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[var epsilon]-contaminated priors in testing point null hypothesis: a procedure to determine the prior probability

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  • Gómez-Villegas, Miguel A.
  • Sanz, Luis

Abstract

In this paper the problem of testing a point null hypothesis from the Bayesian perspective and the relation between this and the classical approach is studied. A procedure to determine the mixed prior distribution is introduced and a justification for this construction based on a measure of discrepancy is given. Then, we compare a lower bound for the posterior probability, when the prior is in the class of [var epsilon]-contaminated distributions, of the point null hypothesis with the p-value.

Suggested Citation

  • Gómez-Villegas, Miguel A. & Sanz, Luis, 2000. "[var epsilon]-contaminated priors in testing point null hypothesis: a procedure to determine the prior probability," Statistics & Probability Letters, Elsevier, vol. 47(1), pages 53-60, March.
    • Handle: RePEc:eee:stapro:v:47:y:2000:i:1:p:53-60
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    References listed on IDEAS

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    1. James Berger & Elías Moreno & Luis Pericchi & M. Bayarri & José Bernardo & Juan Cano & Julián Horra & Jacinto Martín & David Ríos-Insúa & Bruno Betrò & A. Dasgupta & Paul Gustafson & Larry Wasserman &, 1994. "An overview of robust Bayesian analysis," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 3(1), pages 5-124, June.
    2. Miguel Gómez-Villegas & Luis Sanz, 1998. "Reconciling Bayesian and frequentist evidence in the point null testing problem," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 7(1), pages 207-216, June.
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