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


  • Slutskin, Lev

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


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, Publishing House "SINERGIA PRESS", vol. 40(4), pages 129-141.
  • Handle: RePEc:ris:apltrx:0281

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    References listed on IDEAS

    1. Shemyakin, Arkady, 2012. "A new approach to construction of objective priors: Hellinger information," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 28(4), pages 124-137.
    2. Aivazian, Sergei, 2008. "Bayesian Methods in Econometrics," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 9(1), pages 93-130.
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    1. repec:nea:journl:y:2017:i:36:p:12-30 is not listed on IDEAS

    More about this item


    prior probability distributions; Bayesian methodology; Kullback–Leibler divergence; regression analysis;

    JEL classification:

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


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