Relevant statistics for Bayesian model choice

Jean‐Michel Marin

doi:10.1111/rssb.12056

Relevant statistics for Bayesian model choice

2013-12-09

67

OA

AI

Christian P. Robert *

J

Judith Rousseau

DOI：10.1111/rssb.12056

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Abstract

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The choice of the summary statistics that are used in Bayesian inference and in particular in approximate Bayesian computation algorithms has bearings on the validation of the resulting inference. Those statistics are nonetheless customarily used in approximate Bayesian computation algorithms without consistency checks. We derive necessary and sufficient conditions on summary statistics for the corresponding Bayes factor to be convergent, namely to select the true model asymptotically. Those conditions, which amount to the expectations of the summary statistics differing asymptotically under the two models, are quite natural and can be exploited in approximate Bayesian computation settings to infer whether or not a choice of summary statistics is appropriate, via a Monte Carlo validation.

Keywords:

Ancillarity

Approximate Bayesian computation

Asymptotics

Bayes factor

Bayesian model choice

Gaussianity

Likelihood-free methods

Sufficiency

Relevant statistics for Bayesian model choice

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