Journal of the Korean Statistical Society

  • 제28권1호
  • /
  • Pages.73-92
  • /
  • 1999
  • /
  • 1226-3192(pISSN)
  • /
  • 2005-2863(eISSN)
한국통계학회 (The Korean Statistical Society)
권호 표지

A Bayesian Test for Simple Tree Ordered Alternative using Intrinsic Priors

  • Kim, Seong W. (Department of Statistics, University of Missouri-Columbia)
  • 발행 : 1999.03.01
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

In Bayesian model selection or testing problems, one cannot utilize standard or default noninformative priors, since these priors are typically improper and are defined only up to arbitrary constants. The resulting Bayes factors are not well defined. A recently proposed model selection criterion, the intrinsic Bayes factor overcomes such problems by using a part of the sample as a training sample to get a proper posterior and then use the posterior as the prior for the remaining observations to compute the Bayes factor. Surprisingly, such Bayes factor can also be computed directly from the full sample by some proper priors, namely intrinsic priors. The present paper explains how to derive intrinsic priors for simple tree ordered exponential means. Some numerical results are also provided to support theoretical results and compare with classical methods.

키워드

참고문헌

  1. Journal of the American Statistical Association v.84 Estimating a product of means: Bayesian analysis with reference priors Berger, J. O.;Bernado, J. M
  2. Bayesian Statistics 4 On the development of the reference priors Berger, J. O.;Bernardo, J.;Bernardo, J. M.(ed.);Berger, J. O.(ed.);Dawid, A. P.(ed.);Smith, A. F. M.(ed.)
  3. The Annals of Statistics v.22 A unified conditional frequentist and Bayesian test for fixed and sequential simple hypothesis Berger, J. O.;Brown, L. D.;Wolpert, R. L
  4. Bayesian Analysis Ⅴ The Intrinsic Bayes factor for linear modles (with discussion) Berger, J. O.;Pericchi, L.;J. M. Bernado(et al.)(eds.)
  5. Journal of the American Statistical Association v.91 The intrinsic Bayes factor for model selection and prediction Berger, J. O.;Pericchi, L
  6. The Annals of Statistics v.18 Lower bounds on the Bayes factors for multinomial distribution, with application to chi-squared tests of fit Delampady, M.;Berger, J. O
  7. Journal of the American Statistical Association v.74 A predictive approach to model selection Giesser, S.;Eddy, W. F
  8. Technical report, Department of Statistics, University of Connecticut Bayesian model choice: Asymptotics and exact calculations Gelfand, A. E.;Dey, D. K
  9. Indian Association for Productivity Quality and Reliability (IAPQR) volume titled "Frontiers in Reliabilty" Recent developments of Bayesian inference for stress-strength models Chosh, M.;Sun, D
  10. Theory of Probability Jeffreys, H
  11. Journal of the American Statistical Association v.90 Bayes factors Kass, R. E.;Raftery, A. E
  12. Lifetime Data Analysis(under revision) Intrinsic priors for model selection using an encompassing model Kim, S. W.;Sun, D
  13. Annals of the Intitute of Statistical Mathematics Testing hypotheses about the power law process under failure truncation using intrinsic Bayes factors Lingham, R. T.;Sivaganesan, S
  14. The Annals of Statistics v.22 Posterior predictive p-values Meng, X
  15. Technometrics v.5 Theoretical explanation of observed decreasing failure rate Proschan, F
  16. Order restricted statistical inference Robertson, T.;Wright, F. T.;Dykstra, R. L
  17. Journal of Royal Statistical Soceity, ser. v.B46 A predictive model selection criterion San Martini, A.;Spezzaferri, F.
  18. Journal of Royal Statistical Society, ser. v.B44 Bayes factors for linear and long-linear models with vague prior information Spiegelhalter, D. J.;Smith, A. F. M.
  19. Intrinsic priors for testing ordered exponential means Sun, D.;Kim, S. W.
  20. Bayesian Analysis Ⅴ Intrinsic Bayes factors for model selection with autoregressive data Varshavsky, J. A.;J. M. B ernado(et al.)(eds.)