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Constructing Bayesian networks

1. Choose an ordering of variables X1, … ,Xn

2. For i = 1 to n

add Xi to the network

select parents from X1, … ,Xi-1 such that

P (Xi | Parents(Xi)) = P (Xi | X1, ... Xi-1)

This choice of parents guarantees:

P (X1, … ,Xn) = πi =1 P (Xi | X1, … , Xi-1) (chain rule)

= πi =1P (Xi | Parents(Xi)) (by construction)

n

n

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