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

摘要

The reversible jump Markov chain Monte Carlo (RJMCMC) method offers anacross-model simulation approach for Bayesian estimation and model comparison,by exploring the sampling space that consists of several models of varyingdimensions. The implementation of RJMCMC to models like Gibbs random fieldssuffers from computational difficulties: the posterior distribution for eachmodel is termed doubly-intractable since computation of the likelihood functionis rarely available. Consequently, it is simply impossible to simulate atransition of the Markov chain in the presence of likelihood intractability. Inthis paper we present a variant of RJMCMC, called noisy RJMCMC, where wereplace the underlying transition kernel with an approximation based onunbiased estimators. Building upon the theoretical developments of Alquier etal. (2016), we provide convergence guarantees for the noisy RJMCMC algorithm.Our experiments show that the noisy RJMCMC algorithm can be much more efficientthan other exact methods, provided that an estimator with lower variance isused, a fact which is in agreement with our theoretical analysis.