Bayesian Analysis of D-decomposable Bidirected Graphical Models for Discrete Data

This paper deals with the Bayesian analysis of d-decomposable graphical models of marginal independence for discrete data. The model is represented by a bidirected graph with missing edges indicating marginal independence between the corresponding variables. A bidirected graphs is named d-decomposable if it is Markov equivalent to at least one DAG. We use a marginal log-linear parameterisation, 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 a real data set