Lack of confidence in approximate Bayesian computation model choice

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

Robert, Christian P.; Cornuet, Jean-Marie; Marin, Jean-Michel; Pillai, Natesh S. (2011), Lack of confidence in approximate Bayesian computation model choice, Proceedings of the National Academy of Sciences of the United States of America, 108, 37, p. 15112-15117. http://dx.doi.org/10.1073/pnas.1102900108

Type

Article accepté pour publication ou publié

Date

2011

Journal name

Proceedings of the National Academy of Sciences of the United States of America

Volume

108

Number

Pages

15112-15117

Abstract (EN)

Approximate Bayesian computation (ABC) have become a essential tool for the analysis of complex stochastic models. Earlier, Grelaud et al. (2009) advocated the use of ABC for Bayesian model choice in the specific case of Gibbs random fields, relying on a inter-model sufficiency property to show that the approximation was legitimate. Having implemented ABC-based model choice in a wide range of phylogenetic models in the DIY-ABC software (Cornuet et al., 2008), we now present theoretical background as to why a generic use of ABC for model choice is ungrounded, since it depends on an unknown amount of information loss induced by the use of insufficient summary statistics. The approximation error of the posterior probabilities of the models under comparison may thus be unrelated with the computational effort spent in running an ABC algorithm. We then conclude that additional empirical verifications of the performances of the ABC procedure are necessary to conduct model choice.

Subjects / Keywords

DIYABC; Bayes factor; likelihood-free methods; Bayesian model choice; sufficiency

JEL

C11 - Bayesian Analysis: General