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Second-order matching prior family parametrized by sample size and matching probability

Author

Listed:
  • Toyoto Tanaka

    (Tokio Marine & Nichido Fire Insurance Co., Ltd.)

  • Yoshihiro Hirose

    (Hokkaido University)

  • Fumiyasu Komaki

    (The University of Tokyo
    RIKEN Center for Brain Science)

Abstract

We propose a family of priors that satisfies the second-order probability matching property. The posterior quantile of a probability matching prior is exactly or approximately equal to the frequentist one. Most models lack an exact matching prior. If all quantiles of a prior’s posterior converge to the frequentist ones up to $$o(n^{-1/2})$$ o ( n - 1 / 2 ) or $$o(n^{-1})$$ o ( n - 1 ) as the sample size n increases, the prior is called a first-order probability matching prior and a second-order probability matching prior, respectively. Although a second-order matching prior does not necessarily exist, a first-order matching prior always exists. We introduce a class of priors that depend on the sample size and matching probability. We derive the condition under which the family satisfies the second-order probability matching property even when a second-order probability matching prior does not exist. The superiority of the proposed priors is illustrated in several numerical experiments.

Suggested Citation

  • Toyoto Tanaka & Yoshihiro Hirose & Fumiyasu Komaki, 2020. "Second-order matching prior family parametrized by sample size and matching probability," Statistical Papers, Springer, vol. 61(4), pages 1701-1717, August.
    • Handle: RePEc:spr:stpapr:v:61:y:2020:i:4:d:10.1007_s00362-018-1001-5
    DOI: 10.1007/s00362-018-1001-5
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    References listed on IDEAS

    as
    1. Dal Kim & Sang Kang & Woo Lee, 2006. "Noninformative priors for linear combinations of the normal means," Statistical Papers, Springer, vol. 47(2), pages 249-262, March.
    2. Ventura, Laura & Cabras, Stefano & Racugno, Walter, 2009. "Prior Distributions From Pseudo-Likelihoods in the Presence of Nuisance Parameters," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 768-774.
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