Testing Model Specification in Approximate Bayesian Computation Using Asymptotic Properties

Abstract

We present a novel procedure to diagnose model misspecification in situations where inference is performed using approximate Bayesian computation (ABC). Unlike previous procedures, our proposal is based on the asymptotic properties of ABC. We demonstrate theoretically, and empirically that our procedure can consistently detect the presence of model misspecification. The examples demonstrate that our proposal shows good finite-sample properties, outperforming existing approaches. An empirical application to modeling exchange rate log returns using a g-and-k distribution completes the article. Supplementary materials for this article are available online.

KEYWORDS:

• Approximate Bayesian computation
• Bayesian inference
• Misspecification test
• Simulation

Supplementary Materials

We present the main assumptions, and proofs of Theorem 1 and Corollary 1 given in the main text. We also present the details of the four algorithms used in the paper to asses model specification. Finally, we show extended results from the simulation exercises and applications.

Acknowledgments

We thank the associate editor and two anonymous referees for their comments, which greatly improved the article. We also are grateful for the computing resources that were made available by the Centro de Computación Científica Apolo at Universidad EAFIT (http://www.eafit.edu.co/apolo) to conduct the research reported in this article. All remaining errors are our own.

Disclosure Statement

The authors report there are no competing interests to declare.

Notes

1 In the supplementary material in Section 1.5, as suggested by an anonymous referee, we consider an example where the underlying assumptions on the summary statistics are not satisfied. In the case, as one would expect, the size of the test is beyond the nominal level (see Table A2). In addition, the supplementary material also proposes a simulated asymptotic goodness of fit diagnostic (SAGoF), which uses a simulated critical value, rather than the asymptotic version (see Algorithm 5 for details). We thank the referee’s for these suggestions.

2 We perform exercises increasing R in the simulating test, and obtain similar results.

Additional information

Funding

Andrés Ramírez-Hassan was supported by Universidad EAFIT [grant number 952]. David T. Frazier was supported by the ARC [grant number DE200101070].