基于再捕获概率比的种群规模估计
Population size estimation based upon ratios of recapture probabilities
摘要：
在生命科学和社会科学的许多领域，估计难以捉摸的目标人群的规模是一个突出的兴趣。我们的目的是提供一个有效的和可行的方法来估计未知的人口规模，给定的频率分布的计数重复识别的单位的人口的利益。这个计数变量必须是零截断的，因为从未被识别的单元不在样本中。我们考虑几种应用：临床医学，其中兴趣在于估计诊断程序忽略的腺瘤性息肉患者;药物使用者研究，其中兴趣在于估计未确定的隐藏药物使用者的数量;英国瘙痒症的兽医监测，其中兴趣在于估计隐藏的瘙痒症数量;昆虫学和微生物生态学，其中感兴趣的是估计未观察到的生物物种的数量。在所有这些例子中，简单的模型，如齐次泊松是不合适的，因为他们没有考虑到目前和潜在的异质性。Poisson-Gamma（负二项分布）模型提供了一种灵活的替代方案，并且通常会导致拟合良好的模型。它有着悠久的历史，最近被用于Chao-Bunge估计的发展。在这里，我们使用泊松-伽马模型的一个不同的属性：如果我们考虑相邻泊松-伽马概率的比率，那么这些比率与重复识别的计数线性相关。
英文摘要：
Estimating the size of an elusive target population is of prominent interest in many areas in the life and social sciences. Our aim is to provide an efficient and workable method to estimate the unknown population size, given the frequency distribution of counts of repeated identifications of units of the population of interest. This counting variable is necessarily zero-truncated, since units that have never been identified are not in the sample. We consider several applications: clinical medicine, where interest is in estimating patients with adenomatous polyps which have been overlooked by the diagnostic procedure; drug user studies, where interest is in estimating the number of hidden drug users which are not identified; veterinary surveillance of scrapie in the UK, where interest is in estimating the hidden amount of scrapie; and entomology and microbial ecology, where interest is in estimating the number of unobserved species of organisms. In all these examples, simple models such as the homogenous Poisson are not appropriate since they do not account for present and latent heterogeneity. The Poisson-Gamma (negative binomial) model provides a flexible alternative and often leads to well-fitting models. It has a long history and was recently used in the development of the Chao-Bunge estimator. Here we use a different property of the Poisson-Gamma model: if we consider ratios of neighboring Poisson-Gamma probabilities, then these are linearly related to the counts of repeated identifications.
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