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Normalized Power Prior Bayesian Analysis


  • Keying Ye

    (The University of Texas at San Antonio)

  • Yuyan Duan

    (Bristol-Myers Squibb, USA)


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, "undated". "Normalized Power Prior Bayesian Analysis," Working Papers 0058, College of Business, University of Texas at San Antonio.
  • Handle: RePEc:tsa:wpaper:0058

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    References listed on IDEAS

    1. Chaudhuri, Sarbajit, 2007. "Foreign capital, welfare and urban unemployment in the presence of agricultural dualism," Japan and the World Economy, Elsevier, vol. 19(2), pages 149-165, March.
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    4. Harris, John R & Todaro, Michael P, 1970. "Migration, Unemployment & Development: A Two-Sector Analysis," American Economic Review, American Economic Association, vol. 60(1), pages 126-142, March.
    5. Wood, Adrian, 1997. "Openness and Wage Inequality in Developing Countries: The Latin American Challenge to East Asian Conventional Wisdom," World Bank Economic Review, World Bank Group, vol. 11(1), pages 33-57, January.
    6. Corden, W M & Findlay, Ronald, 1975. "Urban Unemployment, Intersectoral Capital Mobility and Development Policy," Economica, London School of Economics and Political Science, vol. 42(165), pages 59-78, February.
    7. Sugata Marjit & Hamid Beladi & Avik Chakrabarti, 2004. "Trade and Wage Inequality in Developing Countries," Economic Inquiry, Western Economic Association International, vol. 42(2), pages 295-303, April.
    8. Chaudhuri, Sarbajit & Yabuuchi, Shigemi, 2007. "Economic liberalization and wage inequality in the presence of labour market imperfection," International Review of Economics & Finance, Elsevier, vol. 16(4), pages 592-603.
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    More about this item


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

    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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