Relevant statistics for Bayesian model choice

• 成果类型: Article
• 署名作者: Marin, Jean-Michel; Pillai, Natesh S.; Robert, Christian P.; Rousseau, Judith
• 署名单位: Universite de Montpellier; Harvard University; Universite PSL; Universite Paris-Dauphine; University of Warwick; Institut Polytechnique de Paris; ENSAE Paris; Universite PSL; Universite Paris-Dauphine
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12056
• 发表日期: 2014
• 页码: 833-859
• 关键词: computation; inference; selection

摘要

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.