Approximate Bayesian computation with semiparametric density ratio model

Abstract

Approximate Bayesian computation (ABC) is a likelihood-free inference method commonly employed for statistical inference in models with unknown or complex likelihood functions. ABC estimates the posterior distributions of model parameters by comparing summary statistics of the simulated and observed data. However, the selection of informative summary statistics can be challenging in practice. In this study, we propose a summary-statistic-free method called ABC with semiparametric empirical likelihood ratio (ABC-SELR). This method utilises the empirical likelihood within the framework of the semiparametric density ratio model to assess the simulated parameters via testing whether the simulated and observed data conform to the same distribution. By eliminating the need for choosing summary statistics, our approach avoids potential information loss. Furthermore, the proposed method captures the shared characteristics between the simulated and observed data, leading to improved efficiency. We demonstrate the accuracy and efficiency of ABC-SELR by comparing with existing ABC methods through numerical simulations.

Keywords:

• ABC
• Bayesian inference
• empirical likelihood
• hypothesis testing
• likelihood free methods

Acknowledgments

The authors are very grateful to the editor and two reviewers for a number of constructive comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was partly supported by the National Natural Science Foundation of China [grant numbers 12001454 and 72033002].