BAYESIAN GRAPHICAL MODELS FOR DISCRETE-DATA

For more than half a century, data analysts have used graphs to represent statistical models, Pn particular, graphical ''conditional independence'' models have emerged as a useful class of models, Applications of such models to probabilistic expert systems, image analysis, and pedigree analysis have motivated much of this work, and several expository texts are now available. Rather less well known is the development of a Bayesian framework for such models, Expert system applications have motivated this work, where the promise of a model that can update itself as data become available, has generated intense interest from the artificial intelligence community, However, the application to a broader range of data problems has been largely overlooked. The purpose of this article is to show how Bayesian graphical models unify and simplify many standard discrete data problems such as Bayesian log linear modeling with either complete or incomplete data, closed population estimation, and double sampling, Since conventional model selection fails in these applications, we construct posterior distributions for quantities of interest by averaging across models, Specifically we introduce Markov chain Monte Carlo model composition, a Monte Carlo method for Bayesian model averaging.