Generalization of Jeffreys divergence-based priors for Bayesian hypothesis testing

• 成果类型: Article
• 署名作者: Bayarri, M. J.; Garcia-Donato, G.
• 署名单位: Universidad de Castilla-La Mancha; University of Valencia
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/j.1467-9868.2008.00667.x
• 发表日期: 2008
• 页码: 981-1003
• 关键词: model selection; approximations; default

摘要

We introduce objective proper prior distributions for hypothesis testing and model selection based on measures of divergence between the competing models; we call them divergence-based (DB) priors. DB priors have simple forms and desirable properties like information (finite sample) consistency and are often similar to other existing proposals like intrinsic priors. Moreover, in normal linear model scenarios, they reproduce the Jeffreys-Zellner-Siow priors exactly, Most importantly, in challenging scenarios such as irregular models and mixture models, DB priors are well defined and very reasonable, whereas alternative proposals are not. We derive approximations to the DB priors as well as Markov chain Monte Carlo and asymptotic expressions for the associated Bayes factors.