Journal of the Italian Statistical Society

, Volume 1, Issue 1, pp 17–32 | Cite as

The application of robust Bayesian analysis to hypothesis testing and Occam's Razor

  • James O. Berger
  • William H. Jefferys
Article

Summary

Robust Bayesian analysis deals simultaneously with a class of possible prior distributions, instead of a single distribution. This paper concentrates on the surprising results that can be obtained when applying the theory to problems of testing precise hypotheses when the “objective” class of prior distributions is assumed. First, an example is given demonstrating the serious inadequacy of P-values for this problem. Next, it is shown how the approach can provide statistical quantification of Occam's Razor, the famous principle of science that advocates choice of the simpler of two hypothetical explanations of data. Finally, the theory is applied to multinomial testing.

Keywords

Bayes factor P-value Occam's Razor Monte-Carlo integration Mercury's perihilion 

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Copyright information

© Societa Italiana di Statistica 1992

Authors and Affiliations

  • James O. Berger
    • 2
  • William H. Jefferys
    • 1
  1. 1.University of TexasUSA
  2. 2.Department of Statistics, Math. Sciences BdgPurdue UniversityWest LafayetteUSA

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