Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
권호 표지
DOI QR코드

DOI QR Code

Note on Properties of Noninformative Priors in the One-Way Random Effect Model

  • Kang, Sang Gil (Department of Liberal Arts, Kyungsung University) ;
  • Kim, Dal Ho (Department of Statistics, Kyungpook National University) ;
  • Cho, Jang Sik (Department of Statistical Information Science, Kyungsung University)
  • Published : 2002.12.01
Download PDF
⟨ Previous Next ⟩

Abstract

For the one-way random model when the ratio of the variance components is of interest, Bayesian analysis is often appropriate. In this paper, we develop the noninformative priors for the ratio of the variance components under the balanced one-way random effect model. We reveal that the second order matching prior matches alternative coverage probabilities up to the second order (Mukerjee and Reid, 1999) and is a HPD(Highest Posterior Density) matching prior. It turns out that among all of the reference priors, the only one reference prior (one-at-a-time reference prior) satisfies a second order matching criterion. Finally we show that one-at-a-time reference prior produces confidence sets with expected length shorter than the other reference priors and Cox and Reid (1987) adjustment.

Keywords

References

  1. Journal of the American Statistical Association v.84 Estimating a Product of Means : Bayesian Analysis with Reference Priors Berger, J. O.;Bernardo, J. M. https://doi.org/10.2307/2289864
  2. Bayesian Statistics Ⅳ On the Development of Reference Priors (with discussion) Berger, J. O.;Bernardo, J. M.;J. M. Bernardo(et al.)
  3. Journal of Royal Statistical Society v.B no.41 Reference Posterior Distributions for Baayesian Inference (with discussion) Bernardo, J. M.
  4. Bayesian Inference in Statistical Analysis Box, G.;Tiao, G.
  5. Communications in Statistics - Theory and Methods v.27 Bayesian Approach to Estimation of Intraclass Correlation using Reference Prior Chung, Y.;Dey D. K. https://doi.org/10.1080/03610929808832225
  6. Journal of Royal Statistical Society v.B no.49 Orthogonal Parameters and Approximate Conditional Inference (with discussion) Cox, D. R.;Reid, N.
  7. Journal of Royal Statistical Society v.B no.63 On Expected Volumes of Multidimensional Confidence Sets Associated with the Usual and Adjusted Likelihoods Datta, G. S.;DiCiccio, T. J. https://doi.org/10.1111/1467-9868.00306
  8. Biometrika v.82 On Priors Providing Frequentist Validity for Bayesian Inference Datta, G. S.;Ghosh, J. K. https://doi.org/10.1093/biomet/82.1.37
  9. Journal of the American Statistical Association v.90 Some Remarks on Noninformative Priors Datta, G. S.;Ghosh, M. https://doi.org/10.2307/2291526
  10. The Annal of Statistics v.24 On the Invariance of Noninformative Priors Datta, G. S.;Ghosh, M. https://doi.org/10.1214/aos/1033066203
  11. Calcutta Statistical Association Bulletin v.50 Some New Results on Probability Matching Priors Datta, G. S.;Ghosh, M.;Mukerjee, R. https://doi.org/10.1177/0008068320000306
  12. Journal of Royal Statistical Society v.B no.56 Frequentist and Bayesian Bartlett Correction of Test Statistics based on Adjusted Profile Likelihood DiCiccio, T. J.;Stern, S. E.
  13. Statistics & Decisions v.13 Frequentist Validity of Highest Posterior Density Regions in the Presence of Nuisance Parameters Ghosh, J. K.;Mukerjee, R.
  14. Biometrics v.12 Confidence Intervals for Vatiance Ratios Specifying Genetic Heritability Graybill, F. A.;Martin, F.;Godfrey, G. https://doi.org/10.2307/3001754
  15. Journal of the American Statistical Association v.60 Inference about Variance Components in the One-Way Model Hill, B. https://doi.org/10.2307/2283247
  16. The Korean Communications in Statistics v.8 On Second Orger Probability Matching Criterion in the One-Way Random Effect Model Kim, D. H.;Kang, S. G.;Lee, W. D.
  17. Biometrika v.80 Frequentist validity of Posterior Quantiles in the Presence of a Nuisance Parameter : Higher Order Asymptotics Mukerjee, R.;Dey, D. K. https://doi.org/10.1093/biomet/80.3.499
  18. Biometrika v.84 Second Order Probability Matching Priors Mukerjee, R.;Ghosh, M. https://doi.org/10.1093/biomet/84.4.970
  19. Biometrika v.86 On A Property of Probability Matching Priors:Matching the Alternative Coverage Probabilities Mukerjee, R.;Reid, N. https://doi.org/10.1093/biomet/86.2.333
  20. Journal of Royal Statistical Society v.B no.61 On Confidence Intervals Associated with the Usual and Adjusted Likelihoods Mukerjee, R.;Reid, N. https://doi.org/10.1111/1467-9868.00212
  21. Communications in Statistics - Theory and Methods v.19 A Comparison of Bayes and Maximum Likelihood Estimation of the intraclass Correlation Coefficient Palmer, J. L.;Broemeling, L. D. https://doi.org/10.1080/03610929008830241
  22. Sequential Methods in Statistics v.16 On the Coverage Probability of Confidence Sets based on a Prior Distribution Stein, C.
  23. Biometrika v.76 Noninformative Priors for One Parameter of Many Tibshirani, R. https://doi.org/10.1093/biomet/76.3.604
  24. Journal of Statistical Planning and Inference v.41 Bayesian Reference Priors Analysis on the Ratio of Variances for the Balanced One-Way Random Effect Model Ye, K. https://doi.org/10.1016/0378-3758(94)90023-X
  25. Journal of Royal Statistical Society v.B no.35 On Formulae for Confidence Points based on Integrals of Weighted Likelihood Welch, B. L.;Peers, H. W.