(*^
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(* This notebook illustrates the use of packages for creating and 
   manipulating Bayesian networks, Temporal Bayesian networks, and 
   their Markov process equivalents. *)
:[font = input; preserveAspect]
Needs["Dynamics`Packages`BayesianNetworks`"]
:[font = input; preserveAspect]
ResetBayesianNetworks[] ;
:[font = input; preserveAspect]
network1 = CreateBayesianNetwork[3] ;
:[font = input; preserveAspect; startGroup]
CurrentBayesianNetwork[] 
:[font = output; output; inactive; preserveAspect; endGroup]
BayesianNetwork[1]
;[o]
BayesianNetwork[1]
:[font = input; preserveAspect; startGroup]
Pr[1]
:[font = print; inactive; preserveAspect; endGroup]
Warning! Undefined probability.
Pr[{1, True},{}]
:[font = input; preserveAspect; startGroup]
Pr[1,2]
:[font = print; inactive; preserveAspect; endGroup]
Warning! Undefined probability.
Pr[{1, True},{{2, True}}]
:[font = input; preserveAspect; startGroup]
Pr[!1,2] = 0.8
:[font = output; output; inactive; preserveAspect; endGroup]
0.8
;[o]
0.8
:[font = input; preserveAspect; startGroup]
Pr[!1,2]
:[font = output; output; inactive; preserveAspect; endGroup]
0.8
;[o]
0.8
:[font = input; preserveAspect; startGroup]
Pr[1,2]
:[font = output; output; inactive; preserveAspect; endGroup]
0.2
;[o]
0.2
:[font = input; preserveAspect; startGroup]
Pr[1,!2] = 0.5
:[font = output; output; inactive; preserveAspect; endGroup]
0.5
;[o]
0.5
:[font = input; preserveAspect; startGroup]
Pr[2,3] = 1.0
:[font = output; output; inactive; preserveAspect; endGroup]
1.
;[o]
1.
:[font = input; preserveAspect; startGroup]
Pr[2,{1,3}] = 0.7
:[font = print; inactive; preserveAspect; endGroup]
Warning! Discrepancy in parent specification.
:[font = input; preserveAspect; startGroup]
Pr[{1, True},{{2, True}},network1]
:[font = output; output; inactive; preserveAspect; endGroup]
0.2
;[o]
0.2
:[font = input; preserveAspect; startGroup]
Pr[!2,3]
:[font = output; output; inactive; preserveAspect; endGroup]
0.
;[o]
0.
:[font = input; preserveAspect; startGroup]
CheckDistribution[network1]
:[font = print; inactive; preserveAspect; endGroup]
Warning! Undefined probability.
Pr[{2, True},{{3, False}}]
Warning! Undefined probability.
Pr[{2, False},{{3, False}}]
Warning! Undefined probability.
Pr[{3, True},{}]
Warning! Undefined probability.
Pr[{3, False},{}]
:[font = input; preserveAspect; startGroup]
Pr[3] = 0.5
:[font = output; output; inactive; preserveAspect; endGroup]
0.5
;[o]
0.5
:[font = input; preserveAspect; startGroup]
Pr[2,!3] = 0.7
:[font = output; output; inactive; preserveAspect; endGroup]
0.7
;[o]
0.7
:[font = input; preserveAspect]
CheckDistribution[network1]
:[font = input; preserveAspect; startGroup]
ShowGraph[DependencyGraph[network1],Directed] ;
:[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 282; pictureHeight = 282; endGroup]
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:[font = input; preserveAspect; startGroup]
Parents[1,network1]
:[font = output; output; inactive; preserveAspect; endGroup]
{2}
;[o]
{2}
:[font = input; preserveAspect]
network2 = CreateBayesianNetwork[3] ;
:[font = input; preserveAspect; startGroup]
CurrentBayesianNetwork[] 
:[font = output; output; inactive; preserveAspect; endGroup]
BayesianNetwork[2]
;[o]
BayesianNetwork[2]
:[font = input; preserveAspect]
Pr[1,{2,3}] = 0.1 ;
:[font = input; preserveAspect]
Pr[1,{!2,3}] = 0.5 ;
:[font = input; preserveAspect]
Pr[1,{2,!3}] = 0.5 ;
:[font = input; preserveAspect]
Pr[1,{!2,!3}] = 0.5 ;
:[font = input; preserveAspect]
Pr[2] = 0.5 ;
:[font = input; preserveAspect]
Pr[3,1] = 0.5 ;
:[font = input; preserveAspect]
Pr[3,!1] = 0.5 ;
:[font = input; preserveAspect; startGroup]
CheckDistribution[network2]
:[font = print; inactive; preserveAspect; endGroup]
Warning! There is a cycle in the dependency graph.
:[font = input; preserveAspect; startGroup]
ResetDistribution[network2]
:[font = print; inactive; preserveAspect; endGroup]
Warning! Setting conditional probability to Null.
Warning! Setting conditional probability to Null.
Warning! Setting conditional probability to Null.
Warning! Setting conditional probability to Null.
Warning! Setting conditional probability to Null.
Warning! Setting conditional probability to Null.
Warning! Setting conditional probability to Null.
Warning! Setting conditional probability to Null.
Warning! Setting conditional probability to Null.
Warning! Setting conditional probability to Null.
Warning! Setting conditional probability to Null.
Warning! Setting conditional probability to Null.
Warning! Setting conditional probability to Null.
Warning! Setting conditional probability to Null.
:[font = input; preserveAspect]
Pr[1,{2,3}] = .1 ;
:[font = input; preserveAspect]
Pr[1,{!2,3}] = .5 ;
:[font = input; preserveAspect]
Pr[1,{2,!3}] = .5 ;
:[font = input; preserveAspect]
Pr[1,{!2,!3}] = .5 ;
:[font = input; preserveAspect]
Pr[2] = .5 ;
:[font = input; preserveAspect]
Pr[3] = .5 ;
:[font = input; preserveAspect]
CheckDistribution[network2] ;
:[font = input; preserveAspect; startGroup]
ShowGraph[DependencyGraph[network2],Directed] ;
:[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 282; pictureHeight = 282; endGroup]
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:[font = input; preserveAspect; startGroup]
TableForm[Table[RandomSample[network2],{10}]]
:[font = output; output; inactive; preserveAspect; endGroup]
TableForm[{{False, True, False}, {False, True, False}, 
 
