Reference priors for discrete graphical models

Alternative parametrizations and reference priors for decomposable discrete graphical models

For a given discrete decomposable graphical model, we identify several alternative parametrizations, and construct the corresponding reference priors for suitable groupings of the parameters. Specifically, assuming that the cliques of the graph are arranged in a perfect order, the parameters we consider are conditional probabilities of clique-residuals given separators, as well as generalized l...

Bayesian model comparison based on expected posterior priors for discrete decomposable graphical models

The implementation of the Bayesian paradigm to model comparison can be problematic. In particular, prior distributions on the parameter space of each candidate model require special care. While it is well known that improper priors cannot be used routinely for Bayesian model comparison, we claim that in general the use of conventional priors (proper or improper) for model comparison should be r...

On Parameter Priors for Discrete DAG Models

We investigate parameter priors for discrete DAG models. It was shown in previous works that a Dirichlet prior on the parameters of a discrete DAG model is inevitable assuming global and local parameter independence for all possible complete DAG structures. A similar result for Gaussian DAG models hinted that the assumption of local independence may be redundant. Herein, we prove that the local...

Efficient Model Determination for Discrete Graphical Models

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 Žrst 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...