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Biometrika 1991 78(2):399-407; doi:10.1093/biomet/78.2.399
© 1991 by Biometrika Trust
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Bayesian analyses for a multiple capture-recapture model

PHILIP J. SMITH

Center for Biostatistics and Epidemiology, Pennsylvania State University College of Medicine Hershey, Pennsylvania 17033, U.S.A.

In multiple capture-recapture surveys, the probability of capture can vary between sampling occasions. The model accounting for this variation is known as Mt. Bayes, empirical Bayes, and Bayes empirical Bayes solutions are given to the problems of interval estimation, decision making, and point estimation of the population size N. When the number of sampling occasions is small to moderate and the number of recaptured units observed on each sampling occasion is moderate, estimates obtained from empirical Bayes and Bayes empirical Bayes methods compare closely to Bayesian methods using a reference prior distribution for the capture probabilities. However, when the number of sampling occasions is large and the number of recaptured units observed on each sampling occasion is small, inferences obtained using different reference priors can differ considerably.

Key Words: Bayes empirical Bayes • Bayes estimator • Empirical Bayes • Highest posterior density region • Laplace approximation • Reference prior


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