Statistics and Computing

, Volume 23, Issue 4, pp 535–549 | Cite as

Likelihood-free parallel tempering

  • Meïli BaragattiEmail author
  • Agnès Grimaud
  • Denys Pommeret


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.


Approximated Bayesian computational Likelihood-free Intractable likelihood Parallel tempering Population-based Monte Carlo Markov chain 



The authors are very grateful to the reviewers and to the Associate Editor for useful comments which enabled us to greatly improve the manuscript.


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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Meïli Baragatti
    • 1
    • 2
    Email author
  • Agnès Grimaud
    • 2
  • Denys Pommeret
    • 2
  1. 1.Ipsogen SALuminy Biotech EntreprisesMarseille Cedex 9France
  2. 2.Institute of Mathematics of Luminy (IML)Aix-Marseille UniversityMarseille Cedex 9France

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