Testing model specification in approximate Bayesian computation

TL;DR

This paper introduces a new diagnostic procedure for detecting model misspecification in approximate Bayesian computation, demonstrating its theoretical consistency, empirical effectiveness, and computational efficiency through examples and an exchange rate application.

Contribution

It proposes a novel, computationally efficient method for diagnosing model misspecification in ABC that outperforms existing approaches requiring re-running inference.

Findings

The procedure can consistently detect model misspecification.

It performs well in finite samples.

It is less computationally demanding than existing methods.

Abstract

We present a procedure to diagnose model misspecification in situations where inference is performed using approximate Bayesian computation. We demonstrate theoretically, and empirically that this procedure can consistently detect the presence of model misspecification. Our examples demonstrates that this approach delivers good finite-sample performance and is computational less onerous than existing approaches, all of which require re-running the inference algorithm. An empirical application to modelling exchange rate log returns using a g-and-k distribution completes the paper.