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Improper priors with well defined Bayes Factors

Author

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  • Rodney W. Strachan
  • Herman K. van Dijk

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.

Suggested Citation

  • Rodney W. Strachan & Herman K. van Dijk, 2005. "Improper priors with well defined Bayes Factors," Discussion Papers in Economics 05/4, Division of Economics, School of Business, University of Leicester.
    • Handle: RePEc:lec:leecon:05/4
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    File URL: https://www.le.ac.uk/economics/research/RePEc/lec/leecon/dp05-4.pdf
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    Cited by:

    1. 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.
    2. Gary Koop & Roberto Leon-Gonzalez & Rodney Strachan, 2008. "Bayesian inference in a cointegrating panel data model," Advances in Econometrics, in: Bayesian Econometrics, pages 433-469, Emerald Group Publishing Limited.
    3. Fabian Paul & Thomas R Weikl, 2016. "How to Distinguish Conformational Selection and Induced Fit Based on Chemical Relaxation Rates," PLOS Computational Biology, Public Library of Science, vol. 12(9), pages 1-17, September.

    More about this item

    Keywords

    Improper prior; Bayes factor; marginal likelihood; shrinkage prior; measure;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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