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Objective Priors for Discrete Parameter Spaces

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

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.

Suggested Citation

  • James O. Berger & Jose M. Bernardo & Dongchu Sun, 2012. "Objective Priors for Discrete Parameter Spaces," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(498), pages 636-648, June.
  • Handle: RePEc:taf:jnlasa:v:107:y:2012:i:498:p:636-648
    DOI: 10.1080/01621459.2012.682538
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    File URL: http://hdl.handle.net/10.1080/01621459.2012.682538
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    Cited by:

    1. Crane, Harry, 2017. "A hidden Markov model for latent temporal clustering with application to ideological alignment in the U.S. Supreme Court," Computational Statistics & Data Analysis, Elsevier, vol. 110(C), pages 19-36.
    2. Chang Xu & Dongchu Sun & Chong He, 2014. "Objective Bayesian analysis for a capture–recapture model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(2), pages 245-278, April.

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