Likelihood-Free Parallel Tempering

TL;DR

This paper introduces a novel likelihood-free Bayesian inference algorithm that combines population-based MCMC with parallel tempering, demonstrating improved performance over existing ABC methods through simulations and real data applications.

Contribution

A new algorithm integrating population-based MCMC with parallel tempering for likelihood-free Bayesian inference, outperforming existing ABC methods.

Findings

The proposed method outperforms existing ABC algorithms in simulations.

The new algorithm shows improved convergence and efficiency on real data.

Performance comparisons demonstrate the advantages of the parallel tempering approach.

Abstract

Approximate Bayesian Computational (ABC) methods (or likelihood-free methods) have appeared in the past fifteen years as useful methods to perform Bayesian analyses when the likelihood is analytically or computationally intractable. Several ABC methods have been proposed: Monte Carlo Markov Chains (MCMC) methods have been developped by Marjoramet al. (2003) and by Bortotet al. (2007) for instance, and sequential methods have been proposed among others by Sissonet al. (2007), Beaumont et al. (2009) and Del Moral et al. (2009). Until now, while ABC-MCMC methods remain the reference, sequential ABC methods have appeared to outperforms them (see for example McKinley et al. (2009) or Sisson et al. (2007)). In this paper a new algorithm combining population-based MCMC methods with ABC requirements is proposed, using an analogy with the Parallel Tempering algorithm (Geyer, 1991). Performances are compared with existing ABC algorithms on simulations and on a real example.