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 Geyer and Thompson [J. Roy. Statist. Soc. Ser. B 54 (1992) 657-699]. 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.