Efficient Model Determination for discrete graphical models

We present a novel methodology for bayesian model determination in discrete decomposable graphical models. We assign, for each given graph, a hyper Dirichlet distribution on the matrix of cell probabilities. To ensure compatibility across models such prior distributions are obtained by marginalisation from the prior conditional on the complete graph. This leads to a prior distribution automatically satisfying the hyperconsistency criterion. Our contribution is twofold. On one hand we improve an existing methodology, the MC3 algorithm by Madigan and York (1995). On the other hand we introduce an original methodology based on the use of the reversible jump sampler by Green (1995) and Giudici and Green (1999). Legal movement, that is leading to a decomposable graph, are identified making use of the junction tree representation of the considered graph