  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.
