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

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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.

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Authors and Affiliations

  1. University of Texas, Texas, USA

    William H. Jefferys

  2. Department of Statistics, Math. Sciences Bdg, Purdue University, 47907, West Lafayette, Indiana, USA

    James O. Berger

Authors
  1. James O. Berger
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  2. William H. Jefferys
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Additional information

Research supported by the National Science Foundation, Grant DMS-8923071, and by NASA Contract NAS5-29285 for the hubble Space Telescope.

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Berger, J.O., Jefferys, W.H. The application of robust Bayesian analysis to hypothesis testing and Occam's Razor. J. It. Statist. Soc. 1, 17–32 (1992). https://doi.org/10.1007/BF02589047

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  • DOI: https://doi.org/10.1007/BF02589047

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