Probability Matching Priors For One-Way Unbalanced Random Effect Models

Statistics and Risk Modeling

Volumn 20, Issue 1-4, 2002, Pages 29-52

  Datta, Gauri Sankar ^a   Kim, Yeong Hwa ^b   Ghosh, Malay ^b  

^a UNIVERSITY OF GEORGIA   (United States)

^b University of Florida ^*  (United States)

Author keywords

first order; Matching; reference priors; second order

Indexed keywords

EID: 18944391053     PISSN: 21931402     EISSN: 21967040     Source Type: Journal    
DOI: 10.1524/strm.2002.20.14.29     Document Type: Article

References (34)

1. Berger,J.O. and Bernardo,J.M.(1989). Estimating a product of means: Bayesian analysis with reference priors. JASA, 84, 200-207.
2. Berger,J.O. and Bernardo,J.M.( 1992a). On the development of reference priors. Bayesian Statistics 4. Eds. J.M. Bernardo, J.Berger, A.P. Dawid, and A.F.M. Smith. Oxford University Press, 35-66.
3. Berger,J.O. and Bernardo,J.M.(1992b). Ordered group reference priors with application to the multinomial problem Biometrika, 79, 25-37.
4. Bernardo,J.M.(1979). Reference posterior distributions for Bayesian inference. JRSS B, 41, 113-147.
5. Bian,G.(1995). Robust Bayesian estimators in a one-way ANOVA model. Test, 4, 115-135.
6. Box,G.E.P. and Tiao,G.C.(1973). Bayesian Inference in Statistical Analysis. Wiley, New York.
7. Burdick,R.K., Maqsood,F. and Graybill,F.A.(1986). Confidence Intervals on the intraclass correlation in the unbalanced one-way classification. Communications in Statistics, Part A, 15, 3353-3378.
8. Chaloner,K.(1987). A Bayesian approach to the estimation of variance components for the unbalanced one-way random model. Technometrics, 29, 323-337.
9. Cox,D.R. and Reid,N.(1987). Parameter orthogonality and approximate conditional inference. JRSS B, 49, 1-39.
10. Datta,G.S.(1996). On priors providing frequentist validity of Bayesian inference for multiple parameter functions. Biometrika, 83, 287-298.
11. Datta,G.S. and Ghosh,J.K(1995a). On priors providing frequentist validity of Bayesian inference. Biometrika, 82, 37-45.
12. Datta,G.S. and Ghosh,J.K(1995b). Noninformative priors for maximal invariant parameter in group models. Test, 4, 95-114.
13. Datta,G.S. and Ghosh,M. (1995a). Hierarchical Bayes estimators of the error variance in one-way ANOVA models. Journal of Statistical Planning and Inference, 45, 399-411.
14. Datta,G.S. and Ghosh,M.( 1995b). Some remarks on noninformative priors. JASA, 90, 1357-1363.
15. Datta,G.S. and Ghosh,M.(1996). On the invariance of noninformative priors. Ann. Stat., 24, 141-159.
16. Ghosh, J.K.(1994). Higher Order Asymptotics. NSF-CBMS Regional Conference Series in Probability and Statistics, V4. Institute of Mathematical Statistics.
17. Ghosh,J.K. and Mukerjee,R.(1992). Non-informative priors (with discussion). Bayesian Statistics 4. Eds. J.M. Bernardo, J. Berger, A.P. Dawid and A.F.M. Smith. Oxford University Press, 195-210.
18. Hill, B.M.(1965). Inference About Variance Components in the One-way Model. JASA, 60, 806-825.
19. Hobert,J.P. and Casella, G. (1996). The effect of improper priors on Gibbs sampling in hierarchical linear mixed models. JASA, 91, 1461-1473.
20. 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.
21. Mukerjee,R. and Ghosh,M.(1997). Second order probability matching priors. Biometrika, 84, 970-975.
22. Nicolaou,A.(1993). Bayesian intervals with good frequentist behavior in the presence of nuisance parameters. JRSS B, 55, 377-390.
23. Peers,H.W.(1965). On confidence sets and Bayesian probability points in the case of several parameters. JRSS B, 27, 9-16.
24. Polasek,W. and Potzelberger,K.(1993). Robust Bayesian Methods in Simple ANOVA models. Theory of Probability and its Applications, 37, 163-166.
25. Polasek,W. and Potzelberger,K.(1994). Robust Bayesian methods in simple ANOVA models. Journal of Statistical Planning and Inference, 40, 295-307.
26. Stein,C.(1985). On coverage probability of confidence sets based on a prior distribution. In Sequential Methods in Statistics, 16, 485-514. Banach Center Publications, Warsaw.
27. Swallow,W.H. and Searle,S.R.(1978). Minimum Variance Quadratic Unbiased Estimation of Variance Components. Technometrics, 20, 265-272.
28. Swamy,P.A.V.B. and Mehta,J.S.(1973). Bayesian Analysis of Error Components Regression Models. JASA, 68, 648-658.
29. Tiao,G.C. and Tan,W.Y.(1965). Bayesian Analysis of Random-effect Models in the Analysis of Variance. I: Posterior Distribution of Variance-components. Biometrika, 52, 37-53.
30. Tibshirani,R.(1989). Noninformative priors for one parameter of many. Biometrika, 76, 604-608.
31. Wald, A.(1940). A note on analysis of variance with unequal class frequencies. Annals of Mathematical Statistics, 11, 96-110.
32. Welch, B.L. and Peers, H.W.(1963). On formula for confidence points based on integrals of weighted likelihoods. JRSS B, 25, 318-329.
33. 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.
34. Yin, M. (1998). Asymptotic expansion for posterior probability in regression model. Statistics Decisions, 16, 349-368.