Asymptotic properties of approximate Bayesian computation

D. T. Frazier, G. M. Martin, C. P. Robert, J Rousseau

Research output: Contribution to journalArticleResearchpeer-review

10 Citations (Scopus)

Abstract

Approximate Bayesian computation allows for statistical analysis using models with intractable likelihoods. In this paper we consider the asymptotic behaviour of the posterior distribution obtained by this method. We give general results on the rate at which the posterior distribution concentrates on sets containing the true parameter, the limiting shape of the posterior distribution, and the asymptotic distribution of the posterior mean. These results hold under given rates for the tolerance used within the method, mild regularity conditions on the summary statistics, and a condition linked to identification of the true parameters. Implications for practitioners are discussed.

Original languageEnglish
Pages (from-to)593-607
Number of pages15
JournalBiometrika
Volume105
Issue number3
DOIs
Publication statusPublished - Sep 2018

Keywords

  • Approximate Bayesian computation
  • Asymptotics
  • Bernstein-von Mises theorem
  • Likelihood-free method
  • Posterior concentration

Cite this

Frazier, D. T. ; Martin, G. M. ; Robert, C. P. ; Rousseau, J. / Asymptotic properties of approximate Bayesian computation. In: Biometrika. 2018 ; Vol. 105, No. 3. pp. 593-607.
@article{540c9d5dcf9740d8ae4c52e214ce2434,
title = "Asymptotic properties of approximate Bayesian computation",
abstract = "Approximate Bayesian computation allows for statistical analysis using models with intractable likelihoods. In this paper we consider the asymptotic behaviour of the posterior distribution obtained by this method. We give general results on the rate at which the posterior distribution concentrates on sets containing the true parameter, the limiting shape of the posterior distribution, and the asymptotic distribution of the posterior mean. These results hold under given rates for the tolerance used within the method, mild regularity conditions on the summary statistics, and a condition linked to identification of the true parameters. Implications for practitioners are discussed.",
keywords = "Approximate Bayesian computation, Asymptotics, Bernstein-von Mises theorem, Likelihood-free method, Posterior concentration",
author = "Frazier, {D. T.} and Martin, {G. M.} and Robert, {C. P.} and J Rousseau",
year = "2018",
month = "9",
doi = "10.1093/biomet/asy027",
language = "English",
volume = "105",
pages = "593--607",
journal = "Biometrika",
issn = "0006-3444",
publisher = "Oxford University Press",
number = "3",

}

Asymptotic properties of approximate Bayesian computation. / Frazier, D. T.; Martin, G. M. ; Robert, C. P.; Rousseau, J.

In: Biometrika, Vol. 105, No. 3, 09.2018, p. 593-607.

Research output: Contribution to journalArticleResearchpeer-review

TY - JOUR

T1 - Asymptotic properties of approximate Bayesian computation

AU - Frazier, D. T.

AU - Martin, G. M.

AU - Robert, C. P.

AU - Rousseau, J

PY - 2018/9

Y1 - 2018/9

N2 - Approximate Bayesian computation allows for statistical analysis using models with intractable likelihoods. In this paper we consider the asymptotic behaviour of the posterior distribution obtained by this method. We give general results on the rate at which the posterior distribution concentrates on sets containing the true parameter, the limiting shape of the posterior distribution, and the asymptotic distribution of the posterior mean. These results hold under given rates for the tolerance used within the method, mild regularity conditions on the summary statistics, and a condition linked to identification of the true parameters. Implications for practitioners are discussed.

AB - Approximate Bayesian computation allows for statistical analysis using models with intractable likelihoods. In this paper we consider the asymptotic behaviour of the posterior distribution obtained by this method. We give general results on the rate at which the posterior distribution concentrates on sets containing the true parameter, the limiting shape of the posterior distribution, and the asymptotic distribution of the posterior mean. These results hold under given rates for the tolerance used within the method, mild regularity conditions on the summary statistics, and a condition linked to identification of the true parameters. Implications for practitioners are discussed.

KW - Approximate Bayesian computation

KW - Asymptotics

KW - Bernstein-von Mises theorem

KW - Likelihood-free method

KW - Posterior concentration

UR - http://www.scopus.com/inward/record.url?scp=85050191248&partnerID=8YFLogxK

U2 - 10.1093/biomet/asy027

DO - 10.1093/biomet/asy027

M3 - Article

AN - SCOPUS:85050191248

VL - 105

SP - 593

EP - 607

JO - Biometrika

JF - Biometrika

SN - 0006-3444

IS - 3

ER -