Bayesian inference for Gibbs random fields using composite likelihoods

TL;DR

This paper investigates the use of composite likelihoods for Bayesian inference in Gibbs random fields, addressing the intractability of likelihood functions in spatial models.

Contribution

It evaluates the effectiveness of various composite likelihood approximations within a Bayesian framework for Gibbs random fields.

Findings

Composite likelihoods provide practical approximations for intractable likelihoods.

Certain composite likelihood methods yield accurate Bayesian posterior estimates.

The approach enhances computational feasibility for complex spatial models.

Abstract

Gibbs random fields play an important role in statistics, for example the autologistic model is commonly used to model the spatial distribution of binary variables defined on a lattice. However they are complicated to work with due to an intractability of the likelihood function. It is therefore natural to consider tractable approximations to the likelihood function. Composite likelihoods offer a principled approach to constructing such approximation. The contribution of this paper is to examine the performance of a collection of composite likelihood approximations in the context of Bayesian inference.