Reliable ABC model choice via random forests

Introduced in the late 1990’s, the ABC method can be considered from several perspectives, ranging from a purely practical motivation towards handling complex likelihoods to non-parametric justifications. We propose here a dierent analysis of ABC techniques and in particular of ABC model selection. Our exploration focus on the idea that generic machine learning tools like random forests (Breiman, 2001) can help in conducting model selection among the highly complex models covered by ABC algorithms. Both theoretical and algorithmic output indicate that posterior probabilities are poorly estimated by ABC. We thus strongly alters how Bayesian model selection is both understood and operated, since we advocate completely abandoning the use of posterior probabilities of the models under comparison as evidence tools. As a substitute, we propose to select the most likely model via a random forest procedure and to compute posterior predictive performances of the corresponding ABC selection method. Indeed, we argue that random forest methods can clearly be adapted to such settings, with a further documented recommendation towards sparse implementation of the random forest tree construction, using severe subsampling and reduced reference tables. The performances of the resulting ABC-random forest methodology are illustrated on several real or realistic population genetics datasets.

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