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MCMC model determination for discrete graphical models

Department of Economics and Quantitative Methods, University of Pavia, Pavia, Italy, ctaranto{at}eco.unipv.it

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 MC ³ 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.

Key Words: Bayesian model selection • contingency table • Dirichlet distribution • dichotomous variables • hyper-Markov distribution • junction tree • Markov chain Monte Carlo

Statistical Modelling, Vol. 4, No. 1, 39-61 (2004)
DOI: 10.1191/1471082X04st063oa


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