Bayesian computation for statistical models with intractable normalizing constants

TL;DR

This paper introduces a novel, asymptotically consistent Monte Carlo method for Bayesian analysis of models with intractable normalizing constants, enabling sampling where traditional methods fail.

Contribution

It presents the first general Bayesian Monte Carlo approach for models with intractable normalizing constants, extending the MCMC-MLE framework.

Findings

Method successfully samples from complex posterior distributions.

Proven asymptotic consistency with a strong law of large numbers.

Demonstrated effectiveness in image segmentation and social network models.

Abstract

This paper deals with some computational aspects in 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 an approach to sample from such posterior distributions. The method can be thought as a Bayesian version of the MCMC-MLE approach of Geyer and Thompson (1992). To the best of our knowledge, this is the first general and asymptotically consistent Monte Carlo method for such problems. We illustrate the method with 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.