On the posterior consistency of mixtures of Dirichlet process priors with censored data

Scandinavian Journal of Statistics

Volumn 30, Issue 3, 2003, Pages 535-547

  Kim, Yongdai ^a  

^a Ewha Womans University   (South Korea)

Author keywords

Censored observation; Dirichlet processes; Posterior consistency

Indexed keywords

EID: 0041861344     PISSN: 03036898     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-9469.00347     Document Type: Article

References (17)

1. Antoniak, C. (1974). Mixtures of Dirichlet processes with applications to Bayesian nonparametric problems. Ann. Statist. 2, 1152-1174.
2. Barron, A. R. (1988). The exponential convergence of posterior probabilities with implications for Bayes estimators of density functions. Technical report, University of Illinois.
3. Barron, A., Schervish, M. J. & Wasserman, L. (1999). The consistency of posterior distributions in nonparametric problems. Ann. Statist. 27, 536-561.
4. Berk, H. R. (1970). Consistency a posteriori. Ann. Math. Statist. 41, 894-906.
5. Carota, C. & Parmigiani, G. (1996). On Bayes factors for nonparametric alternatives. In Bayesian Statistics Vol. 5 (eds. J. M. Bernardo, J. O. Berger, A. P. Dawid, & A. F. M. Smith), 507-511. Oxford University Press, London.
6. Chen, Y. Y., Hollander, M. & Langberg, N. A. (1982). Small-sample results for the Kaplan-Meier estimator. J. Amer. Statist. Assoc. 67, 141-144.
7. Diaconis, P. & Freedman, D. A. (1986). On inconsistent Bayes estimates of locations. Ann. Statist. 14, 68-87.
8. Doss, H. (1994). Bayesian nonparametric estimation for incomplete data via successive substitution sampling. Ann. Statist. 22, 1763-1786.
9. Gill, R. & Johansen, S. (1990). A survey of product-integration with a view toward application in survival analysis. Ann. Statist. 18, 1501-1555.
10. Ghosal, S., Ghosh, J. K. & Ramamoorthi, R. V. (1999). Posterior consistency of Dirichlet mixtures in density estimation, Ann. Statist. 27, 143-158.
11. Ghosal, S., Ghosh, J. K. & A. W. van der Vaart, (2000). Convergence rate of posterior distributions. Ann. Statist. 28, 500-531.
12. Hjort, N. L. (1990). Nonparametric Bayes estimators based on beta processes in models for life history data. Ann. Statist. 18, 1259-1294.
13. Kaplan, E. L. & Meier, P. (1958). Nonparametric estimation from incomplete observations. J. Amer. Statist. Assoc. 53, 457-481.
14. Kim, Y. & Lee, J. (2001). On posterior consistency of survival models. Annals of Statistics, 29, 666-686.
15. Miller, R. G., Jr (1983). What price Kaplan-Meier? Biometrics 40, 601-609.
16. Shen, X. & Wasserman, L. (2001). Rates of convergence of posterior distributions. Ann. Statist. 29, 680-714.
17. Walker, S. & Muliere, P. (1997). Beta-Stacy processes and a generalization of the polya-urn scheme. Ann. Statist. 25, 1762-1780.