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

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
External document link
http://fr.arXiv.org/abs/1101.5091
Date
2011-01
Publisher
Université Paris-Dauphine
Published in
Paris
Pages
20
Metadata
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Author(s)
Pillai, Natesh S.
Marin, Jean-Michel cc
Robert, Christian P.
Abstract (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.
Subjects / Keywords
sufficiency; Bayes factor; model choice; ABC
JEL
C11 - Bayesian Analysis: General