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On limiting posterior distributions

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Abstract

In this article, a theorem is developed on limiting posterior distributions of asymptotically pivotal quantities. The theorem, called the posterior limit theorem (PLT), provides a set of sufficient conditions for an asymptotically pivotal quantity to have a limiting posterior distribution coincident with its limiting sampling distribution. It can be applied to the real data analysis without any specified functional form of likelihood. We present various illustrative applications of our theorem.

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Authors and Affiliations

  1. Department of Statistics, Dankook University, Korea

    Hyungtae Hwang

  2. Department of Statisties, Ewha Womans University, Korea

    Beongsoo So

  3. Department of Statistics, Seoul National University, Korea

    Yongdai Kim

Authors
  1. Hyungtae Hwang
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  2. Beongsoo So
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  3. Yongdai Kim
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Corresponding author

Correspondence to Yongdai Kim.

Additional information

The second and third authors are supported in part by KOSEF through the Statistical Research Center for Complex Systems at Seoul National University

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Hwang, H., So, B. & Kim, Y. On limiting posterior distributions. TEST 14, 567–580 (2005). https://doi.org/10.1007/BF02595418

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  • DOI: https://doi.org/10.1007/BF02595418

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