Asymptotic properties of approximate Bayesian computation

David Frazier (), Gael Martin (), Christian Robert () and Judith Rousseau ()

No 12/17, Monash Econometrics and Business Statistics Working Papers from Monash University, Department of Econometrics and Business Statistics

Abstract: Approximate Bayesian computation is becoming an accepted tool for statistical analysis in models with intractable likelihoods. With the initial focus being primarily on the practical import of this algorithm, exploration of its formal statistical properties has begun to attract more attention. In this paper we consider the asymptotic behaviour of the posterior distribution obtained by this method. We give general results on: (i) the rate at which the posterior concentrates on sets containing the true parameter (vector); (ii) the limiting shape of the posterior; and (iii) the asymptotic distribution of the ensuing 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. Important implications of the theoretical results for practitioners are discussed.

Keywords: asymptotic properties; Bayesian consistency; Bernstein-von Mises theorem; likelihood-free methods. (search for similar items in EconPapers)
Pages: 32
Date: 2017
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