Exceptions to Bartlett’s Paradox
A sensible Bayesian model selection or comparison strategy implies selecting the model with the highest posterior probability. While some improper priors have attractive properties such as, eg, lower frequentist risk, it is generally claimed that Bartlett’s paradox implies that using improper priors for the parameters in alternative models results in Bayes factors that are not well defined, thus preventing model comparison in this case. In this paper we demonstrate this latter result is not generally true and so expand the class of priors that may be used for computing posterior odds to include some improper priors. We give a new representation of the issue of undefined Bayes factors and, from this representation, develop classes of improper priors from which well defined Bayes factors may be derived. The approaches involve either augmenting or normalising the prior measure for the parameters. One of these classes includes the well known and commonly employed shrinkage prior. Estimation of Bayes factors is demonstrated for a simple cointegration analysis.
|Date of creation:||Jan 2004|
|Contact details of provider:|| Postal: Department of Economics, University of Keele, Keele, Staffordshire, ST5 5BG - United Kingdom|
Phone: +44 (0)1782 584581
Fax: +44 (0)1782 717577
Web page: http://www.keele.ac.uk/depts/ec/cer/
More information through EDIRC
|Order Information:|| Postal: Centre for Economic Research, Research Institute for Public Policy and Management, Keele University, Staffordshire ST5 5BG - United Kingdom|
Web: http://www.keele.ac.uk/depts/ec/cer/pubs_kerps.htm Email:
When requesting a correction, please mention this item's handle: RePEc:kee:kerpuk:2004/03. 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: (Martin E. Diedrich)
If references are entirely missing, you can add them using this form.