Approximate Bayesian computation with semiparametric density ratio model

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.