Statistical Science

Unified frequentist and Bayesian testing of a precise hypothesis

J. O. Berger, B. Boukai, and Y. Wang

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In this paper, we show that the conditional frequentist method of testing a precise hypothesis can be made virtually equivalent to Bayesian testing. The conditioning strategy proposed by Berger, Brown and Wolpert in 1994, for the simple versus simple case, is generalized to testing a precise null hypothesis versus a composite alternative hypothesis. Using this strategy, both the conditional frequentist and the Bayesian will report the same error probabilities upon rejecting or accepting. This is of considerable interest because it is often perceived that Bayesian and frequentist testing are incompatible in this situation. That they are compatible, when conditional frequentist testing is allowed, is a strong indication that the "wrong" frequentist tests are currently being used for postexperimental assessment of accuracy. The new unified testing procedure is discussed and illustrated in several common testing situations.

Article information

Statist. Sci., Volume 12, Number 3 (1997), 133-160.

First available in Project Euclid: 22 August 2002

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Bayes factor likelihood ratio composite hypothesis conditional test error probabilities


Berger, J. O.; Boukai, B.; Wang, Y. Unified frequentist and Bayesian testing of a precise hypothesis. Statist. Sci. 12 (1997), no. 3, 133--160. doi:10.1214/ss/1030037904.

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See also

  • Includes: Dennis V. Lindley. Comment by Dennis V. Lindley.
  • Includes: Thomas A. Louis. Comment by Thomas A. Louis.
  • Includes: David Hinkley. Comment by David Hinkley.
  • Includes: J. O. Berger, B. Boukai, Y. Wang. Rejoinder by J. O. Berger, B. Boukai and Y. Wang.