Statistical Modelling 4 (2004), 39–61
MCMC model determination for discrete graphical models
Claudia Tarantola
eMail: ctaranto@eco.unipv.it
Abstract:
In this paper we compare two alternative MCMC samplers for the Bayesian
analysis of discrete graphical models; we present both a hierarchical
and a non-hierarchical version of them. We first consider the
MC3 algorithm by Madigan and York (1995), for which
we propose
an extension which 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.
Keywords:
Bayesian model selection; contingency table; Dirichlet distribution;
dichotomous variables; hyper Markov distribution; junction tree;
Markov Chain Monte Carlo.
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