Bayesian estimation of graphical log-inear marginal models

Bayesian methods for graphical log-linear marginal models have not been developed as much as traditional frequentist approaches. The likelihood function cannot be analytically expressed in terms of the marginal log-linear interactions, but only in terms of cell counts or probabilities. No conjugate analysis is feasible, and MCMC methods are needed.We present a fully automatic and efficient MCMC strategy for quantitative learning, based on the DAG representation of the model. While the prior is expressed in terms of the marginal log-linear interactions, the proposal is on the probability parameter space. In order to obtain an efficient algorithm, we use as proposal values draws from a Gibbs sampling on the probability parameters.