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Generalization of Jeffreys divergence-based priors for Bayesian hypothesis testing

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  • M. J. Bayarri
  • G. García-Donato

Abstract

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. Copyright (c) 2008 Royal Statistical Society.

Suggested Citation

  • M. J. Bayarri & G. García-Donato, 2008. "Generalization of Jeffreys divergence-based priors for Bayesian hypothesis testing," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(5), pages 981-1003.
  • Handle: RePEc:bla:jorssb:v:70:y:2008:i:5:p:981-1003
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    References listed on IDEAS

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    1. José M. Bernardo & Raúl Rueda, 2002. "Bayesian Hypothesis Testing: a Reference Approach," International Statistical Review, International Statistical Institute, vol. 70(3), pages 351-372, December.
    2. José Bernardo, 2005. "Intrinsic credible regions: An objective Bayesian approach to interval estimation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 14(2), pages 317-384, December.
    3. Liang, Feng & Paulo, Rui & Molina, German & Clyde, Merlise A. & Berger, Jim O., 2008. "Mixtures of g Priors for Bayesian Variable Selection," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 410-423, March.
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    Cited by:

    1. repec:spr:testjl:v:26:y:2017:i:2:d:10.1007_s11749-016-0516-0 is not listed on IDEAS
    2. repec:eee:stapro:v:137:y:2018:i:c:p:292-296 is not listed on IDEAS
    3. Sang Gil Kang & Woo Dong Lee & Yongku Kim, 2017. "Objective Bayesian testing on the common mean of several normal distributions under divergence-based priors," Computational Statistics, Springer, vol. 32(1), pages 71-91, March.

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