Bayesian Analysis of Marginal Log-Linear Graphical Models for Three Way Contingency Tables

This paper deals with the Bayesian analysis of graphical models of marginal independence for three way contingency tables. We use a marginal log-linear parametrization, under which the model is defined through suitable zero-constraints on the interaction parameters calculated within marginal distributions. We undertake a comprehensive Bayesian analysis of these models, involving suitable choices of prior distributions, estimation, model determination, as well as the allied computational issues. The methodology is illustrated with reference to two real data sets.