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

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.

受生物和症状监测应用的推动，本文关注在考虑人口规模影响后检测泊松分布均值变化的问题。提出了广义似然比（GLR）方案族，并在经典渐近设定下确立了其渐近最优性性质。然而，数值模拟研究表明，GLR方案有时不如基于加权似然比或调整人口规模影响的自适应阈值方法的两类特设方案有效。为了解释这一点，在一个更适合我们有限样本数值模拟的新渐近设定下进行了进一步的渐近最优性分析。此外，我们将我们的方法扩展到具有任意概率分布的一般设定，以及涉及泊松过程的乘性强度模型的连续时间设定，但还需要进一步的研究。