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 1e-26) + (0.12 x 9e-26) = 1.32e-26 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 1e-26) + (0.88 x 9e-26) = 8.68e-26 - λ(c1) = λD(c1) = 2e-24 = 2e-24 - λ(c2) = λD(c2) = 2e-24 = 2e-24 - belief change = 0 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 5.43e-26 x 1.32e-26) + (0.7 x 5.43e-26 x 8.68e-26) + (0.45 x 4.57e-26 x 1.32e-26) + (0.22 x 4.57e-26 x 8.68e-26) = 4.5867652e-51 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 5.43e-26 x 1.32e-26) + (0.3 x 5.43e-26 x 8.68e-26) + (0.55 x 4.57e-26 x 1.32e-26) + (0.78 x 4.57e-26 x 8.68e-26) = 5.4132348e-51 - λ(d1) = 1 - λ(d2) = 1 - belief change = 5.551115123e-17 - - -******************************************************************************** -Iteration 98 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 4e-48 0.1 - a2 0.09 4e-48 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 1e-26 2e-24 - a2 9e-26 2e-24 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 1e-26 2e-24 - a2 9e-26 2e-24 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 5.43e-26 2e-24 0.543 - b2 4.57e-26 2e-24 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 5.43e-26 2e-24 - b2 4.57e-26 2e-24 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 1.32e-26 2e-24 0.132 - c2 8.68e-26 2e-24 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 1.32e-26 2e-24 - c2 8.68e-26 2e-24 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 4.5867652e-51 1 0.45867652 - d2 5.4132348e-51 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x2e-24 + [(0.97)]x2e-24 = 2e-24 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x2e-24 + [(0.4)]x2e-24 = 2e-24 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x2e-24 + [(0.76)]x2e-24 = 2e-24 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x2e-24 + [(0.88)]x2e-24 = 2e-24 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x1.32e-26) + (0.7x8.68e-26)]x1 + [(0.8x1.32e-26) + (0.3x8.68e-26)]x1 = 1e-25 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x1.32e-26) + (0.22x8.68e-26)]x1 + [(0.55x1.32e-26) + (0.78x8.68e-26)]x1 = 1e-25 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x5.43e-26) + (0.45x4.57e-26)]x1 + [(0.8x5.43e-26) + (0.55x4.57e-26)]x1 = 1e-25 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x5.43e-26) + (0.22x4.57e-26)]x1 + [(0.3x5.43e-26) + (0.78x4.57e-26)]x1 = 1e-25 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 2e-24 = 2e-26 - πB(a2) = π(a2).λC(a2) = 0.09 x 2e-24 = 1.8e-25 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 2e-24 = 2e-26 - πC(a2) = π(a2).λB(a2) = 0.09 x 2e-24 = 1.8e-25 -π message B --> D - πD(b1) = π(b1) = 5.43e-26 = 5.43e-26 - πD(b2) = π(b2) = 4.57e-26 = 4.57e-26 -π message C --> D - πD(c1) = π(c1) = 1.32e-26 = 1.32e-26 - πD(c2) = π(c2) = 8.68e-26 = 8.68e-26 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 2e-24 x 2e-24 = 4e-48 - λ(a2) = λB(a2).