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Definition of a prior distribution in Bayesian analysis by minimizing Kullback–Leibler divergence under data availability

Author

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  • Slutskin, Lev

    (Institute of Economics of Russian Academy of Sciences (IERAS), Moscow, Russian Federation)

Abstract

A formal rule for selection of a prior probability distribution based on minimization of the Kullback–Leibler divergence, when data obtained from previous observations are available, is suggested. Contrary to a usual requirement in empirical Bayesian analysis, parameters for different observations are not assumed to be independent. In the case when both observations and parameters are normal, the procedure is equivalent to the ML–II approach. However regression coefficients obtained by minimization of the Kullback–Leibler divergence are different from the ML–II estimates. Finally, it is shown that in the case of normal distributions Kullback–Leibler divergence achieves asymptotically its only minimum at the true prior distribution

Suggested Citation

  • Slutskin, Lev, 2015. "Definition of a prior distribution in Bayesian analysis by minimizing Kullback–Leibler divergence under data availability," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 40(4), pages 129-141.
    • Handle: RePEc:ris:apltrx:0281
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    References listed on IDEAS

    as
    1. Aivazian, Sergei, 2008. "Bayesian Methods in Econometrics," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 9(1), pages 93-130.
    2. Shemyakin, Arkady, 2012. "A new approach to construction of objective priors: Hellinger information," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 28(4), pages 124-137.
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    Cited by:

    1. Slutskin, L., 2017. "Graphical Statistical Methods for Studying Causal Effects. Bayesian Networks," Journal of the New Economic Association, New Economic Association, vol. 36(4), pages 12-30.

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    More about this item

    Keywords

    prior probability distributions; Bayesian methodology; Kullback–Leibler divergence; regression analysis;
    All these keywords.

    JEL classification:

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

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