A note on identifiability and maximum likelihood estimation for a heterogeneous capture-recapture model

This article discusses identifiability and maximum likelihood estimation for a closed population capture-recapture model with heterogeneity in capture probabilities. The model assumes that the individual capture probabilities arise from a discrete distribution over the interval Considering the complete likelihood, without applying any conditioning, we prove that identifiability holds under a restriction on the number of support points of the mixing distribution. Under this identifiability assumption, we present a simple closed-form iterative algorithm for maximum likelihood estimation. Interval estimation is carried by a bootstrap resampling procedure. The proposed methods are illustrated on a literature real data set and a simulation study is carried to assess the frequentist merits of different population size estimators.