MCMC Model determination for Discrete Graphical Models

In this paper we compare two alternative MCMC samplers for the Bayesian analysis of discrete graphical models; we present both a hierarchical and a nonhierarchical version of them. We first consider the MC3 algorithm by Madigan and York (1995) for which we propose an extension that allows for a hierarchical prior on the cell counts. We then describe a novel methodology based on a reversible jump sampler. As a prior distribution we assign, for each given graph, a hyper-Dirichlet distribution on the matrix of cell probabilities. Two applications to real data are presented.