Bayesian Estimation of Population Size via Capture-Recapture Model with Time Variation and Behavioral Response

Xiaoyin Wang^1*, Zhuoqiong He², Dongchu Sun²

¹Department of Mathematics, Towson Univeristy, Towson, MD, USA.
¹Department of Statistics, University of Missouri-Columbia, Columbia, MO, USA.
²Department of Statistics, University of Missouri-Columbia, Columbia, MO, USA.

DOI: 10.4236/oje.2015.51001                

Abstract

We consider the problem of population estimation using capture-recapture data, where capture probabilities can vary between sampling occasions and behavioural responses. The original model is not identifiable without further restrictions. The novelty of this article is to expand the current research practice by developing a hierarchical Bayesian approach with the assumption that the odds of recapture bears a constant relationship to the odds of initial capture. A real-data example of deer mice population is given to illustrate the proposed method. Three simulation studies are developed to inspect the performance of the proposed Bayesian estimates. Compared with the maximum likelihood estimates discussed in Chao et al. (2000), the hierarchical Bayesian estimate provides reasonably better population estimation with less mean square error; moreover, it is sturdy to underline relationship between the initial and re-capture probabilities. The sensitivity study shows that the proposed Bayesian approach is robust to the choice of hyper-parameters. The third simulation study reveals that both relative bias and relative RMSE approach zero as population size increases. A R-package is developed and used in both data example and simulation.

Keywords

Bayes Estimation, Behavioural Response, Capture-Recapture Model, Gibbs Sampling, Hierarchical Prior, Population Estimation, Time Variation

Conflicts of Interest

The authors declare no conflicts of interest.

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