Forming post-strata via Bayesian treed capture-recapture models
1 Department of Statistical Science, Southern Methodist University, 3225 Daniel Avenue, Dallas, Texas 75275-0332, U.S.A. swang{at}mail.smu.edu, 2 Department of Applied Statistics, Yonsei University, ShinChon Dong 134, SeoDaeMun Gu, Seoul, 120-749, Korea johanlim{at}yonsei.ac.kr, 3 Department of Statistical Science, Southern Methodist University, 3225 Daniel Avenue, Dallas, Texas 75275-0332, U.S.A. slstokes{at}mail.smu.edu
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Abstract |
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For the problem of dual system estimation, we propose a Bayesian treed capture-recapture model to account for heterogeneity of capture probabilities where individual auxiliary information is available. The model 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. The attractive features of the proposed model include reduction of correlation bias, robustness and practical flexibility as well as simplicity and interpretability. In addition, it provides a systematic and effective way of forming post-strata for the Sekar–Deming estimator of population size. We compare the performance of estimators based on this model to those of alternative estimators in three scenarios.
Key Words: Bayesian model selection; Binary tree; Census undercount estimation; Dual system estimation; Heterogeneity; Parallel tempering.
Received September 2004. Revised March 2006.