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Improper priors with well defined Bayes Factors

By Rodney W. Strachan and Herman K. van Dijk

Abstract

While some improper priors have attractive properties, it is generally claimed that\ud Bartlett’s paradox implies that using improper priors for the parameters in alternative\ud models results in Bayes factors that are not well defined, thus preventing model comparison\ud in this case. In this paper we demonstrate, using well understood principles\ud underlying what is already common practice, that this latter result is not generally\ud true and so expand the class of priors that may be used for computing posterior odds\ud to two classes of improper priors: the shrinkage prior; and a prior based upon a nesting\ud argument. Using a new representation of the issue of undefined Bayes factors,\ud we develop classes of improper priors from which well defined Bayes factors result.\ud However, as the use of such priors is not free of problems, we include discussion on\ud the issues with using such priors for model comparison

Topics: Improper prior, marginal likelihood, Bayes factor, shrinkage prior, measure
Publisher: Dept. of Economics, University of Leicester
Year: 2005
OAI identifier: oai:lra.le.ac.uk:2381/4436

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