suppose you have this bayesian network: p(a,b,c) = p(c|b) p(b|a) p(a)

a -> b -> c

are a and c conditionally independent given b?

If yes, why are they independent? How can I show that?

  • $\begingroup$ yes. what's the question? $\endgroup$ – Memming Nov 30 '15 at 0:41
  • $\begingroup$ why are they independent? $\endgroup$ – user1844505 Nov 30 '15 at 15:36

Per edited question: this is super simple. One way to show it is:

$p(a,c|b) = \frac{p(a,b,c)}{p(b)} = \frac{p(a,b)}{p(b)}p(c|b) = p(a|b) p(c|b)$


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