Bayesian analysis of one‐inflated models for elusive population size estimation

The identification and treatment of “one‐inflation” in estimating the size of an elusive population has received increasing attention in capture–recapture literature in recent years. The phenomenon occurs when the number of units captured exactly once clearly exceeds the expectation under a baseline count distribution. Ignoring one‐inflation has serious consequences for estimation of the population size, which can be drastically overestimated. In this paper we propose a Bayesian approach for Poisson, geometric, and negative binomial one‐inflated count distributions. Posterior inference for population size will be obtained applying a Gibbs sampler approach. We also provide a Bayesian approach to model selection. We illustrate the proposed methodology with simulated and real data and propose a new application in official statistics to estimate the number of people implicated in the exploitation of prostitution in Italy.