Weakly informative priors and well behaved Bayes factors

Rodney Strachan and Herman van Dijk

No EI 2005-40, Econometric Institute Research Papers from Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute

Abstract: Bartlett's paradox has been taken to imply that using improper priors results in Bayes factors that are not well defined, preventing model comparison in this case. We use well understood principles underlying what is already common practice, to demonstrate that this implication is not true for some improper priors, such as the Shrinkage prior due to Stein (1956). While this result would appear to expand the class of priors that may be used for computing posterior odds, we warn against the straightforward use of these priors. Highlighting the role of the prior measure in the behaviour of Bayes factors, we demonstrate pathologies in the prior measures for these improper priors. Using this discussion, we then propose a method of employing such priors by setting rules on the rate of diffusion of prior certainty.

Keywords: Bayes factor; improper prior; marginal likelihood; shrinkage prior (search for similar items in EconPapers)
JEL-codes: C11 C15 C32 C52 (search for similar items in EconPapers)
Date: 2005-11-07
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Citations: View citations in EconPapers (2)

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