Early detection of a change in poisson rate after accounting for population size effects

Yajun Mei, Sung Won Han, Kwok Leung Tsui

Research output: Contribution to journalArticle

36 Citations (Scopus)

Abstract

Motivated by applications in bio and syndromic surveillance, this article is concerned with the problem of detecting a change in the mean of Poisson distributions after taking into account the effects of population size. The family of generalized likelihood ratio (GLR) schemes is proposed and its asymptotic optimality properties are established under the classical asymptotic setting. However, numerical simulation studies illustrate that the GLR schemes are at times not as efficient as two families of ad-hoc schemes based on either the weighted likelihood ratios or the adaptive threshold method that adjust the effects of population sizes. To explain this, a further asymptotic optimality analysis is developed under a new asymptotic setting that is more suitable to our finite-sample numerical simulations. In addition, we extend our approaches to a general setting with arbitrary probability distributions, as well as to the continuous-time setting involving the multiplicative intensity models for Poisson processes, but further research is needed.

Original languageEnglish
Pages (from-to)597-624
Number of pages28
JournalStatistica Sinica
Volume21
Issue number2
DOIs
Publication statusPublished - 2011 Jan 1
Externally publishedYes

Fingerprint

Size Effect
Likelihood Ratio
Population Size
Asymptotic Optimality
Siméon Denis Poisson
Weighted Likelihood
Adaptive Threshold
Numerical Simulation
Poisson distribution
Poisson process
Surveillance
Continuous Time
Multiplicative
Probability Distribution
Simulation Study
Arbitrary
Likelihood ratio
Family
Asymptotic optimality
Numerical simulation

Keywords

  • Change-point
  • CUSUM
  • Generalized likelihood ratio
  • Monitoring
  • Poisson observations
  • Stopping time

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

Early detection of a change in poisson rate after accounting for population size effects. / Mei, Yajun; Han, Sung Won; Tsui, Kwok Leung.

In: Statistica Sinica, Vol. 21, No. 2, 01.01.2011, p. 597-624.

Research output: Contribution to journalArticle

@article{155de1dc0cb84bc9b77ac70901fb5ea0,
title = "Early detection of a change in poisson rate after accounting for population size effects",
abstract = "Motivated by applications in bio and syndromic surveillance, this article is concerned with the problem of detecting a change in the mean of Poisson distributions after taking into account the effects of population size. The family of generalized likelihood ratio (GLR) schemes is proposed and its asymptotic optimality properties are established under the classical asymptotic setting. However, numerical simulation studies illustrate that the GLR schemes are at times not as efficient as two families of ad-hoc schemes based on either the weighted likelihood ratios or the adaptive threshold method that adjust the effects of population sizes. To explain this, a further asymptotic optimality analysis is developed under a new asymptotic setting that is more suitable to our finite-sample numerical simulations. In addition, we extend our approaches to a general setting with arbitrary probability distributions, as well as to the continuous-time setting involving the multiplicative intensity models for Poisson processes, but further research is needed.",
keywords = "Change-point, CUSUM, Generalized likelihood ratio, Monitoring, Poisson observations, Stopping time",
author = "Yajun Mei and Han, {Sung Won} and Tsui, {Kwok Leung}",
year = "2011",
month = "1",
day = "1",
doi = "10.5705/ss.2011.027a",
language = "English",
volume = "21",
pages = "597--624",
journal = "Statistica Sinica",
issn = "1017-0405",
publisher = "Institute of Statistical Science",
number = "2",

}

TY - JOUR

T1 - Early detection of a change in poisson rate after accounting for population size effects

AU - Mei, Yajun

AU - Han, Sung Won

AU - Tsui, Kwok Leung

PY - 2011/1/1

Y1 - 2011/1/1

N2 - Motivated by applications in bio and syndromic surveillance, this article is concerned with the problem of detecting a change in the mean of Poisson distributions after taking into account the effects of population size. The family of generalized likelihood ratio (GLR) schemes is proposed and its asymptotic optimality properties are established under the classical asymptotic setting. However, numerical simulation studies illustrate that the GLR schemes are at times not as efficient as two families of ad-hoc schemes based on either the weighted likelihood ratios or the adaptive threshold method that adjust the effects of population sizes. To explain this, a further asymptotic optimality analysis is developed under a new asymptotic setting that is more suitable to our finite-sample numerical simulations. In addition, we extend our approaches to a general setting with arbitrary probability distributions, as well as to the continuous-time setting involving the multiplicative intensity models for Poisson processes, but further research is needed.

AB - Motivated by applications in bio and syndromic surveillance, this article is concerned with the problem of detecting a change in the mean of Poisson distributions after taking into account the effects of population size. The family of generalized likelihood ratio (GLR) schemes is proposed and its asymptotic optimality properties are established under the classical asymptotic setting. However, numerical simulation studies illustrate that the GLR schemes are at times not as efficient as two families of ad-hoc schemes based on either the weighted likelihood ratios or the adaptive threshold method that adjust the effects of population sizes. To explain this, a further asymptotic optimality analysis is developed under a new asymptotic setting that is more suitable to our finite-sample numerical simulations. In addition, we extend our approaches to a general setting with arbitrary probability distributions, as well as to the continuous-time setting involving the multiplicative intensity models for Poisson processes, but further research is needed.

KW - Change-point

KW - CUSUM

KW - Generalized likelihood ratio

KW - Monitoring

KW - Poisson observations

KW - Stopping time

UR - http://www.scopus.com/inward/record.url?scp=79952597933&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79952597933&partnerID=8YFLogxK

U2 - 10.5705/ss.2011.027a

DO - 10.5705/ss.2011.027a

M3 - Article

VL - 21

SP - 597

EP - 624

JO - Statistica Sinica

JF - Statistica Sinica

SN - 1017-0405

IS - 2

ER -