Likelihood-free Model Choice

This document is an invited chapter covering the specificities of ABC model choice, intended for the incoming Handbook of ABC by Sisson, Fan, and Beaumont (2015). Beyond exposing the potential pitfalls of ABC based posterior probabilities, the review emphasizes mostly the solution proposed by Pudlo et al. (2014) on the use of random forests for aggregating summary statistics and for replacing posterior probability approximations by posterior classification errors.