Asymptotic Properties of Approximate Bayesian Computation

2016/07/23 by David T. Frazier, Frazier, David T., Gael M. Martin +5
Mathematics · #Computation (stat.CO) #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Statistics Theory (math.ST) #math.ST #stat.CO #stat.ME #stat.TH

paper · pdf · doi:10.48550/arxiv.1607.06903

This 31 pages paper is a revised version of the paper, including supplementary material

arxiv created 2018/05/08 · arxiv updated 2018/05/09

Abstract

Approximate Bayesian computation allows for statistical analysis in 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, its limiting shape, 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.

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