Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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On a Bayesian P-value with the Coherence Property

  • Published : 2003.12.01
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Abstract

Schervish(1996) and Lavine and Schervish(1999) have shown that the classical P-values and the Bayes factors fail to achieve the so-called coherence property, respectively. In this paper, we propose a new type of Bayesian P-value, namely the type LR Bayesian P-value, satisfying the coherence property. The proposed Bayesian P-values are very easy to use with since they are simple functions of likelihood ratio. Their performances are discussed and compared with those of other methods under several situations.

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References

  1. Journal of the American Statistical Association v.82 Testing a point null hypothesis: the irreconcilability of p-values and evidence Berger,J.O.;Sellke,T. https://doi.org/10.2307/2289131
  2. Journal of the American Statistical Association v.82 Reconciling Bayesian and frequentist evidence in the one sided testing problem Casella,G.;Berger,J.O. https://doi.org/10.2307/2289130
  3. The Annals of Mathematical Statistics v.40 Simultaneous test procedures-Some theory of multiple comparisons Gabriel,K.R. https://doi.org/10.1214/aoms/1177697819
  4. The Korean Communications in Statistics v.8 no.3 A Bayesian hypothesis testing procedure possessing the concept of significance level Hwang,H.T.
  5. The Korean Communications in Statistics v.9 no.3 A study on Bayesian p-values Hwang,H.T.;Oh,H.J. https://doi.org/10.5351/CKSS.2002.9.3.725
  6. Theory of probability (3 ed.) Jeffreys,H.
  7. Journal of the American Statistical Association v.90 Bayes factors Kass,R.E.;Raftery,A.E. https://doi.org/10.2307/2291091
  8. The American Statistician v.53 no.2 Bayes factors : What they are and what they are not Lavine,M.;Schervish,M.J. https://doi.org/10.2307/2685729
  9. Bayesian Statistics : an Introduction Lee,P.M.
  10. The Bayesian Choice: a decision theoretic motivation Robert,C.P.
  11. Theory of Statistics Schervish,M.J.
  12. The American Statistician v.50 no.3 P-values: What they are and what they are not Schervish,M.J. https://doi.org/10.2307/2684655