Nonparametric priors for vectors of survival functions

Statistica Sinica

Volumn 20, Issue 4, 2010, Pages 1455-1484

  Epifani, Ilenia ^a   Lijoi, Antonio ^b,c  

^a POLITECNICO DI MILANO   (Italy)

^b UNIVERSITY OF PAVIA   (Italy)

^c Collegio Carlo Alberto ^*  (Italy)

Author keywords

Bayesian nonparametrics; Completely random measures; Dependent stable processes; L vy copulas; Posterior distribution; Right censored data; Survival function

Indexed keywords

EID: 78349265306     PISSN: 10170405     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (33)

1. Basu, B. (1971). Bivariate failure rate. J. Amer. Statist. Assoc. 66, 103-104.
2. Bulla, P., Muliere, P. andWalker, S. G. (2007). Bayesian nonparametric estimation of a bivariate survival function. Statist. Sinica 17, 427-444.
3. Cont, R. and Tankov, P. (2004). Financial Modelling with Jump Processes. Chapman & Hall/CRC, Boca Raton, FL.
4. De Blasi, P., Peccati, G. and Prünster, I. (2009). Asymptotics for posterior hazards. Ann. Statist. 37, 1906-1945.
5. De Iorio, M., Müller, P., Rosner, G. L. and MacEachern, S. N. (2004). An ANOVA model for dependent random measures. J. Amer. Statist. Assoc. 99, 205-215.
6. Dey, J., Erickson, R. V. and Ramamoorthi, R. V. (2003). Some aspects of neutral to the right priors. Internat. Statist. Rev. 71, 383-401.
7. Doksum, K. (1974). Tailfree and neutral random probabilities and their posterior distributions. Ann. Probab. 2, 183-201.
8. Draghici, L. and Ramamoorthi, R. V. (2003). Consistency of Dykstra-Laud priors. Sankhyā 65, 464-481.
9. Dunson, D. B., Xue, Y. and Carin, L. (2008). The matrix stick-breaking process: flexible Bayes meta-analysis. J. Amer. Statist. Assoc. 103, 317-327.
10. Dunson, D. B. and Park, J.-H. (2008). Kernel stick-breaking processes Biometrika 95, 307-323.
11. Dykstra, R. L. and Laud, P. (1981). A Bayesian nonparametric approach to reliability. Ann. Statist. 9, 356-367.
12. Ferguson, T. S. (1974). Prior distributions on spaces of probability measures. Ann. Statist. 2, 615-629.
13. Ferguson, T.S. and Phadia, E.G. (1979). Bayesian nonparametric estimation based on censored data. Ann. Statist. 7, 163-186.
14. Ghosh, J. K., Hjort, N. L., Messan, C. and Ramamoorthi, R. V. (2006). Bayesian bivariate survival estimation. J. Statist. Plann. Inference 136, 2297-2308.
15. Gill, R. D. and Johansen, S. (1990). A survey of product-integration with a view toward application in survival analysis. Ann. Statist. 18, 1501-1555.
16. Griffin, J. E. and Steel, M. F. J. (2006). Order-based dependent Dirichlet processes. J. Amer. Statist. Assoc. 101, 179-194.
17. Hjort, N. L. (1990). Nonparametric Bayes estimators based on beta processes in models for life history data. Ann. Statist. 18, 1259-1294.
18. Ishwaran, H. and Zarepour, M. (2009). Series representations for multivariate generalized gamma processes via a scale invariance principle. Statist. Sinica 19, 1665-1682.
19. James, L.F. (2005). Bayesian Poisson process partition calculus with an application to Bayesian Lévy moving averages. Ann. Statist. 33, 1771-1799.
20. Kallsen, J. and Tankov, P. (2006). Characterization of dependence of multidimensional Lévy processes using Lèvy copulas. J. Multivariate Anal. 97, 1551-1572.
21. Kim, Y. and Lee, J. (2001). On posterior consistency of survival models. