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. Each marginal independence model
corresponds to a particular factorization of the cell probabilities and a conjugate
analysis based on Dirichlet prior can be performed. We illustrate a comprehensive
Bayesian analysis of such models, involving suitable choices of prior parameters,
estimation, model determination, as well as the allied computational issues. The
posterior distributions of the marginal log-linear parameters is indirectly obtained
using simple Monte Carlo schemes. The methodology is illustrated using two real
data sets.