Empirical bayes detection of a change in distribution

Rohana J. Karunamuni, Shunpu Zhang

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

The problem of detection of a change in distribution is considered. Shiryayev (1963, Theory Probab. Appl., 8, pp. 22-46, 247-264 and 402-413; 1978, Optimal Stopping Rules, Springer, New York) solved the problem in a Bayesian framework assuming that the prior on the change point is Geometric (p). Shiryayev showed that the Bayes solution prescribes stopping as soon as the posterior probability of the change having occurred exceeds a fixed level. In this paper, a myopic policy is studied. An empirical Bayes stopping time is investigated for detecting a change in distribution when the prior is not completely known.

Original languageEnglish (US)
Pages (from-to)229-246
Number of pages18
JournalAnnals of the Institute of Statistical Mathematics
Volume48
Issue number2
DOIs
StatePublished - Jan 1 1996

Fingerprint

Empirical Bayes
Optimal Stopping Rule
Stopping Time
Change Point
Posterior Probability
Bayes
Exceed
Policy
Framework

Keywords

  • Bayes sequential rules
  • Change points
  • Empirical Bayes
  • Statistical process control
  • Stopping times

ASJC Scopus subject areas

  • Statistics and Probability

Cite this

Empirical bayes detection of a change in distribution. / Karunamuni, Rohana J.; Zhang, Shunpu.

In: Annals of the Institute of Statistical Mathematics, Vol. 48, No. 2, 01.01.1996, p. 229-246.

Research output: Contribution to journalArticle

Karunamuni, Rohana J. ; Zhang, Shunpu. / Empirical bayes detection of a change in distribution. In: Annals of the Institute of Statistical Mathematics. 1996 ; Vol. 48, No. 2. pp. 229-246.
@article{a0043342856248ec8848df9dd2d29e28,
title = "Empirical bayes detection of a change in distribution",
abstract = "The problem of detection of a change in distribution is considered. Shiryayev (1963, Theory Probab. Appl., 8, pp. 22-46, 247-264 and 402-413; 1978, Optimal Stopping Rules, Springer, New York) solved the problem in a Bayesian framework assuming that the prior on the change point is Geometric (p). Shiryayev showed that the Bayes solution prescribes stopping as soon as the posterior probability of the change having occurred exceeds a fixed level. In this paper, a myopic policy is studied. An empirical Bayes stopping time is investigated for detecting a change in distribution when the prior is not completely known.",
keywords = "Bayes sequential rules, Change points, Empirical Bayes, Statistical process control, Stopping times",
author = "Karunamuni, {Rohana J.} and Shunpu Zhang",
year = "1996",
month = "1",
day = "1",
doi = "10.1007/BF00054787",
language = "English (US)",
volume = "48",
pages = "229--246",
journal = "Annals of the Institute of Statistical Mathematics",
issn = "0020-3157",
publisher = "Springer Netherlands",
number = "2",

}

TY - JOUR

T1 - Empirical bayes detection of a change in distribution

AU - Karunamuni, Rohana J.

AU - Zhang, Shunpu

PY - 1996/1/1

Y1 - 1996/1/1

N2 - The problem of detection of a change in distribution is considered. Shiryayev (1963, Theory Probab. Appl., 8, pp. 22-46, 247-264 and 402-413; 1978, Optimal Stopping Rules, Springer, New York) solved the problem in a Bayesian framework assuming that the prior on the change point is Geometric (p). Shiryayev showed that the Bayes solution prescribes stopping as soon as the posterior probability of the change having occurred exceeds a fixed level. In this paper, a myopic policy is studied. An empirical Bayes stopping time is investigated for detecting a change in distribution when the prior is not completely known.

AB - The problem of detection of a change in distribution is considered. Shiryayev (1963, Theory Probab. Appl., 8, pp. 22-46, 247-264 and 402-413; 1978, Optimal Stopping Rules, Springer, New York) solved the problem in a Bayesian framework assuming that the prior on the change point is Geometric (p). Shiryayev showed that the Bayes solution prescribes stopping as soon as the posterior probability of the change having occurred exceeds a fixed level. In this paper, a myopic policy is studied. An empirical Bayes stopping time is investigated for detecting a change in distribution when the prior is not completely known.

KW - Bayes sequential rules

KW - Change points

KW - Empirical Bayes

KW - Statistical process control

KW - Stopping times

UR - http://www.scopus.com/inward/record.url?scp=0030356598&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030356598&partnerID=8YFLogxK

U2 - 10.1007/BF00054787

DO - 10.1007/BF00054787

M3 - Article

AN - SCOPUS:0030356598

VL - 48

SP - 229

EP - 246

JO - Annals of the Institute of Statistical Mathematics

JF - Annals of the Institute of Statistical Mathematics

SN - 0020-3157

IS - 2

ER -