Improper priors with well defined Bayes Factors

Rodney Strachan and Herman van Dijk

No EI 2004-18, Econometric Institute Research Papers from Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute

Abstract: 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, e.g., low 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 expand the class of priors that may be used for computing posterior odds to include some improper priors. Our approach is to 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. This approach involves either augmenting or normalising the prior measure for the parameters. One of these classes of priors includes the well known and commonly employed shrinkage prior. Estimation of Bayes factors is demonstrated for a reduced rank model.

Keywords: Bayes factor; improper prior; marginal likelihood; measure; shrinkage prior (search for similar items in EconPapers)
JEL-codes: C11 C15 C32 C52 (search for similar items in EconPapers)
Date: 2004-05-19
References: Add references at CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
https://repub.eur.nl/pub/1277/ei200418.pdf (application/pdf)

Related works:
Working Paper: Improper priors with well defined Bayes Factors (2005)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:ems:eureir:1277

Access Statistics for this paper

More papers in Econometric Institute Research Papers from Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute Contact information at EDIRC.
Bibliographic data for series maintained by RePub (peter.vanhuisstede@eur.nl this e-mail address is bad, please contact repec@repec.org).