Bayesian computation via empirical likelihood

TL;DR

This paper introduces the BCel algorithm, a Bayesian computation method using empirical likelihood that avoids model simulations, reduces computational time, and evaluates its own performance, demonstrated through various complex models.

Contribution

It presents a novel empirical likelihood-based Bayesian computation method that bypasses simulations and includes performance assessment, improving efficiency for complex models.

Findings

BCel algorithm effectively estimates parameters in complex models.

The method reduces computational time compared to traditional ABC.

Performance evaluation via effective sample size is feasible with BCel.

Abstract

Approximate Bayesian computation (ABC) has become an essential tool for the analysis of complex stochastic models when the likelihood function is numerically unavailable. However, the well-established statistical method of empirical likelihood provides another route to such settings that bypasses simulations from the model and the choices of the ABC parameters (summary statistics, distance, tolerance), while being convergent in the number of observations. Furthermore, bypassing model simulations may lead to significant time savings in complex models, for instance those found in population genetics. The BCel algorithm we develop in this paper also provides an evaluation of its own performance through an associated effective sample size. The method is illustrated using several examples, including estimation of standard distributions, time series, and population genetics models.