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Estimating the size of an elusive target population is of prominent interestin many areas in the life and social sciences. Our aim is to provide anefficient and workable method to estimate the unknown population size, giventhe frequency distribution of counts of repeated identifications of units ofthe population of interest. This counting variable is necessarilyzero-truncated, since units that have never been identified are not in thesample. We consider several applications: clinical medicine, where interest isin estimating patients with adenomatous polyps which have been overlooked bythe diagnostic procedure; drug user studies, where interest is in estimatingthe number of hidden drug users which are not identified; veterinarysurveillance of scrapie in the UK, where interest is in estimating the hiddenamount of scrapie; and entomology and microbial ecology, where interest is inestimating the number of unobserved species of organisms. In all theseexamples, simple models such as the homogenous Poisson are not appropriatesince they do not account for present and latent heterogeneity. ThePoisson-Gamma (negative binomial) model provides a flexible alternative andoften leads to well-fitting models. It has a long history and was recently usedin the development of the Chao-Bunge estimator. Here we use a differentproperty of the Poisson-Gamma model: if we consider ratios of neighboringPoisson-Gamma probabilities, then these are linearly related to the counts ofrepeated identifications.

Population size estimation based upon ratios of recapture probabilities