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Biometrika Advance Access published online on October 12, 2009
Biometrika, doi:10.1093/biomet/asp052
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© 2009 Biometrika Trust

Miscellanea

Adaptive approximate Bayesian computation

Mark A. Beaumont

School of Biological Sciences, University of Reading, PO Box 68, Whiteknights, Reading RG6 6BX, U.K. m.a.beaumont{at}reading.ac.uk

Jean-Marie Cornuet

Department of Epidemiology and Public Health, Imperial College, London SW7 2AZ, U.K. jmcornuet{at}ensam.inra.fr

Jean-Michel Marin

Institut de Mathématiques et Modélisation de Montpellier, Université Montpellier 2, Case Courrier 51, 34095 Montpellier cedex 5, France Jean-Michel.Marin{at}univ-montp2.fr

Christian P. Robert

Centre de Recherche en Mathématiques de la Décision, Université Paris Dauphine, 75775 Paris cedex 16, France xian{at}ceremade.dauphine.fr

Received for publication 1 July 2008. Revision received 1 April 2009.
  Abstract

Sequential techniques can enhance the efficiency of the approximate Bayesian computation algorithm, as in Sisson et al.’s (2007) partial rejection control version. While this method is based upon the theoretical works of Del Moral et al. (2006), the application to approximate Bayesian computation results in a bias in the approximation to the posterior. An alternative version based on genuine importance sampling arguments bypasses this difficulty, in connection with the population Monte Carlo method of Cappé et al. (2004), and it includes an automatic scaling of the forward kernel. When applied to a population genetics example, it compares favourably with two other versions of the approximate algorithm.

Key Words: Importance sampling • Markov chain Monte Carlo • Partial rejection control • Sequential Monte Carlo


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