Statistica Sinica 13(2003), 477-494

BAYES ESTIMATION OF POPULATION SIZE FROM

CAPTURE-RECAPTURE MODELS WITH TIME VARIATION

AND BEHAVIOR RESPONSE

Shen-Ming Lee$^1$, Wen-Han Hwang$^1$ and Li-Hui Huang$^2$

$^1$Feng-Chia University and $^2$the Overseas Chinese Institute of Technology

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.

Key words and phrases: Bayes estimation, behavior response, capture-recapture model, Gibbs sampling, Markov chain Monte Carlo method, population size, time variation.