Estimating the size of a population from three incomplete lists: a Bayesian approach

We consider the problem of estimating the size N of a closed population from three incomplete lists. Estimation of N is based on capture-recapture type models. Our approach uses graphical models to deal with some possible dependences between the lists. Our parametriza-tion involves marginal and conditional capture probabilities rather than clique probabilities, which facilitates the incorporation of the prior information available on capture. We link both parametriza-tions and we show that assuming an hyper-Dirichlet distribution for the clique parameter of any sub-model boils down to assume that some capture probabilities follow independently beta distributions (and conversely). Prior information on capture is incorporated via a descending procedure which guarantees that the prior distributions are, in a certain sense, compatible across the different models. As far as N is concerned, an improper prior is usually adopted for N ; as a result, the posterior distribution of N may not exist. We provide a necessary and sufficient condition for it exists, when inference is based on a Bayesian model averaging