Improper priors with well defined Bayes Factors
AbstractA 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.
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Bibliographic InfoPaper provided by Erasmus University Rotterdam, Econometric Institute in its series Econometric Institute Report with number EI 2004-18.
Date of creation: 19 May 2004
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Bayes factor; improper prior; marginal likelihood; shrinkage prior; measure;
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- Hoogerheide, Lennart F. & Kaashoek, Johan F. & van Dijk, Herman K., 2007.
"On the shape of posterior densities and credible sets in instrumental variable regression models with reduced rank: An application of flexible sampling methods using neural networks,"
Journal of Econometrics,
Elsevier, vol. 139(1), pages 154-180, July.
- HOOGERHEIDE, Lennart F. & KAASHOEK, Johan F. & VAN DIJK, Herman K., 2005. "On the shape of posterior densities and credible sets in instrumental variable regression models with reduced rank: An application of flexible sampling methods using neural networks," CORE Discussion Papers 2005029, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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