Exceptions to Bartlett’s Paradox

Rodney Strachan and Herman van Dijk

No KERP 2004/03, Keele Economics Research Papers from Centre for Economic Research, Keele University

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, 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.

Keywords: Improper prior; Bayes factor; marginal likelihood; shrinkage prior; measure. (search for similar items in EconPapers)
JEL-codes: C11 C15 C32 C52 (search for similar items in EconPapers)
Pages: 25 pages
Date: 2004-01
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