Multiple Comparison for the One-Way ANOVA with the Power Prior

Title & Authors
Multiple Comparison for the One-Way ANOVA with the Power Prior
Bae, Re-Na; Kang, Yun-Hee; Hong, Min-Young; Kim, Seong-W.;

Abstract
Inference on the present data will be more reliable when the data arising from previous similar studies are available. The data arising from previous studies are referred as historical data. The power prior is defined by the likelihood function based on the historical data to the power $\small{a_0}$, where $\small{0\;{\le}\;a_0\;{\le}\;1}$. The power prior is a useful informative prior for Bayesian inference such as model selection and model comparison. We utilize the historical data to perform multiple comparison in the one-way ANOVA model. We demonstrate our results with some simulated datasets under a simple order restriction between the treatments.
Keywords
Bayes factor;historical data;Markov Chain Monte Carlo;order restricted inference;power prior;
Language
English
Cited by
1.
Differences of Multiple Comparison Methods for Treatment Means,;;;;;;;;

Laboraroty Animal Research, 2009. vol.25. 4, pp.413-418
References
1.
Bartholomew, D. J. (1959a). A test of homogeneity for ordered alternatives. Biometrika, 46, 36-48

2.
Bartholomew, D. J. (1959b). A test of homogeneity for ordered alternatives. II. Biometrika, 46, 328-335

3.
Bartholomew, D. J. (1961a). A test of homogeneity of means under restricted alternatives (with discussions). Journal of the Royal Statistical Society, Ser. B, 23, 239-281

4.
Bartholomew, D. J. (1961b). Ordered tests in the analysis of variance. Biometrika, 48, 325-332

5.
Berger, J. O. and Pericchi, L. R. (1996). The intrinsic Bayes factor for model selection and prediction. Journal of the American Statistical Association, 91, 109-122

6.
Bohrer, R. and Francis, G. K. (1972). Sharp one-sided confidence bounds over positive regions. The Annals of Mathematical Statistics, 43, 1541-1548

7.
Ibrahim, J. G. and Chen, M. H. (2000). Power prior distributions for regression models. Statistical Science, 15, 46-60

8.
Gelfand, A. E., Hills, S. E., Racine-poon, A. and Smith, A. F. M. (1900). Illustration of Bayesian inference in normal data models using Gibbs sampling. Journal of the American Statistical Association, 85, 972-985

9.
Gopalan, R. and Berry, D. A. (1998). Bayesian multiple comparisons using Dirichlet process priors. Journal of the American Statistical Association, 93, 1130-1139

10.
Hayter, A. J. (1990). A one-sided studentized range test for testing against a simple ordered alternative. Journal of the American Statistical Association, 85, 778-785

11.
Kim, S. W. and Sun, D. (2000). Intrinsic priors for model selection using an encompassing model with applications to censored failure time data. Lifetime Data Analysis, 6, 251-269

12.
Kim, H. J. and Kim, S. W. (2001). Two-sample Bayesian tests using intrinsic Bayes factors for multivariate normal observations. Communications in Statistics-Computation and Simulation, 30, 426-436

13.
Liu, L. (2001). Simultaneous statistical inference for monotone dose-response mean. Doctoral dessertation, Memorial University of Newfoundland, St. John's, Canada

14.
Pauler, D. K., Wakefield, J. C. and Kass, R. E. (1999). Bayes factors and approximations for variance component models. Journal of the American Statistical Association, 94, 1242-1253

15.
Son, Y. and Kim, S. W. (2005). Bayesian single change point detection in a sequence of multivariate normal observations. Journal of Theoretical and Applied Statistics, 39, 373-387