The marginal factorization of Bayesian networks and its application

A Bayesian network consists of a directed acyclic graph (DAG) and a set of conditional probability distributions (CPDs); they together define a joint probability distribution (jpd). The structure of the DAG dictates how a jpd can be factorized as a product of CPDs. This CPD factorization view of Bayesian networks has been well recognized and studied in the uncertainty community. In this article, we take a different perspective by studying a marginal factorization view of Bayesian networks. In particular, we propose an algebraic characterization of equivalent DAGs based on the marginal factorization of a jpd defined by a Bayesian network. Moreover, we show a simple method to identify all the compelled edges in a DAG. © 2004 Wiley Periodicals, Inc.