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.
Highlights
The capture-recapture sampling methods were originally designed to estimate wildlife populations
Comparing the proposed constraint with the constant ratio constraint, which presumes that p j1 = θ p j0, we found that the proposed constant odds ratio assumption is more convenient and practical because there is no need for another layer of constraint on the constant ratio to ensure that neither initial capture nor recapture probabilities exceed 1.0
We propose a Bayesian hierarchical approach to estimate the population size of model Mtb with a new relationship between recapture probability and initial capture probability base on odds
Summary
The capture-recapture sampling methods were originally designed to estimate wildlife populations. We assume that the odds ratio of recapture probability and initial probability is a constant, as was initially proposed by Wang [22] in her doctoral dissertation; hierarchical prior distributions with vague information are assigned to the unknown parameters after logistic transformation; and Markov chain Monte Carlo (MCMC) methods are used to implement the Bayesian computation. Otis et al [5] provides an interesting data set on the deer mice study that was used by Chao et al [2] Altogether, there are 110 distinct mice caught out of 283 captures in 5 consecutive days This same data set is used here to illustrate the proposed Bayesian approach of population estimation.
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