Relevant statistics for Bayesian model choice

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

Rousseau, Judith; Robert, Christian P.; Pillai, Natesh S.; Marin, Jean-Michel (2014), Relevant statistics for Bayesian model choice, Journal of the Royal Statistical Society. Series B, Statistical Methodology, 76, 5, p. 833-859. http://dx.doi.org/10.1111/rssb.12056

Type

Article accepté pour publication ou publié

External document link

http://fr.arxiv.org/abs/1110.4700

Date

2014

Journal name

Journal of the Royal Statistical Society. Series B, Statistical Methodology

Volume

Number

5; 5

Publisher

Wiley

Pages

833-859

Abstract (EN)

The choice of the summary statistics in Bayesian inference and in particular in ABC algorithms is paramount to produce a valid outcome. We derive necessary and sufficient conditions on those statistics for the corresponding Bayes factor to be convergent, namely to asymptotically select the true model. Those conditions which amount to the means of the summary statistics to asymptotically differ under both models are then usable in ABC settings to determine which summary statistics are appropriate, most generally via a standard Monte Carlo validation.

Subjects / Keywords

Bayesian model choice; Gaussianity; Likelihood-free methods; Sufficiency; Bayes factor; Asymptotics; Approximate Bayesian computation; Ancillarity

JEL

C15 - Statistical Simulation Methods: General
C11 - Bayesian Analysis: General