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Bayesian analysis of a multiple-recapture model. (English) Zbl 0937.62573
Summary: In the Bayesian analysis of a multiple-recapture census, different diffuse prior distributions can lead to markedly different inferences about the population size $N$. Through consideration of the Fisher information matrix it is shown that the number of captures in each sample typically provides little information about $N$. This suggests that if there is no prior information about capture probabilities, then knowledge of just the sample sizes and not the number of recaptures should leave the distribution of $N$ unchanged. A prior model that has this property is identified and the posterior distribution is examined. In particular, asymptotic estimates of the posterior mean and variance are derived. Differences between Bayesian and classical point and interval estimators are illustrated through examples.
##### MSC:
 62F15 Bayesian inference 62P10 Applications of statistics to biology and medical sciences
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