Why approximate Bayesian computational (ABC) methods cannot handle model choice problems

Pillai, Natesh S.; Marin, Jean-Michel; Robert, Christian P.

Pillai, Natesh S.; Marin, Jean-Michel; Robert, Christian P. (2011-01), Why approximate Bayesian computational (ABC) methods cannot handle model choice problems. https://basepub.dauphine.fr/handle/123456789/5728

Type

Document de travail / Working paper

Lien vers un document non conservé dans cette base

http://fr.arXiv.org/abs/1101.5091

Date

2011-01

Éditeur

Université Paris-Dauphine

Ville d’édition

Paris

Métadonnées

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Auteur(s)

Pillai, Natesh S.
Marin, Jean-Michel

Robert, Christian P.

Résumé (EN)

Approximate Bayesian computation (ABC), also known as likelihood-free methods, have become a favourite tool for the analysis of complex stochastic models, primarily in population genetics but also in financial analyses. We advocated in Grelaud et al. (2009) the use of ABC for Bayesian model choice in the specific case of Gibbs random fields (GRF), relying on a sufficiency property mainly 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 DIY ABC software (Cornuet et al., 2008), we present theoretical evidence that the general use of ABC for model choice is fraught with danger in the sense that no amount of computation, however large, can guarantee a proper approximation of the posterior probabilities of the models under comparison.

Mots-clés

sufficiency; Bayes factor; model choice; ABC

JEL

C11 - Bayesian Analysis: General