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\noindent Statistica Sinica {\bf 13}(2003), 477-494
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\centerline{\large\bf BAYES ESTIMATION OF POPULATION SIZE FROM}
\vspace{2pt}
\centerline{\large\bf CAPTURE-RECAPTURE MODELS WITH TIME VARIATION}
\vspace{2pt}
\centerline{\large\bf AND BEHAVIOR RESPONSE}
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\centerline{Shen-Ming Lee$^1$, Wen-Han Hwang$^1$ and Li-Hui Huang$^2$}
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\centerline{\it $^1$Feng-Chia University
and $^2$the Overseas Chinese Institute of Technology}
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\begin{quotation}
\noindent {\it Abstract:}
This paper considers size estimation of a closed population using
capture-recapture models when the capture probabilities vary with
time (or trapping occasion) and behavior response. A unified approach via the
Bayesian framework is proposed to make inferences about the population size for
four specific models. Based on data augmentation considerations, we show how
Gibbs sampling associated with an adaptive rejection sampling technique can be
applied to calculate Bayes estimates in our setting. The prior distributions
that we have chosen are all noninformative except as regards the behavior
response parameter. A simulation study investigates the performance of the
proposed procedure and compares it with the maximum likelihood estimates
derived by Chao, Chu and Hsu (2000). The estimates are also applied to capture
data of deer mice discussed in the literature. The results show that Gibbs
sampling provides a useful inference procedure for estimating population size,
particularly when the capture probability is high or the amount of recapture
information is sufficient.\par
\vspace{9pt}
\noindent {\it Key words and phrases:}
Bayes estimation, behavior response, capture-recapture model, Gibbs sampling,
Markov chain Monte Carlo method, population size, time variation.\par
\end{quotation}
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