I'm trying to understand how to calculate the likelihood of a combination of binary variables given the network structure and probabilities seen here: Given a bayesian network as follows:
As far as I understand, the decomposition of the network would be as follows: $$P(a,b,c,d,e) = P(A) * P(B) * P(C|A, B) * P(D|C) * P(E|C)$$
However applying this to the data set A=0, B=0, C=0, D=0, E=1 (as in the first example) gives me $$= (1-0.1) * (1-0.2) * (1-0.2) * (1-0.2) * 0.8 = 0.368.$$
Have I mis-represented the equation, or am I mis-reading the probabilities data?
I think I've resolved it: given the data entry was complete (except for A & C) the probability of the dataset did not depend on the values of B, D,E. Therefore the probability of the data vector is P(A) * P(C|A, B). Is this correct?