Evidence and Bayes Factor Estimation for Gibbs Random Fields

Abstract

Gibbs random fields play an important role in statistics. However, they are complicated to work with due to an intractability of the likelihood function and there has been much work devoted to finding computational algorithms to allow Bayesian inference to be conducted for such so-called doubly intractable distributions. This article extends this work and addresses the issue of estimating the evidence and Bayes factor for such models. The approach that we develop is shown to yield good performance. Supplementary materials for this article are available online.

Key Words:

• Exchange algorithm
• Ising model
• Population MCMC

SUPPLEMENTARY MATERIALS

C code: The supplementary files for this article include C programs that can be used to replicate the Ising model study and exponential random graph example in Section 6 of this article. Please see the file README.txt contained within the accompanying tar file for more details.

ACKNOWLEDGMENTS

Nial Friel’s research was supported by a Science Foundation Ireland Research Frontiers Program grant, 09/RFP/MTH2199.