Model Misspecification in Approximate Bayesian Computation: Consequences and Diagnostics

We analyze the behavior of Approximate Bayesian Computation (ABC) when the model generating the simulated data differs from that generating the observed data, i.e., when the data simulator in ABC is misspecified. We demonstrate theoretically and in simple, but practically relevant, examples that the performance of ABC can be poor when the model is misspecified. Graphical and posterior predictive checks are proposed as a means of detecting model misspecification in ABC. Lastly, theoretical results demonstrate that under regularity conditions a version of the ABC accept/reject approach concentrates on sets containing an appropriately defined pseudo-true parameter value.