Likelihood-free parallel tempering

Approximate Bayesian Computational (ABC) methods, or likelihood-free methods, have appeared in the past fifteen years as useful methods to perform Bayesian analysis when the likelihood is analytically or computationally intractable. Several ABC methods have been proposed: MCMC methods have been developed by Marjoram et al. [2003] and by Bortot et al. [2007] for instance, and sequential methods have been proposed among others by Sisson et al. [2007], Beaumont et al. [2009] and Del Moral et al. [2009]. Recently, sequential ABC methods have appeared as an alternative to ABC-PMC methods [see for instance McKinley et al., 2009, 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]. Performance is compared with existing ABC algorithms on simulations and on a real example.