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In this paper, we consider capture-recapture experiments with heterogenouscatchability. In the setting we consider, the widespread Huggins-Alho estimatoris not very suitable and we introduce and study a new generalizedHorvitz-Thompson estimator. Our motivation is Respondent Driven Sampling (RDS),a prime example for such a setting where the capture probability is dependenton both the unknown population size as well as on an observable covariate, thenetwork degree of an individual, due to peer recruitment. After discussing thetheoretical properties of the new estimator, with full details given in theappendix, we evaluate it on various empirical and simulated data-sets, focusingon an RDS survey in a population in rural Uganda in which the population sizeis known a priori. The results thus obtained demonstrate that the adjustedestimator is less biased than the naive Lincoln-Petersen estimator.

Analysis of a capture-recapture estimator for the size of populations  with heterogenous catchability, and its evaluation on RDS data from rural  Uganda