HARNESSING HETEROGENEITY: A PRECISION APPROACH TO ADVANCED POPULATION ESTIMATION

Population size estimation is a critical endeavor, often requiring innovative methods when counting every individual isn't feasible. Capture-recapture, initially developed for wildlife population estimation, offers a valuable approach. In the context of human populations, this method involves creating lists of individuals sampled from the population, providing the foundation for estimating the total population size. In scenarios where the sampling period is relatively short, it is reasonable to assume a closed population—devoid of births, deaths, immigration, or emigration—resulting in a constant population size throughout the study period. Parametric and nonparametric capture-recapture methods have been proposed, with the choice depending on how capture probabilities are specified for different individuals across various sample occasions. Models of the "time-only" type consider variations in capture probabilities over time, while "individual-only" models account for heterogeneity among individuals. In practice, it's often observed that capture probabilities fluctuate both across individuals and sampling occasions, necessitating models that embrace such complexity. Both parametric and nonparametric models exist in the latter category, addressing these variations. Non-parametric approaches, such as sample coverage, have been developed by Chao, Lee, and Jeng, while martingales approaches have been explored by Lloyd and Yip. Parametric models, like Sanathanan's mixed logit model, attempt to express capture probabilities as additive functions of subject and sampling effect parameters. However, caution is needed to ensure the model's consistency, as the introduction of subject parameters can challenge the estimation of population size.