λC(a2) = 2e-24 x 2e-24 = 4e-48 - belief change = 0 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 2e-26) + (0.6 x 1.8e-25) = 1.086e-25 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 2e-26) + (0.4 x 1.8e-25) = 9.14e-26 - λ(b1) = λD(b1) = 1e-25 = 1e-25 - λ(b2) = λD(b2) = 1e-25 = 1e-25 - belief change = 2.220446049e-16 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 2e-26) + (0.12 x 1.8e-25) = 2.64e-26 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 2e-26) + (0.88 x 1.8e-25) = 1.736e-25 - λ(c1) = λD(c1) = 1e-25 = 1e-25 - λ(c2) = λD(c2) = 1e-25 = 1e-25 - belief change = 2.775557562e-17 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 5.43e-26 x 1.32e-26) + (0.7 x 5.43e-26 x 8.68e-26) + (0.45 x 4.57e-26 x 1.32e-26) + (0.22 x 4.57e-26 x 8.68e-26) = 4.5867652e-51 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 5.43e-26 x 1.32e-26) + (0.3 x 5.43e-26 x 8.68e-26) + (0.55 x 4.57e-26 x 1.32e-26) + (0.78 x 4.57e-26 x 8.68e-26) = 5.4132348e-51 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - - -******************************************************************************** -Iteration 99 -******************************************************************************** - -status of random variable `A': - domain π(A) λ(A) belief ----------------------------------------------------------------- - a1 0.01 4e-48 0.1 - a2 0.09 4e-48 0.9 - - domain πB(A) λB(A) ----------------------------------------------------------------- - a1 2e-26 2e-24 - a2 1.8e-25 2e-24 - - domain πC(A) λC(A) ----------------------------------------------------------------- - a1 2e-26 2e-24 - a2 1.8e-25 2e-24 - - -status of random variable `B': - domain π(B) λ(B) belief ----------------------------------------------------------------- - b1 1.086e-25 1e-25 0.543 - b2 9.14e-26 1e-25 0.457 - - domain πD(B) λD(B) ----------------------------------------------------------------- - b1 5.43e-26 1e-25 - b2 4.57e-26 1e-25 - - -status of random variable `C': - domain π(C) λ(C) belief ----------------------------------------------------------------- - c1 2.64e-26 1e-25 0.132 - c2 1.736e-25 1e-25 0.868 - - domain πD(C) λD(C) ----------------------------------------------------------------- - c1 1.32e-26 1e-25 - c2 8.68e-26 1e-25 - - -status of random variable `D': - domain π(D) λ(D) belief ----------------------------------------------------------------- - d1 4.5867652e-51 1 0.45867652 - d2 5.4132348e-51 1 0.54132348 - -λ message B --> A - λB(a1) = [p(b1|a1)].λ(b1) + [p(b2|a1)].λ(b2) = [(0.03)]x1e-25 + [(0.97)]x1e-25 = 1e-25 - λB(a2) = [p(b1|a2)].λ(b1) + [p(b2|a2)].λ(b2) = [(0.6)]x1e-25 + [(0.4)]x1e-25 = 1e-25 -λ message C --> A - λC(a1) = [p(c1|a1)].λ(c1) + [p(c2|a1)].λ(c2) = [(0.24)]x1e-25 + [(0.76)]x1e-25 = 1e-25 - λC(a2) = [p(c1|a2)].λ(c1) + [p(c2|a2)].λ(c2) = [(0.12)]x1e-25 + [(0.88)]x1e-25 = 1e-25 -λ message D --> B - λD(b1) = [p(d1|b1,c1).