On Consistency of Approximate Bayesian Computation

Understand

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 identification of the true parameters.