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On the robustness of the predictive distribution for sampling from finite populations

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  • Bose, Sudip
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    Abstract

    Let [pi]N be the prior distribution on the number of items belonging to each of K([greater-or-equal, slanted]2) categories in a population of size N. It is shown that the marginal probability distribution of an ordered sample of items selected without replacement does not depend on N, provided the distributions {[pi]N} satisfy a simple relationship. This relationship holds for prior distributions in the multivariate Pólya-Eggenberger family. This distribution is also the same as that of an iid sample with the limit of [pi]N as prior. Thus one has non-dependence of the predictive distribution on the population size and one can quantify the sensitivity of the predictive to uncertainty about the prior.

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 69 (2004)
    Issue (Month): 1 (August)
    Pages: 21-27

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    Handle: RePEc:eee:stapro:v:69:y:2004:i:1:p:21-27

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    Related research

    Keywords: Finite population Hypergeometric Limit distribution Multinomial Multivariate Multivariate hypergeometric Polya urn model Polya-Eggenberger distributions Predictive distribution Sampling distribution Sampling without replacement;

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    1. Bose, Sudip & Kedem, Benjamin, 1996. "Non-dependence of the predictive distribution on the population size," Statistics & Probability Letters, Elsevier, vol. 27(1), pages 43-47, March.
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