A note on the difficulties associated with the analysis of capture-recapture experiments with heterogeneous capture probabilities

A variety of methods have been proposed to estimate the size of a closed population non-parametrically using capture-recapture data when the capture probabilities are heterogeneous. None of the methods have been proven to be unbiased in all circumstances and in simulations they tend to perform well in some cases but poorly in others. Here we examine random effects models and conclude that if the capture probabilities are heterogeneous then without the imposition of conditions the population size is not identifiable. A necessary condition for identifiability is given, with the derivation of a sufficient condition remaining an open problem.

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