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Normalized Power Prior Bayesian Analysis

Author

Listed:
  • Keying Ye

    (The University of Texas at San Antonio)

  • Yuyan Duan

    (Bristol-Myers Squibb, USA)

Abstract

The elicitation of power prior distributions is based on the availability of historical data, and is realized by raising the likelihood function of the historical data to a fractional power. However, an arbitrary positive constant before the like- lihood function of the historical data could change the inferential results when one uses the original power prior. This raises a question that which likelihood function should be used, one from raw data, or one from a su±cient-statistics. We propose a normalized power prior that can better utilize the power parameter in quantifying the heterogeneity between current and historical data. Furthermore, when the power parameter is random, the optimality of the normalized power priors is shown in the sense of maximizing Shannon's mutual information. Some comparisons between the original and the normalized power prior approaches are made and a water-quality monitoring data is used to show that the normalized power prior is more sensible.

Suggested Citation

  • Keying Ye & Yuyan Duan, 2008. "Normalized Power Prior Bayesian Analysis," Working Papers 0058, College of Business, University of Texas at San Antonio.
  • Handle: RePEc:tsa:wpaper:00103mss
    as

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    File URL: http://interim.business.utsa.edu/wps/MSS/0058MSS-432-2008.pdf
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    References listed on IDEAS

    as
    1. Ibrahim J.G. & Chen M-H. & Sinha D., 2003. "On Optimality Properties of the Power Prior," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 204-213, January.
    2. Zellner, A., 1988. "Optimal Information-Processing And Bayes' Theorem," Papers m8803, Southern California - Department of Economics.
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    More about this item

    Keywords

    Bayesian analysis; historical data; normalized power prior; power prior; prior elicitation; Shannon's mutual information.;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

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