Permissible boundary prior function as a virtually proper prior density

Takemi Yanagimoto, Toshio Ohnishi

Research output: Contribution to journalArticle

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.

Original languageEnglish
Pages (from-to)789-809
Number of pages21
JournalAnnals of the Institute of Statistical Mathematics
Volume66
Issue number4
DOIs
Publication statusPublished - Jan 1 2014

Fingerprint

Improper Prior
Regularity Conditions
Empirical Bayes Method
Unknown

All Science Journal Classification (ASJC) codes

  • Statistics and Probability

Cite this

Permissible boundary prior function as a virtually proper prior density. / Yanagimoto, Takemi; Ohnishi, Toshio.

In: Annals of the Institute of Statistical Mathematics, Vol. 66, No. 4, 01.01.2014, p. 789-809.

Research output: Contribution to journalArticle

@article{00cb82d831f942d48cc3998fc9f19812,
title = "Permissible boundary prior function as a virtually proper prior density",
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.",
author = "Takemi Yanagimoto and Toshio Ohnishi",
year = "2014",
month = "1",
day = "1",
doi = "10.1007/s10463-013-0421-1",
language = "English",
volume = "66",
pages = "789--809",
journal = "Annals of the Institute of Statistical Mathematics",
issn = "0020-3157",
publisher = "Springer Netherlands",
number = "4",

}

TY - JOUR

T1 - Permissible boundary prior function as a virtually proper prior density

AU - Yanagimoto, Takemi

AU - Ohnishi, Toshio

PY - 2014/1/1

Y1 - 2014/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84903381196&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84903381196&partnerID=8YFLogxK

U2 - 10.1007/s10463-013-0421-1

DO - 10.1007/s10463-013-0421-1

M3 - Article

AN - SCOPUS:84903381196

VL - 66

SP - 789

EP - 809

JO - Annals of the Institute of Statistical Mathematics

JF - Annals of the Institute of Statistical Mathematics

SN - 0020-3157

IS - 4

ER -