πD(c1) + p(d1|b1,c2).πD(c2)].λ(d1) + [p(d2|b1,c1).πD(c1) + p(d2|b1,c2).πD(c2)].λ(d2) = [(0.2x1.32e-26) + (0.7x8.68e-26)]x1 + [(0.8x1.32e-26) + (0.3x8.68e-26)]x1 = 1e-25 - λD(b2) = [p(d1|b2,c1).πD(c1) + p(d1|b2,c2).πD(c2)].λ(d1) + [p(d2|b2,c1).πD(c1) + p(d2|b2,c2).πD(c2)].λ(d2) = [(0.45x1.32e-26) + (0.22x8.68e-26)]x1 + [(0.55x1.32e-26) + (0.78x8.68e-26)]x1 = 1e-25 -λ message D --> C - λD(c1) = [p(d1|b1,c1).πD(b1) + p(d1|b2,c1).πD(b2)].λ(d1) + [p(d2|b1,c1).πD(b1) + p(d2|b2,c1).πD(b2)].λ(d2) = [(0.2x5.43e-26) + (0.45x4.57e-26)]x1 + [(0.8x5.43e-26) + (0.55x4.57e-26)]x1 = 1e-25 - λD(c2) = [p(d1|b1,c2).πD(b1) + p(d1|b2,c2).πD(b2)].λ(d1) + [p(d2|b1,c2).πD(b1) + p(d2|b2,c2).πD(b2)].λ(d2) = [(0.7x5.43e-26) + (0.22x4.57e-26)]x1 + [(0.3x5.43e-26) + (0.78x4.57e-26)]x1 = 1e-25 -π message A --> B - πB(a1) = π(a1).λC(a1) = 0.01 x 2e-24 = 2e-26 - πB(a2) = π(a2).λC(a2) = 0.09 x 2e-24 = 1.8e-25 -π message A --> C - πC(a1) = π(a1).λB(a1) = 0.01 x 2e-24 = 2e-26 - πC(a2) = π(a2).λB(a2) = 0.09 x 2e-24 = 1.8e-25 -π message B --> D - πD(b1) = π(b1) = 1.086e-25 = 1.086e-25 - πD(b2) = π(b2) = 9.14e-26 = 9.14e-26 -π message C --> D - πD(c1) = π(c1) = 2.64e-26 = 2.64e-26 - πD(c2) = π(c2) = 1.736e-25 = 1.736e-25 - -updating π & λ values -node A: - π(a1) = p(a1) = (0.01) = 0.01 - π(a2) = p(a2) = (0.09) = 0.09 - λ(a1) = λB(a1).λC(a1) = 1e-25 x 1e-25 = 1e-50 - λ(a2) = λB(a2).λC(a2) = 1e-25 x 1e-25 = 1e-50 - belief change = 1.387778781e-16 -node B: - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 2e-26) + (0.6 x 1.8e-25) = 1.086e-25 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 2e-26) + (0.4 x 1.8e-25) = 9.14e-26 - λ(b1) = λD(b1) = 1e-25 = 1e-25 - λ(b2) = λD(b2) = 1e-25 = 1e-25 - belief change = 0 -node C: - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 2e-26) + (0.12 x 1.8e-25) = 2.64e-26 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 2e-26) + (0.88 x 1.8e-25) = 1.736e-25 - λ(c1) = λD(c1) = 1e-25 = 1e-25 - λ(c2) = λD(c2) = 1e-25 = 1e-25 - belief change = 0 -node D: - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 1.086e-25 x 2.64e-26) + (0.7 x 1.086e-25 x 1.736e-25) + (0.45 x 9.14e-26 x 2.64e-26) + (0.22 x 9.14e-26 x 1.736e-25) = 1.83470608e-50 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 1.086e-25 x 2.64e-26) + (0.3 x 1.086e-25 x 1.736e-25) + (0.55 x 9.14e-26 x 2.64e-26) + (0.78 x 9.14e-26 x 1.736e-25) = 2.16529392e-50 - λ(d1) = 1 - λ(d2) = 1 - belief change = 0 - -the maximum number of iterations was achieved, terminating... -beliefs for variable `A': - domain belief ----------------------------------- - a1 0.1 - a2 0.9 - -beliefs for variable `B': - domain belief ----------------------------------- - b1 0.543 - b2 0.457 - -beliefs for variable `C': - domain belief ----------------------------------- - c1 0.132 - c2 0.868 - -beliefs for variable `D': - domain belief ----------------------------------- - d1 0.45867652 - d2 0.54132348 - diff --git a/packages/CLPBN/clpbn/bp/simple-loop.seq.txt b/packages/CLPBN/clpbn/bp/simple-loop.seq.txt deleted file mode 100644 index ff7fec8b6..000000000 --- a/packages/CLPBN/clpbn/bp/simple-loop.seq.txt +++ /dev/null @@ -1,85 +0,0 @@ -Variable: A -Domain: a1, a2 -Parents: -Childs: B, C -cpt ----------------- -a1 0.01 -a2 0.09 - -Variable: B -Domain: b1, b2 -Parents: A -Childs: D -cpt a1, a2, ----------------------------- -b1 0.03 0.6 -b2 0.97 0.4 - -Variable: C -Domain: c1, c2 -Parents: A -Childs: D -cpt a1, a2, ----------------------------- -c1 0.24 0.12 -c2 0.76 0.88 - -Variable: D -Domain: d1, d2 -Parents: B, C -Childs: -cpt b1,c1, b1,c2, b2,c1, b2,c2, ----------------------------------------------------- -d1 0.2 0.7 0.45 0.22 -d2 0.8 0.3 0.55 0.78 - -initializing solver - schedule = sequential - maxIter = 100 - accuracy = 0 -sending pi message from `A' to `B' - πB(a1) = π(a1).λC(a1) = 0.01 x 1 = 0.01 - πB(a2) = π(a2).λC(a2) = 0.09 x 1 = 0.09 - π(b1) = p(b1|a1).πB(a1) + p(b1|a2).πB(a2) = (0.03 x 0.01) + (0.6 x 0.09) = 0.0543 - π(b2) = p(b2|a1).πB(a1) + p(b2|a2).πB(a2) = (0.97 x 0.01) + (0.4 x 0.09) = 0.0457 -sending pi message from `B' to `D' - πD(b1) = π(b1) = 0.0543 = 0.0543 - πD(b2) = π(b2) = 0.0457 = 0.0457 - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 0.0543 x 1) + (0.7 x 0.0543 x 1) + (0.45 x 0.0457 x 1) + (0.22 x 0.0457 x 1) = 0.079489 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 0.0543 x 1) + (0.3 x 0.0543 x 1) + (0.55 x 0.0457 x 1) + (0.78 x 0.0457 x 1) = 0.120511 -sending pi message from `A' to `C' - πC(a1) = π(a1).λB(a1) = 0.01 x 1 = 0.01 - πC(a2) = π(a2).λB(a2) = 0.09 x 1 = 0.09 - π(c1) = p(c1|a1).πC(a1) + p(c1|a2).πC(a2) = (0.24 x 0.01) + (0.12 x 0.09) = 0.0132 - π(c2) = p(c2|a1).πC(a1) + p(c2|a2).πC(a2) = (0.76 x 0.01) + (0.88 x 0.09) = 0.0868 -sending pi message from `C' to `D' - πD(c1) = π(c1) = 0.0132 = 0.0132 - πD(c2) = π(c2) = 0.0868 = 0.0868 - π(d1) = p(d1|b1,c1).πD(b1).πD(c1) + p(d1|b1,c2).πD(b1).πD(c2) + p(d1|b2,c1).πD(b2).πD(c1) + p(d1|b2,c2).πD(b2).πD(c2) = (0.2 x 0.0543 x 0.0132) + (0.7 x 0.0543 x 0.0868) + (0.45 x 0.0457 x 0.0132) + (0.22 x 0.0457 x 0.0868) = 0.00458677 - π(d2) = p(d2|b1,c1).πD(b1).πD(c1) + p(d2|b1,c2).πD(b1).πD(c2) + p(d2|b2,c1).πD(b2).πD(c1) + p(d2|b2,c2).πD(b2).πD(c2) = (0.8 x 0.0543 x 0.0132) + (0.3 x 0.0543 x 0.0868) + (0.55 x 0.0457 x 0.0132) + (0.78 x 0.0457 x 0.0868) = 0.00541323 - -beliefs for variable `A': - domain belief ----------------------------------- - a1 0.1 - a2 0.9 - -beliefs for variable `B': - domain belief ----------------------------------- - b1 0.543 - b2 0.457 - -beliefs for variable `C': - domain belief ----------------------------------- - c1 0.132 - c2 0.868 - -beliefs for variable `D': - domain belief ----------------------------------- - d1 0.45867652 - d2 0.54132348 -