Markov Chain Monte Carlo Model Determination for Hierarchical and Graphical Log-linear Models

SUMMARY The Bayesian approach to comparing models involves calculating the posterior probability of each plausible model. For high-dimensional contingency tables, the set of plausible models is very large. We focus attention on reversible jump Markov chain Monte Carlo (Green, 1995) and develop strategies for calculating posterior probabilities of hierarchical, graphical or decomposable log-linear models. Even for tables of moderate size, these sets of models may be very large. The choice of suitable prior distributions for model parameters is also discussed in detail, and two examples are presented. For the rst example, a 2 34 table, the model probabilities calculated using our reversible jump approach are compared with model probabilities calculated exactly or by using an alternative approximation. The second example is a 2 6 contingency table for which exact methods are infeasible, due to the large number of possible models.