Forming Post-strata Via Bayesian Treed Capture-Recapture Models

For the problem of dual system estimation, we propose a treed Capture Recapture Model (CRM) to account for heterogeneity of capture probabilities where individual auxiliary information is available. A treed CRM uses a binary tree to partition the covariate space into “homogeneous” regions, within each of which the capture response can be described adequately by a simple model that assumes equal catchability. In this paper, a Bayesian approach is presented to fit and search promising treed CRMs. We compare the performance of estimators based on this approach to those of alternative models in three examples. The attractive features of the proposed models include reduction of correlation bias, robustness, practical flexibility as well as simplicity and interpretability. In addition, they provide a systematic and effective way to form poststrata for the Sekar and Deming estimator of population size.