Calculating Likelihoods in Bayesian Networks

We investigate the problem of calculating likelihoods in Bayesian networks. This is highly relevant to the issue of explanation in such networks and is in many ways complementary to the MAP approach which searches for the explanation that is most probable given evidence. Likelihoods are also of general statistical interest and can be useful if the value of a particular variable is to be maximized. After looking at the simple case where only parents of nodes are considered in the explanation set, we go on to look at tree-structured networks and then at a general approach for obtaining likelihoods