Séance Séminaire

Séminaire de Probabilités et Statistique

Approximate Bayesian computation via empirical likelihood

Joint work with Christian P. Robert and Kerrie Mengersen.

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 population genetics models.