Bayesian computation for statistical models with intractable normalizing constants

This paper deals with a computational aspect of the Bayesian analysis of statistical models with intractable normalizing constants. In the presence of intractable normalizing constants in the likelihood function, traditional MCMC methods cannot be applied. We propose here a general approach to sample from such posterior distributions that bypasses the computation of the normalizing constant. Our method can be thought as a Bayesian version of the MCMC-MLE approach of [8]. To the best of our knowledge, this is the first general and asymptotically consistent Monte Carlo method for such problems, even though [12] has made some progress in this direction. We illustrate our approach on examples from image segmentation and social network modeling. We study as well the asymptotic behavior of the algorithm and obtain a strong law of large numbers for empirical averages. AMS 2000 subject classifications: Primary 60J27, 60J35, 65C40.