A beta-binomial model for estimating the size of a heterogeneous population

This paper compares the properties of various estimators for a beta-binomial model for estimating the size of a heterogeneous population. It is found that maximum likelihood and conditional maximum likelihood estimators perform well for a large population with a large capture proportion. The jackknife and the sample coverage estimators are biased for low capture probabilities. The performance of the martingale estimator is satisfactory, but it requires full capture histories. The Gibbs sampler and Metropolis-Hastings algorithm provide reasonable posterior estimates for informative priors.