Summary: Bayesian computation for statistical models with
intractable normalizing constants
Yves F. Atchad´e
, Nicolas Lartillot
and Christian Robert
(First version March 2008; revised Nov. 2008)
Abstract: This paper deals with a computational aspect of the Bayesian analysis of statisti-
cal models with intractable normalizing constants. In the presence of intractable normalizing
constants in the likelihood function, traditional MCMC methods cannot be applied. We pro-
pose 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 . To the best of our knowledge, this is the first general
and asymptotically consistent Monte Carlo method for such problems, even though  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.
Keywords and phrases: Monte Carlo methods, Adaptive MCMC, Bayesian inference,
Ising model, Image segmentation, Social network modeling, Wang-Landau.