   {False, True, True}, {False, False, True}, {False, False, True}, 
 
   {True, False, True}, {False, True, False}, {True, False, True}, 
 
   {True, False, True}, {False, False, True}}]
;[o]
False   True    False

False   True    False

False   True    True

False   False   True

False   False   True

True    False   True

False   True    False

True    False   True

True    False   True

False   False   True
:[font = input; preserveAspect]
Needs["Dynamics`Packages`MarkovProcesses`"]
:[font = input; preserveAspect]
ResetMarkovProcesses[]
:[font = input; preserveAspect; startGroup]
process1 = CreateMarkovProcess[3] 
:[font = output; output; inactive; preserveAspect; endGroup]
MarkovProcess[1]
;[o]
MarkovProcess[1]
:[font = input; preserveAspect]
SetTransitionProbability[1,1,0.3,process1] ;
SetTransitionProbability[1,2,0.7,process1] ;
SetTransitionProbability[2,3,1.0,process1] ;
SetTransitionProbability[3,3,0.3,process1] ;
SetTransitionProbability[3,1,0.7,process1] ;
:[font = input; preserveAspect]
CheckDistribution[process1]
:[font = input; preserveAspect; startGroup]
ShowGraph[TransitionGraph[process1],Directed] ;

:[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 282; pictureHeight = 282; endGroup]
%!
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:[font = input; preserveAspect; startGroup]
TableForm[Edges[TransitionGraph[process1]]]
:[font = output; output; inactive; preserveAspect; endGroup]
TableForm[{{0.3, 0.7, 0}, {0, 0, 1.}, {0.7, 0, 0.3}}]
;[o]
0.3   0.7   0

0     0     1.

