Bayesian one-inflated models for population size estimation

We present a Bayesian approach to a class of counting models for capture–recapture in presence of “one–inflation”. One–inflation has received has received an increasing attention in capture–recapture literature in recent years, particularly in estimating the size of illegal populations. The phenomenon consists in the observation of an excess of individuals cap- tured exactly once. If we do not explicitly model this aspect in the counting distribution, we can overestimate the population size. Bayesian model selection and the role of prior distributions are discussed. Applications to real data for the estimate of the size of some illegal populations are used to illustrate the proposed methodology.