Model comparison for Gibbs random fields using noisy reversible jump Markov chain Monte Carlo

TL;DR

This paper introduces a noisy RJMCMC algorithm for Bayesian model comparison in Gibbs random fields, overcoming computational challenges by using unbiased estimators, with proven convergence and improved efficiency over exact methods.

Contribution

It presents a novel noisy RJMCMC method that handles intractable likelihoods in Gibbs random fields, with theoretical guarantees and practical efficiency improvements.

Findings

Noisy RJMCMC converges under certain conditions.

The method outperforms exact algorithms in efficiency.

Controlled variance estimators are crucial for performance.

Abstract

The reversible jump Markov chain Monte Carlo (RJMCMC) method offers an across-model simulation approach for Bayesian estimation and model comparison, by exploring the sampling space that consists of several models of possibly varying dimensions. A naive implementation of RJMCMC to models like Gibbs random fields suffers from computational difficulties: the posterior distribution for each model is termed doubly-intractable since computation of the likelihood function is rarely available. Consequently, it is simply impossible to simulate a transition of the Markov chain in the presence of likelihood intractability. A variant of RJMCMC is presented, called noisy RJMCMC, where the underlying transition kernel is replaced with an approximation based on unbiased estimators. Based on previous theoretical developments, convergence guarantees for the noisy RJMCMC algorithm are provided. The experiments show that the noisy RJMCMC algorithm can be much more efficient than other exact methods, provided that an estimator with controlled Monte Carlo variance is used, a fact which is in agreement with the theoretical analysis.