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Bayesian computation via empirical likelihood

  1. Christian P. Roberte,f,g,1
  1. aSchool of Mathematical Sciences, Queensland University of Technology, Brisbane, QLD 4001, Australia;
  2. bCentre de Biologie pour la Gestion des Populations, Institut National de la Recherche Agronomique, 34988 Montferrier-sur-Lez Cedex, France;
  3. cUniversité Montpellier 2, Institut de Mathématiques et de Modélisation de Montpellier, 34095 Montpellier Cedex 5, France;
  4. dInstitut de Biologie Computationnelle, Montpellier, France;
  5. eUniversité Paris Dauphine, Centre de Recherche en Mathematiques de la Decision, 75775 Paris Cedex 16, France;
  6. fInstitut Universitaire de France, Paris, France; and
  7. gCentre de Recherche en Statistique et Economie, 92245 Malakoff Cedex, France

  1. Edited by Stephen E. Fienberg, Carnegie Mellon University, Pittsburgh, PA, and approved December 7, 2012 (received for review May 25, 2012)

Abstract

Approximate Bayesian computation has become an essential tool for the analysis of complex stochastic models when the likelihood function is numerically unavailable. However, the well-established statistical method of empirical likelihood provides another route to such settings that bypasses simulations from the model and the choices of the approximate Bayesian computation parameters (summary statistics, distance, tolerance), while being convergent in the number of observations. Furthermore, bypassing model simulations may lead to significant time savings in complex models, for instance those found in population genetics. The Bayesian computation with empirical likelihood algorithm we develop in this paper also provides an evaluation of its own performance through an associated effective sample size. The method is illustrated using several examples, including estimation of standard distributions, time series, and population genetics models.

Footnotes

  • ↵1To whom correspondence should be addressed. E-mail: Christian.Robert{at}ceremade.dauphine.fr.

  • Author contributions: C.P.R. designed research; K.L.M., P.P., and C.P.R. performed research; K.L.M., P.P., and C.P.R. analyzed data; and K.L.M., P.P., and C.P.R. wrote the paper.

  • The authors declare no conflict of interest.

  • This article is a PNAS Direct Submission.

  • This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1208827110/-/DCSupplemental.

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