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Biometrika 1973 60(1):141-153; doi:10.1093/biomet/60.1.141
© 1973 by Biometrika Trust
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Sequential recapture

P. R. FREEMAN

University College London

The second stage of a capture-recapture experiment, in which individuals are sampled randomly from a finite population of size N, R of whom are known to be marked in some way, is considered as a process of a sequential sampling. Using a beta-Pascal prior for N, constant cost of sampling and quadratic loss, optimal stopping boundaries are derived such that the prior expectation of the total cost of sampling plus loss due to error of estimation is minimized. These are compared with the simple stopping rules of using a fixed sample size or sampling until a fixed number of marked or unmarked items have been observed. Efficiencies of between 40% and 100% relative to the optimum are obtained. When observations are expensive, using a fixed number of marked items is found to be almost fully efficient.

Key Words: Preposterior analysis • Dynamic programming • Bayesian inference • Sequential experiments • Population size estimation • Capture-recapture experiments • Decision theory approach to sampling • Tagging


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