Approximate Bayesian computation via empirical likelihood
K. L. Mengersen (QUT, Brisbane), P. Pudlo (Universite Montpellier 2), C. P. Robert (Universite Paris-Dauphine)
(Submitted on 25 May 2012)
Approximate Bayesian computation (ABC) has now become an essential tool for the analysis of complex stochastic models when the likelihood function is unavailable. The well-established statistical method of empirical likelihood however 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 provably convergent in the number of observations. Furthermore, avoiding model simulations leads to significant time savings in complex models, such as those used in population genetics. The ABCel 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 and quantile distributions, and time series and population genetics models.