Improper priors with well defined Bayes Factors

Rodney Strachan and Herman van Dijk

No 05/4, Discussion Papers in Economics from Division of Economics, School of Business, University of Leicester

Abstract: While some improper priors have attractive properties, 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, using well understood principles underlying what is already common practice, that this latter result is not generally true and so expand the class of priors that may be used for computing posterior odds to two classes of improper priors: the shrink age prior; and a prior based upon a nesting argument. Using a new representation of the issue of undefined Bayes factors, we develop classes of improper priors from which well defined Bayes factors result. However, as the use of such priors is not free of problems, we include discussion on the issues with using such priors for model comparison.

Keywords: Improper prior; Bayes factor; marginal likelihood; shrinkage prior; measure (search for similar items in EconPapers)
Date: 2005-03
New Economics Papers: this item is included in nep-ecm
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Working Paper: Improper priors with well defined Bayes Factors (2004)
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