A new Bayesian method for nonparametric capture-recapture models in presence of heterogeneity

Capture-recapture models are among the oldest and most popular methods for estimating how large a wild animal population is, though the usefulness of these models goes beyond zoological matters having been applied, among others, to epidemiological studies, socio-demographic investigations and even to software reliability problems. The intrinsic heterogeneity of individuals has been recognized as a potential source of bias in the estimation procedures. To account for this heterogeneity in the model a hierarchical structure has been proposed where the probabilities that each animal is caught in a single occasion are modeled as i. i. d. draws from a common unknown distribution F. is general agreement since the work by Burnham and Overton (1978) that modelling F with a simple parametric curve may lead to unsatisfactory results. Hence other nonparametric solutions have been developed (Smith and van Belle 1984, Chao 1989, Norris and Pollock 1996). Recently Basu (1998) proposed a Bayesian nonparametric solution that uses a Dirichlet process prior for F. Here we propose an alternative Bayesian approach that relies on a different parameterization which still maintains no assumptions on the shape of F but drives the problem back to a finite-dimensional setting. Our approach avoids some identifiablity problems related to such recapture models and, at the same time, allows for a formal Bayesian default analysis. Results of analyses conducted on computer simulations as well as on on-field experiments and other real data sets show good performance of this method in comparison with some of the estimators commonly used in the classical capture-recapture literature.