Question: Recall that any directed acyclic graph G has an associated family of probability distributions, which consists of all probability distributions that can be represented by

Recall that any directed acyclic graph G has an associated family of probability distributions, which consists of all probability distributions that can be represented by a Bayes net with structure G. Consider the the six directed acyclic graphs in Figure S13.1.

a. Assume all we know about the joint distribution P(A, B, C) is that it can be represented by the product P(A | B, C)P(B | C)P(C). Which of the six graphs are guaranteed to be able to represent P(A, B, C)?

b. Now assume all we know about the joint distribution P(A, B, C) is that it can be represented by the product P(C | B)P(B | A)P(A). Which of the six graphs are guaranteed to be able to represent P(A, B, C)?

Figure S13.1

A A B G B G4 C C A A B G

A A B G B G4 C C A A B G B G5 A A B G3 B G6 C C

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