IDEAS home Printed from https://ideas.repec.org/a/ris/apltrx/0199.html
   My bibliography  Save this article

A new approach to construction of objective priors: Hellinger information

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://pe.cemi.rssi.ru/pe_2012_4_124-137.pdf
    File Function: Full text
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Sareen, Samita, 2003. "Reference Bayesian inference in nonregular models," Journal of Econometrics, Elsevier, vol. 113(2), pages 265-288, April.
    2. Malay Ghosh & Victor Mergel & Ruitao Liu, 2011. "A general divergence criterion for prior selection," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(1), pages 43-58, February.
    3. Wang, Haiying & Sun, Dongchu, 2012. "Objective Bayesian analysis for a truncated model," Statistics & Probability Letters, Elsevier, vol. 82(12), pages 2125-2135.
    4. Holger Scholl, 1998. "Shannon optimal priors on independent identically distributed statistical experiments converge weakly to Jeffreys' prior," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 7(1), pages 75-94, June.
    5. 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.
    6. Hashimoto, Shintaro, 2021. "Predictive probability matching priors for a certain non-regular model," Statistics & Probability Letters, Elsevier, vol. 174(C).
    7. Carmen Fernández & Mark Steel, 1998. "Reference priors for non-Normal two-sample problems," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 7(1), pages 179-205, June.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ris:apltrx:0199. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Anatoly Peresetsky (email available below). General contact details of provider: http://appliedeconometrics.cemi.rssi.ru/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.