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Divergent Priors and Well Behaved Bayes Factors

Author

Listed:
  • Rodney W. Strachan

    (School of Economics, University of Queensland, Australia)

  • Herman K. van Dijk

    (Econometric Institute, Erasmus University Rotterdam)

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.

Suggested Citation

  • Rodney W. Strachan & Herman K. van Dijk, 2014. "Divergent Priors and Well Behaved Bayes Factors," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 6(1), pages 1-31, March.
    • Handle: RePEc:psc:journl:v:6:y:2014:i:1:p:1-31
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    References listed on IDEAS

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    Cited by:

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    3. Matthieu Droumaguet & Anders Warne & Tomasz Wozniak, 2015. "Granger Causality and Regime Inference in Bayesian Markov-Switching VARs," Department of Economics - Working Papers Series 1191, The University of Melbourne.
    4. Warne, Anders & Coenen, Günter & Christoffel, Kai, 2013. "Predictive likelihood comparisons with DSGE and DSGE-VAR models," Working Paper Series 1536, European Central Bank.

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    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
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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