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

Abstract

Motivated by applications in bio and syndromic surveillance, this arti- cle 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 opti- mality 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.