Semi-parametric Bayesian approach for population size estimation modelling the excess of singletons

The phenomenon of one-inflation has received increasing attention in the recent literature on capture– recapture analysis. When data consist of frequencies of number of captures, the phenomenon manifests as an excess of units captured exactly once. We distinguish two possible causes for modelling the excess of singletons, namely, the erroneous inclusion of out-of-scope units, and a behavioural effect preventing subsequent captures after the first one. Accordingly, we propose two families of semi-parametric one- inflated models to estimate the number of uncaptured units. We consider a Bayesian approach by fitting a Dirichlet process mixture model as the base model, and extend this class to include one-inflation. The proposed base model and its two one-inflated counterparts are used to estimate the number of criminals involved in prostitution exploitation activities in Italy. We further assess the performance of the proposed models on three datasets available in the literature, as well as on simulated data