I'm trying to understand the fully worked example 5.2 in "Bayesian Reasoning and Machine Learning" by David Barber. Frustratingly the explanations around the example are all about potentials and factor graphs but the example itself is probability based. To make sure I've understood the theory I'm therefore trying to convert the problem to a factor graph representation. I have two problems at the moment:
1) Converting the probability p(a,b,c)=p(a|b)p(b|c)p(c) into the corresponding bayesian graph.
2) Converting the bayesian graph to a factor graph with potential nodes in the correct place.
For 1 I believe the following is correct but not sure:
For 2 I think the following is correct:
I'm not sure on the latter though if the 'c' variable node should have another single function node on it U3(c). If it shouldn't under what circumstances can that occur.