Simple methods for constructing parameter priors for model choice among Bayesian networks are presented. In particular, we study several assumptions that permit the construction of parameter priors for a large number of Bayesian networks from a small set of assessments. We then present a method for directly computing the marginal likelihood of every Bayesian network given a random sample with no missing observations. We apply this methodology to discrete Bayesian networks and to Gaussian Bayesian networks. We show that the only parameter prior for complete discrete Bayesian networks that satisfies our assumptions is the Dirichlete distribution. Similarly, we show that the only parameter prior for complete Gaussian Bayesian networks that satisfies our assumptions is the Wishart distribution. Our analysis is based on new characterizations of the Dirichlete and Wishart distributions.

Joint work with David Heckerman, Microsoft Research.