Permissible boundary prior function as a virtually proper prior density

Takemi Yanagimoto, Toshio Ohnishi

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)789-809
Number of pages21
JournalAnnals of the Institute of Statistical Mathematics
Issue number4
Publication statusPublished - Aug 2014

All Science Journal Classification (ASJC) codes

  • Statistics and Probability


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