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A new approach to construction of objective priors: Hellinger information

Author

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  • Shemyakin, Arkady

    (University of St. Thomas, St. Paul, USA)

Abstract

Non-informative priors play crucial role in objective Bayesian analysis. Most popular ways of construction of non-informative priors are provided by the Jeffreys rule, matching probability principle, and reference prior approach. An alternative construction of non-informative priors is suggested based on the concept of Hellinger information related to Hellinger distance. Under certain regularity conditions, limit behavior of the Hellinger distance as the difference in the parameter values goes down to zero is closely related to Fisher information. In this case our approach generalizes the Jeffreys rule. However, what is more interesting, Hellinger information can be also used to describe information properties of the parametric set in non-regular situations, when Fisher information does not exist. Non-informative priors based on Hellinger information are studied for the non-regular class of distributions defined by Ghosal and Samanta and for some interesting examples outside of this class.

Suggested Citation

  • 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.
    • Handle: RePEc:ris:apltrx:0199
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    References listed on IDEAS

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    1. Ghosal Subhashis & Samanta Tapas, 1997. "Expansion Of Bayes Risk For Entropy Loss And Reference Prior In Nonregular Cases," Statistics & Risk Modeling, De Gruyter, vol. 15(2), pages 129-140, February.
    2. S. Ghosal, 1997. "Reference priors in multiparameter nonregular cases," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 6(1), pages 159-186, June.
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    Cited by:

    1. 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.
    2. 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

    non-informative priors; reference priors; Jeffreys’ rule; Hellinger distance; Hellinger information.;
    All these keywords.

    JEL classification:

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

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