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Permissible boundary prior function as a virtually proper prior density

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  • Takemi Yanagimoto
  • Toshio Ohnishi

Abstract

Regularity conditions for an improper prior function to be regarded as a virtually proper prior density are proposed, and their implications are discussed. The two regularity conditions require that a prior function is defined as a limit of a sequence of proper prior densities and also that the induced posterior density is derived as a smooth limit of the sequence of corresponding posterior densities. This approach is compared with the assumption of a degenerated prior density at an unknown point, which is familiar in the empirical Bayes method. The comparison study extends also to the assumption of an improper prior function discussed separately from any proper prior density. Properties and examples are presented to claim potential usefulness of the proposed notion. Copyright The Institute of Statistical Mathematics, Tokyo 2014

Suggested Citation

  • Takemi Yanagimoto & Toshio Ohnishi, 2014. "Permissible boundary prior function as a virtually proper prior density," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(4), pages 789-809, August.
    • Handle: RePEc:spr:aistmt:v:66:y:2014:i:4:p:789-809
    DOI: 10.1007/s10463-013-0421-1
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    1. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
    2. José Manuel Corcuera & Federica Giummolè, 1999. "A Generalized Bayes Rule for Prediction," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 26(2), pages 265-279, June.
    3. Paul L. Speckman, 2003. "Fully Bayesian spline smoothing and intrinsic autoregressive priors," Biometrika, Biometrika Trust, vol. 90(2), pages 289-302, June.
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