Advanced Search
MyIDEAS: Login to save this paper or follow this series

Resolving some paradoxes and problems with Bayesian precise hypothesis testing

Contents:

Author Info

  • Jeffrey A. Mills

    ()

Registered author(s):

    Abstract

    Bayesian hypothesis testing of a precise null hypothesis suffers from a paradox discovered by Jeffreys (1939), Lindley (1957) and Bartlett (1957). This paradox appears to indicate that the usual priors, both proper and improper, are inappropriate for testing precise null hypotheses, and lead to difficulties in specifying prior distributions that could be widely accepted as appropriate in this situation. This paper considers an alternative hypothesis testing procedure and derives the Bayes factor for this procedure, which turns out to be B = p(?0 | x)/sup?[p(?i | x)], the ratio of the posterior density function evaluated at the value in the null hypothesis, ?0, and evaluated at its supremum. This leads to a Bayesian hypothesis testing procedure in which the Jeffreys-Lindley-Bartlett paradox does not occur. Further, under the proposed procedure, the prior does not depend on the hypotheses to be tested, there is no need to place non-zero mass on a particular point in a continuous distribution, and the same hypothesis testing procedure applies for all continuous and discrete distributions. Further, the resulting test procedure is robust to reasonable variations in the prior, uniformly most powerful and easy to interpret correctly in practice. Several examples are given to illustrate the use and performance of the test. A justification for the proposed procedure is given based on the argument that scientific inference always at least implicitly involves and requires precise alternative working hypotheses.

    Download Info

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
    File URL: http://www.artsci.uc.edu/collegedepts/economics/research/docs/Wppdf/2009-01.pdf
    Download Restriction: no

    Bibliographic Info

    Paper provided by University of Cincinnati, Department of Economics in its series University of Cincinnati, Economics Working Papers Series with number 2009-01.

    as in new window
    Length:
    Date of creation: 2009
    Date of revision: 2009
    Handle: RePEc:cin:ucecwp:2009-01

    Contact details of provider:
    Postal: Cincinnati, OH 45221-0371
    Phone: (513) 556-2670
    Fax: (513) 556-2669
    Email:
    Web page: http://www.business.uc.edu/economics/
    More information through EDIRC

    Related research

    Keywords:

    This paper has been announced in the following NEP Reports:

    References

    No references listed on IDEAS
    You can help add them by filling out this form.

    Citations

    Lists

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    Statistics

    Access and download statistics

    Corrections

    When requesting a correction, please mention this item's handle: RePEc:cin:ucecwp:2009-01. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Sourushe Zandvakili).

    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 references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.

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