Learning Bayesian networks: The combination of knowledge and statistical data

We describe a Bayesian approach for learning Bayesian networks from a combination of prior knowledge and statistical data. First and foremost, we develop a methodology for assessing informative priors needed for learning. Our approach is derived from a set of assumptions made previously as well as the assumption oflikelihood equivalence, which says that data should not help to discriminate network structures that represent the same assertions of conditional independence. We show that likelihood equivalence when combined with previously made assumptions implies that the user's priors for network parameters can be encoded in a single Bayesian network for the next case to be seen--aprior network--and a single measure of confidence for that network. Second, using these priors, we show how to compute the relative posterior probabilities of network structures given data.