The mode oriented stochastic search (MOSS) algorithm for log-linear models with conjugate priors

We describe a novel stochastic search algorithm for rapidly identifying regions of high posterior probability in the space of decomposable, graphical and hierarchical log-linear models. Our approach is based on the Diaconis–Ylvisaker conjugate prior for log-linear parameters. We discuss the computation of Bayes factors through Laplace approximations and the Bayesian iterative proportional fitting algorithm for sampling model parameters. We use our model determination approach in a sparse eight-way contingency table.