Bayesian analysis of a multiple-recapture model |
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Authors: | Paul H. Garthwaite Keming Yu Peter B. Hope |
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Affiliation: | 1. Department of Mathematical Sciences , University of Aberdeen , Aberdeen, AB9 2TY, United Kingdom;2. Department of Statistics , The Open University , Milton Keynes, MK7 6AA, United Kingdom;3. Mathematical Statistics and Operational Research , University of Exeter , Exeter, EX4 4QE, United Kingdom |
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Abstract: | 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 Nunchanged. 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. |
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Keywords: | Bayesian inference mark-recapture Fisher information noninformative prior distributions |
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