Bayesian capture-recapture methods for error detection and estimation of population size: Heterogeneity and dependence

SUMMARY This paper considers estimation of the unknown size N of a population based on multiple capture-recapture samples. We extend the Bayesian multiple recapture model to accommodate possible heterogeneity and dependence among the samples and possible heterogeneity within the samples. In the dependent model, we show that posterior inference for N is independent of almost all the nuisance parameters. We develop a flexible Bayesian model for heterogeneity within samples and demonstrate how Gibbs sampling can be used to calculate the Bayesian estimator for N and other quantities of interest. The performance of the proposed estimators is evaluated by simulation under both correct and incorrect model specifications, and we illustrate our methods in two examples about software review and estimation of a cottontail rabbit population.