Estimating the size of a closed population by modeling latent and observed heterogeneity
Abstract
The paper describes a new class of capture-recapture models for closed populations when individual covariates are available. The novelty consists in combining a latent class model for the distribution of the capture history, where the class weights and the conditional distributions given the latent may depend on covariates, with a model for the marginal distribution of the available covariates as in Liu2017. In addition, any general form of serial dependence is allowed when modeling capture histories conditionally on the latent and covariates. A Fisher-scoring algorithm for maximum likelihood estimation is proposed, and the Implicit Function Theorem is used to show that the mapping between the marginal distribution of the observed covariates and the probabilities of being never captured is one-to-one. Asymptotic results are outlined, and a procedure for constructing likelihood based confidence intervals for the population size is presented. Two examples based on real data are used to illustrate the proposed approach
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.