Some remarks on noninformative priors

Journal of the American Statistical Association

Volumn 90, Issue 432, 1995, Pages 1357-1363

  Datta, Gauri Sankar ^a   Ghosh, Malay ^b  

^a UNIVERSITY OF GEORGIA   (United States)

^b UNIVERSITY OF FLORIDA   (United States)

Author keywords

Jeffreys s priors; Many parameters; Probability matching criterion; Random effects models; Reference priors; Reverse reference priors

Indexed keywords

EID: 21344468866     PISSN: 01621459     EISSN: 1537274X     Source Type: Journal    
DOI: 10.1080/01621459.1995.10476640     Document Type: Article

References (24)

1. Berger, J. (1992), “Discussion of Ghosh and Mukerjee,” in Bayesian Statistics 4, eds. J. M. Bernardo, J. O. Berger, A. P. Dawid, and A. F. M. Smith, Oxford, U.K.: Oxford University Press, pp. 205–206.
2. Berger, J., and Bernardo, J. M. (1989), “Estimating a Product of Means: Bayesian Analysis With Reference Priors,” Journal of the American Statistical Association, 84, 200–207.
3. —— (1992a), “On the Development of Reference Priors” (with discussion), in Bayesian Statistics 4, eds. J. M. Bernardo, J. O. Berger, A. P. Dawid, and A. F. M. Smith, Oxford, U.K.: Oxford University Press, pp. 35–60.
4. —— (1992b), “Reference Priors in a Variance Components Problem,” in Bayesian Analysis in Statistics and Econometrics, eds. P. K. Goel and N. S. Iyengar, New York: Springer-Verlag, pp. 177–194.
5. Bernardo, J. M. (1979), “Reference Posterior Distributions for Bayesian Inference” (with discussion), Journal of the Royal Statistical Society, Ser. B, 41, 113–147.
6. Chhikara, R. S., and Folks, J. L. (1989), The Inverse Gaussian Distribution, New York: Marcel Dekker.
7. Clarke, B., and Sun, D. (1993), “Reference Priors Under the Chi-Squared Distance,” preprint.
8. Clarke, B., and Wasserman, L. (1995), “Information Tradeoff,” Test, to appear.
9. Cox, D. R., and Reid, N. (1987), “Orthogonal Parameters and Approximate Conditional Inference” (with discussion), Journal of the Royal Statistical Society, Ser. B, 49, 1–39.
10. Datta, G. S., and Ghosh, M. (1995), “Hierarchical Bayes Estimators of the Error Variance in One-Way ANOVA Models,” Journal of Statistical Planning and Inference, 45, 399–411.
11. —— (1996), “On the Invariance of Noninformative Priors,” Annals of Statistics, to appear.
12. Dawid, A. P., Stone, M., and Zidek, J. V. (1973), “Marginalization Paradoxes in Bayesian and Structural Inference” (with discussion), Journal of the Royal Statistical Society, Ser. B, 35, 189–233.
13. Efron, B. (1986), “Why Isn’t Everyone a Bayesian?” (with discussion), The American Statistician, 40, 1–11.
14. Ghosh, J. K., and Mukerjee, R. (1992), “Non-Informative Priors” (with discussion), in Bayesian Statistics 4, eds. J. M. Bernardo, J. O. Berger, A. P. Dawid, and A. F. M. Smith, Oxford, U.K.: Oxford University Press, pp. 195–210.
15. Jeffreys, H. (1961), Theory of Probability, Oxford, U.K.: Oxford University Press.
16. Laplace, P. (1812), Theorie Analytique Des Probabilities, Paris: Courcier.
17. Morris, C. N., and Normand, S. L. (1992), “Hierarchical Models for Combining Information and for Meta-Analyses” (with discussion), in Bayesian Statistics 4, eds. J. M. Bernardo, J. O. Berger, A. P. Dawid, and A. F. M. Smith, Oxford, U.K.: Oxford University Press, pp. 321–344.
18. Mukerjee, R., and Dey, D. K. (1993), “Frequentist Validity of Posterior Quantiles in the Presence of a Nuisance Parameter: Higher-Order Asymptotics,” Biometrika, 80, 499–505.
19. Peers, H. W. (1965), “On Confidence Points and Bayesian Probability Points in the Case of Several Parameters,” Journal of the Royal Statistical Society, Ser. B, 27, 9–16.
20. Stein, C. (1985), “On Coverage Probability of Confidence Sets Based on a Prior Distribution,” in Sequential Methods in Statistics, Banach Center Publications, 16, Warsaw: Polish Scientific Publishers, pp. 485–514.
21. Stone, M., and Dawid, A. P. (1972), “Un-Bayesian Inference in Routine Statistical Problems,” Biometrika, 59, 369–375.
22. Tibshirani, R. (1989), “Noninformative Priors for One Parameter of Many,” Biometrika, 76, 705–608.
23. Welch, B. L., and Peers, H. W. (1963), “On Formulae for Confidence Points Based on Intervals of Weighted Likelihoods,” Journal of the Royal Statistical Society, Ser. B, 25, 318–329.
24. Ye, K. (1994), “Bayesian Reference Prior Analysis on the Ratio of Variances for Balanced One-Way Random Effect Model,” Journal of Statistical Planning and Inference, 41, 267–280.