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Objective Priors for Discrete Parameter Spaces

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  • James O. Berger
  • Jose M. Bernardo
  • Dongchu Sun
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    Abstract

    This article considers the development of objective prior distributions for discrete parameter spaces. Formal approaches to such development—such as the reference prior approach—often result in a constant prior for a discrete parameter, which is questionable for problems that exhibit certain types of structure. To take advantage of structure, this article proposes embedding the original problem in a continuous problem that preserves the structure, and then using standard reference prior theory to determine the appropriate objective prior. Four different possibilities for this embedding are explored, and applied to a population-size model, the hypergeometric distribution, the multivariate hypergeometric distribution, the binomial-beta distribution, and the binomial distribution. The recommended objective priors for the first, third, and fourth problems are new.

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    File URL: http://hdl.handle.net/10.1080/01621459.2012.682538
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    Bibliographic Info

    Article provided by Taylor & Francis Journals in its journal Journal of the American Statistical Association.

    Volume (Year): 107 (2012)
    Issue (Month): 498 (June)
    Pages: 636-648

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    Handle: RePEc:taf:jnlasa:v:107:y:2012:i:498:p:636-648

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    Cited by:
    1. Chang Xu & Dongchu Sun & Chong He, 2014. "Objective Bayesian analysis for a capture–recapture model," Annals of the Institute of Statistical Mathematics, Springer, vol. 66(2), pages 245-278, April.

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