Abstract

Approximate Bayesian computation (ABC), also known as likelihood-free methods, have become a standard tool for the analysis of complex models, primarily in population genetics. The development of new ABC methodology is undergoing a rapid increase in the past years, as shown by multiple publications, conferences and even software. While one valid interpretation of ABC based estimation is connected with nonparametrics, the setting is quite different for model choice issues. We examined in Grelaud et al. (2009, Bayesian Analysis) the use of ABC for Bayesian model choice in the specific of Gaussian random fields (GRF), relying on a sufficient property only enjoyed by GRFs to show that the approach was legitimate. Despite having previously suggested the use of ABC for model choice in a wider range of models in the DIYABC software (Cornuet et al., 2008, Bioinformatics), we present in Robert et al. (2011, PNAS ) evidence that the general use of ABC for model choice can be a real problem. Finally, in Marin et al. (2014, JRSS B ), we derive necessary and sufficient conditions on summary statistics for the corresponding Bayes factor to be convergent, namely to asymptotically select the true model. In this talk, we will present these different results.

Marin, Pillai, Robert and Rousseau (2014) Relevant statistics for Bayesian model choice, to appear in the Journal of the Royal Statistical Society, Series B

Robert, Cornuet, Marin and Pillai (2011) Lack of confidence in approximate Bayesian computation model choice, Proceedings of the National Academy of Science, 108(37), 15112-15117

Grelaud, Robert, Marin, Rodolphe and Taly (2009) ABC likelihood-free methods for model choice in Gibbs random fields, Bayesian Analysis, 4(2), 317-336

Cornuet, Santos, Beaumont, Robert, Marin, Balding, Guillemaud and Estoup (2008) Inferring population history with DIY ABC : a user-friendly approach Approximate Bayesian Computation, Bioinformatics, 24(23), 2713-2719