Bayesian analysis of one–inflated models for population size estimation

The treatment of one inflation in estimating the size of an elusive population has received an increasing attention from researchers in recent years. The inflation of counts "one", that is the presence of an excess of "one"s, larger than compatible with any distributional assumption, deserves specific attention due to its effect on usual estimators for the population size. One-inflation may lead to overestimation of the usual estimators when not accounted for, while in general, when the observed counting model presents other sources of heterogeneity and this is ignored by the estimation procedure, it may produce severe underestimation in the population size. In this paper we propose a Bayesian approach that considers one inflation in count data models for capture recapture. An application to real data for the estimate of the size of some illegal populations is used to illustrate the proposed methodology.