# 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 language English 593-607 15 Biometrika 105 3 https://doi.org/10.1093/biomet/asy027 Published - 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.
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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

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