如何用matlab的BNT软建立一个贝叶斯网络及条件概率表

Question

如题所述

Answer 1

            对上述信息建立贝叶斯网络，代码如下

                      

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N=8;  

dag=zeros(N,N);  

A=1;S=2;T=3;L=4;B=5;E=6;X=7;D=8;  

dag(A,T)=1;  

dag(S,[L B])=1;  

dag([T L],E)=1;  

dag(B,D)=1;  

dag(E,[X D])=1;  

discrete_nodes=1:N;  

node_sizes=2*ones(1,N);  

bnet=mk_bnet(dag,node_sizes,'names',{'A','S','T','L','B','E','X','D'},'discrete',discrete_nodes);  

bnet.CPD{A}=tabular_CPD(bnet,A,[0.99,0.01]);  

bnet.CPD{S}=tabular_CPD(bnet,S,[0.5,0.5]);  

bnet.CPD{T}=tabular_CPD(bnet,T,[0.99,0.95,0.01,0.05]);  

bnet.CPD{L}=tabular_CPD(bnet,L,[0.99,0.9,0.01,0.1]);  

bnet.CPD{B}=tabular_CPD(bnet,B,[0.7,0.4,0.3,0.6]);  

bnet.CPD{E}=tabular_CPD(bnet,E,[1,0,0,0,0,1,1,1]);  

bnet.CPD{X}=tabular_CPD(bnet,X,[0.95,0.02,0.05,0.98]);  

bnet.CPD{D}=tabular_CPD(bnet,D,[0.9,0.2,0.3,0.1,0.1,0.8,0.7,0.9]);  

draw_graph(dag)  

                    说明：有N=8个节点，建立有向无环图dag，并且这些点的值是离散的，这里1=False 2=True，node_sizes给出了所有状态

                    mk_bnet中names后的{}里面给出了各个节点的别名

                    利用tabular_CPD设置各个变量的边缘概率，对于A和S，定义顺序是False True；对于T、L和B这类，顺序是FF  FT TF TT；对于D这类，顺序是FFF FFT FTF FTT TFF TFT TTF TTT

       ç®€å•æ£€æŸ¥ä¸‹A的概率

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engine=jtree_inf_engine(bnet);  

evidence=cell(1,N);  

[engine,loglik]=enter_evidence(engine,evidence);  

m=marginal_nodes(engine,A);  

m.T()  

现在可以给定任意条件，然后计算概率了。

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例如要计算任意组合条件下，个体分别得Tub、lung cancer和bronchitis的概率。下面代码计算了P（T=True|A=False,S=True,X=True,D=False）的概率  

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engine=jtree_inf_engine(bnet);  

evidence=cell(1,N);  

evidence{A}=1;  

evidence{S}=2;  

evidence{X}=2;  

evidence{D}=1;  

[engine,loglik]=enter_evidence(engine,evidence);  

m=marginal_nodes(engine,T);  

m.T(2)