EARLY DETECTION OF A CHANGE IN POISSON RATE AFTER ACCOUNTING FOR POPULATION SIZE EFFECTS

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 as...

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Bibliographic Details
Published in:Statistica Sinica 2011-04, Vol.21 (2), p.597-624
Main Authors: Mei, Yajun, Han, Sung Won, Tsui, Kwok-Leung
Format: Article
Language:English
Subjects:
False alarms
Mathematical constants
Modeling
Performance metrics
Population estimates
Population size
Statistics
Stopping distances
Surveillance
Thyroid cancer
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Summary: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.
ISSN:1017-0405
1996-8507
DOI:10.5705/ss.2011.027a