0.7   0     0.3
:[font = input; preserveAspect; startGroup]
RandomTrajectory[1,10,process1]
:[font = output; output; inactive; preserveAspect; endGroup]
{1, 1, 2, 3, 1, 2, 3, 1, 1, 1, 2}
;[o]
{1, 1, 2, 3, 1, 2, 3, 1, 1, 1, 2}
:[font = input; preserveAspect; startGroup]
EstimateSteadyState[1,10,process1]
:[font = output; output; inactive; preserveAspect; endGroup]
{0.3870633729, 0.2481955441, 0.364741083}
;[o]
{0.387063, 0.248196, 0.364741}
:[font = input; preserveAspect; startGroup]
ShowGraph[MultiStagePhaseSpaceDiagram[1,6,10,process1],Directed] ;
:[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 282; pictureHeight = 282; endGroup]
%!
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:[font = input; preserveAspect; startGroup]
process2 = CreateMarkovProcess[2] 
:[font = output; output; inactive; preserveAspect; endGroup]
MarkovProcess[2]
;[o]
MarkovProcess[2]
:[font = input; preserveAspect]
SetTransitionProbability[1,1,1.0,process2] ;
SetTransitionProbability[1,2,0.3,process2] ;
:[font = input; preserveAspect; startGroup]
CheckDistribution[process2]
:[font = print; inactive; preserveAspect; endGroup]
Warning! Transition probabilities must sum to one.{1., 0.3}
Warning! Transition probabilities must sum to one.{0, 0}
:[font = input; preserveAspect]
ResetDistribution[process2]
:[font = input; preserveAspect]
SetTransitionProbability[1,2,1.0,process2] ;
SetTransitionProbability[2,2,1.0,process2] ;
:[font = input; preserveAspect]
CheckDistribution[process2]
:[font = input; preserveAspect; startGroup]
EstimateSteadyState[1,10,process2]
:[font = output; output; inactive; preserveAspect; endGroup]
{0., 1.}
;[o]
{0., 1.}
:[font = input; preserveAspect]
Needs["Dynamics`Packages`TemporalBayesianNetworks`"]
:[font = input; preserveAspect]
network3 = CreateTemporalBayesianNetwork[2] ;
:[font = input; preserveAspect]
Pr[X[1,0]] = 0.5 ;
Pr[X[2,0]] = 0.5 ;
Pr[X[1,1], X[1,0]] = 0.3 ;
Pr[X[1,1],!X[1,0]] = 0.8 ;
Pr[X[2,1],{X[2,0],X[1,1]}] = 0.2 ;
Pr[X[2,1],{X[2,0],!X[1,1]}] = 0.5 ;
Pr[X[2,1],{!X[2,0],X[1,1]}] = 0.3 ;
Pr[X[2,1],{!X[2,0],!X[1,1]}] = 0.9 ;
:[font = input; preserveAspect; startGroup]
ShowGraph[DependencyGraph[network3], Directed] ;
:[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 282; pictureHeight = 282; endGroup]
%!
%%Creator: Mathematica
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:[font = input; preserveAspect; startGroup]
ShowLabeledGraph[DependencyGraph[network3], VertexLabels[network3]] ;
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%!
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[(X[1,0])] .04 .04 0 1 Mshowa
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:[font = input; preserveAspect]
CheckDistribution[network3]
:[font = input; preserveAspect; startGroup]
process3 = TemporalBayesianNetworkToMarkovProcess[network3] 
:[font = output; output; inactive; preserveAspect; endGroup]
MarkovProcess[3]
;[o]
MarkovProcess[3]
:[font = input; preserveAspect; startGroup]
TableForm[Edges[TransitionGraph[process3]]] 
:[font = output; output; inactive; preserveAspect; endGroup]
TableForm[{{0.02, 0.18, 0.56, 0.24}, {0.1, 0.1, 0.64, 0.16}, 
 
   {0.07000000000000000002, 0.63, 0.21, 0.09}, {0.35, 0.35, 0.24, 0.06}}]
;[o]
0.02   0.18   0.56   0.24

0.1    0.1    0.64   0.16

0.07   0.63   0.21   0.09

0.35   0.35   0.24   0.06
:[font = input; preserveAspect]
CheckDistribution[process3]
:[font = input; preserveAspect; startGroup]
ShowLabeledGraph[TransitionGraph[process3]] ;
:[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 282; pictureHeight = 282; endGroup]
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^*)