Bayesian diagnostic techniques for detecting hierarchical structure

Bayesian Analysis

Volumn 2, Issue 4, 2007, Pages 735-760

  Yan, Guofen ^a   Sedransk, J ^b  

^a UNIVERSITY OF VIRGINIA   (United States)

^b CASE WESTERN RESERVE UNIVERSITY   (United States)

Author keywords

F statistic; Model assessment; Partial posterior predictive p value; Posterior predictive distribution; Posterior predictive p value

Indexed keywords

EID: 83055174365     PISSN: 19360975     EISSN: 19316690     Source Type: Journal    
DOI: 10.1214/07-BA230     Document Type: Article

References (17)

1. Bayarri, M.J. and Berger, J.O. (2000). "P-values for composite null models," Journal of the American Statistical Association, 95, 1127-1142.
2. Bayarri, M.J. and Castellanos, M.E. (2007). "Bayesian checking of hierarchical models," Statistical Science, in press.
3. Box, G.E.P. (1980). "Sampling and Bayes inference in scientific modeling and robustness," Journal of the Royal Statistical Society A, 143, 383-430.
4. Calvin, J.A. and Sedransk, J. (1991). "Bayesian and Frequentist Predictive Inference for the Patterns of Care Studies," Journal of the American Statistical Association, 86, 36-48.
5. Geisser, S. (1993). Predictive Inference: An Introduction, Chapman & Hall, New York, NY.
6. Gelfand, A.E., Dey, D.K., and Chang, H. (1992). "Model determination using predictive distributions with implementation via sampling-based methods," In Bayesian Statistics 4, eds. J.M. Bernardo et al., Oxford University Press, London, 147-167.
7. Gelman, A., Carlin, J.B., Stern, H.S., and Rubin, D.B. (2004). Bayesian Data Analysis, 2nd Edition, Chapman & Hall/CRC, London.
8. Gelman, A., Meng, X.L., and Stern, H. (1996). "Posterior predictive assessment of model fitness via realized discrepancies (with discussion)," Statistica Sinica, 6, 733-807.
9. Hjort, N.L., Dahl, F.A., and Steinbakk, G. H. (2006). "Post-processing posterior predictive p values," Journal of the American Statistical Association, 101, 1157-1174.
10. Marshall, E.C. and Spiegelhalter, D.J. (2003). "Approximate cross-validatory predictive checks in disease mapping models," Statistics in Medicine, 22, 1649-1660.
11. Nandram, B., Sedransk, J., and Pickle, L. (1999). "Bayesian analysis of mortality rates for U.S. health service areas," Sankhya B 61, 145-165.
12. Nandram, B., Sedransk, J., and Pickle, L. (2000). "Bayesian analysis and mapping of mortality rates for chronic obstructive pulmonary disease," Journal of the American Statistical Association, 95, 1110-1118.
13. Robins, J.M., van der Vaart, A., and Ventura, V. (2000). "Asymptotic distribution of p-values in composite null models (with discussion)," Journal of the American Statistical Association, 95, 1143-1172.
14. Rubin, D.B. (1984). "Bayesianly justifiable and relevant frequency calculations for the applied statistician," The Annals of Statistics, 12, 1151-1172.
15. Sinharay, S. and Stern, H.S. (2003). "Posterior predictive model checking in hierarchical models," Journal of Statistical Planning and Inference, 111, 209-221.
16. Stern, H.S. and Cressie, N. (2000). "Posterior predictive model checks for disease mapping models," Statistics in Medicine, 19, 2377-2397.
17. Yan, G. (2003). Evaluation of Bayesian Diagnostic Methods for Hierarchical Data, Ph.D. dissertation, Department of Statistics, Case Western Reserve University, Cleveland, Ohio.