ABC likelihood-freee methods for model choice in Gibbs random fields

TL;DR

This paper develops an ABC-based method for model selection in Gibbs random fields, overcoming the challenge of intractable likelihoods by leveraging sufficient statistics and importance sampling, with applications in spatial data and protein structure analysis.

Contribution

It introduces a novel ABC algorithm tailored for model choice in Gibbs random fields, utilizing a common sufficient statistic across models to improve accuracy.

Findings

Effective model choice demonstrated in spatial and protein data.

Importance sampling enhances posterior probability estimation.

Method overcomes normalising constant issues in Gibbs models.

Abstract

Gibbs random fields (GRF) are polymorphous statistical models that can be used to analyse different types of dependence, in particular for spatially correlated data. However, when those models are faced with the challenge of selecting a dependence structure from many, the use of standard model choice methods is hampered by the unavailability of the normalising constant in the Gibbs likelihood. In particular, from a Bayesian perspective, the computation of the posterior probabilities of the models under competition requires special likelihood-free simulation techniques like the Approximate Bayesian Computation (ABC) algorithm that is intensively used in population genetics. We show in this paper how to implement an ABC algorithm geared towards model choice in the general setting of Gibbs random fields, demonstrating in particular that there exists a sufficient statistic across models. The accuracy of the approximation to the posterior probabilities can be further improved by importance sampling on the distribution of the models. The practical aspects of the method are detailed through two applications, the test of an iid Bernoulli model versus a first-order Markov chain, and the choice of a folding structure for two proteins.