title: Reliable ABC model choice via random forests.
abstract: Approximate Bayesian computation (ABC) methods provide an elaborate approach to Bayesian inference on complex models, including model choice. Both theoretical arguments and simulation experiments indicate, however, that model posterior probabilities may be poorly evaluated by standard ABC techniques.
  
  
  
  We propose a novel approach based on a machine learning tool named random forests (RF) to conduct selection among the highly complex models covered by ABC algorithms. We thus modify the way Bayesian model selection is both understood and operated, in that we rephrase the inferential goal as a classification problem, first predicting the model that best fits the data with RF and postponing the approximation of the posterior probability of the selected model for a second stage also relying on RF. Compared with earlier implementations of ABC model choice, the ABC RF approach offers several potential improvements: (i) it often has a larger discriminative power among the competing models, (ii) it is more robust against the number and choice of statistics summarizing the data, (iii) the computing effort is drastically reduced (with a gain in computation efficiency of at least 50) and (iv) it includes an approximation of the posterior probability of the selected model. The call to RF will undoubtedly extend the range of size of datasets and complexity of models that ABC can handle. We illustrate the power of this novel methodology by analyzing controlled experiments as well as genuine population genetics datasets.
  
  
  
  The proposed methodology is implemented in the R package abcrf available on the CRAN.
  
  
  
  jean-michel.marin@umontpellier.fr
  
  
  
  Supplementary data are available at Bioinformatics online.
authors.affiliation: Université de Montpellier, IMAG, Montpellier, Institut de Biologie Computationnelle (IBC), Montpellier.
authors.forename: Pierre
authors.initials: P
authors.lastname: Pudlo
authors.affiliation: Université de Montpellier, IMAG, Montpellier, Institut de Biologie Computationnelle (IBC), Montpellier.
authors.forename: Jean-Michel
authors.initials: JM
authors.lastname: Marin
authors.affiliation: Institut de Biologie Computationnelle (IBC), Montpellier, CBGP, INRA, Montpellier.
authors.forename: Arnaud
authors.initials: A
authors.lastname: Estoup
authors.affiliation: CBGP, INRA, Montpellier.
authors.forename: Jean-Marie
authors.initials: JM
authors.lastname: Cornuet
authors.affiliation: Institut de Biologie Computationnelle (IBC), Montpellier, CBGP, INRA, Montpellier.
authors.forename: Mathieu
authors.initials: M
authors.lastname: Gautier
authors.affiliation: Université Paris Dauphine, CEREMADE, Paris, France and University of Warwick, Coventry, UK.
authors.forename: Christian P
authors.initials: CP
authors.lastname: Robert
mesh_terms: D000465:Algorithms; D001499:Bayes Theorem; D003198:Computer Simulation; D005828:Genetics, Population; D008957:Models, Genetic