On Consistency of Approximate Bayesian Computation

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

No 19/15, Monash Econometrics and Business Statistics Working Papers from Monash University, Department of Econometrics and Business Statistics

Abstract: Approximate Bayesian computation (ABC) methods have become increasingly prevalent of late, facilitating as they do the analysis of intractable, or challenging, statistical problems. With the initial focus being primarily on the practical import of ABC, exploration of its formal statistical properties has begun to attract more attention. The aim of this paper is to establish general conditions under which ABC methods are Bayesian consistent, in the sense of producing draws that yield a degenerate posterior distribution at the true parameter (vector) asymptotically (in the sample size). We derive conditions under which arbitrary summary statistics yield consistent inference in the Bayesian sense, with these conditions linked to identiÖcation of the true parameters. Using simple illustrative examples that have featured in the literature, we demonstrate that identiÖcation, and hence consistency, is unlikely to be achieved in many cases, and propose a simple diagnostic procedure that can indicate the presence of this problem. We also formally explore the link between consistency and the use of auxiliary models within ABC, and illustrate the subsequent results in the Lotka-Volterra predator-prey model.

Keywords: Bayesian consistency; likelihood-free methods; conditioning; auxiliary modelbased ABC; ordinary differential equations; Lotka-Volterra model. (search for similar items in EconPapers)
JEL-codes: C11 C15 C18 (search for similar items in EconPapers)
Date: 2015
New Economics Papers: this item is included in nep-ecm
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