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another example of bayesian network.md

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conditional probability table

each row contains the conditional probability of each node value for a conditional

  • each row much be sum 1
  • A ndoe with no parent has only one row , representing the prior probabilieties of each possible value of variable this

inference

p(x1,x2, .. , xn) =$\prod_{i=1}^{n}$ (xi|parent(xi)

$P(xy) = P(x)P(y)$ $P(A) = A \in {{a1,a2,an}}$ $\sum_{i}^{n} P(ai)=1$ P(x1,y2,z3)= $P(X = x1 \land Y=y2 \land Z =z3)$ P(a ,-b) = P(A = T $\land$ B=F) P(j , m, a ,-b, -e) = P( j|a ) P(m|a) P(a|-b $\land$ -e) P(-b )P(-e)

P(R|G) = P(R = T | G = T ) = $P(R,G) /P(G )=\sum_{S} P(R,S,G)/P(R,SG)+P(~R,~S,G)+P(R,~S,G)+P(~R,S,G)$ DỂ TRA CỨU XÁC SUẤT TRONG BN PHẢI MỞ RỘNG ASSGINMENT SAO CHO CÁC BIẾN CỦA ASSIGNMENT ĐỒNG THỜI XUẤT HIỆN TRONG MỘT CBT

$P(G|R) = P(GR)/P(R)= \sum_{s}P(G,S,R)/P(G)= P(G,S,R)+P(G,~S,R)/P(R)$

NOTATION

  • X denote the query bariable
  • e denotes the set of evidence variables E1,...,En and e is a particular observed even sự kiện mà ta quan sát được P(R|G) đậy e là cỏ ước
  • hidden những biến không xuất hiện tron công thức
  • A typical query asks for the posterior probability $P(X|e)$

Inference by emulation P(X|e)= $\alpha \sum_{y} P(X,e,y)$ $\alpha$ is the denominator P(B|j,m) = $\alpha P(B,j,m) = \sum_{e}\alpha P(B,j,m,e) = \alpha \sum_{e} P(B,j,m,e) = \alpha \sum_{e} \sum_{a} P(B,j,m,e,a)$