Likelihood-free parallel tempering

  • Authors:

  • Meïli Baragatti;Agnès Grimaud;Denys Pommeret

  • Affiliations:

  • Ipsogen SA, Luminy Biotech Entreprises, Marseille Cedex 9, France 13288 and Institute of Mathematics of Luminy (IML), Aix-Marseille University, Marseille Cedex 9, France 13288;Institute of Mathematics of Luminy (IML), Aix-Marseille University, Marseille Cedex 9, France 13288;Institute of Mathematics of Luminy (IML), Aix-Marseille University, Marseille Cedex 9, France 13288

  • Venue:
  • Statistics and Computing
  • Year:
  • 2013

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Abstract

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. (2012). 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.