In Chapter 8 of Pattern Recognition and Machine Learning the joint probability of p(a,b,c) is calculated applying the rule product and Bayes:
p(a,b,c) = p(c|a,b)* p(b|a)*p(a)
But if you apply the same rule we get p(a,b,c) = p(a|b,c) * p(b|c) * p(c)
First question p(a|b,c) * p(b|c) * p(c) = p(c|a,b)* p(b|a)*p(a) ?
Bishop represents the p(a,b,c) = p(c|a,b)* p(b|a)p(a) in a Bayesian Network but if you use p(a|b,c) * p(b|c) * p(c) = p(c|a,b) p(b|a)*p(a) we have other representation. The representation is the same?
The representation of the two bayesian networks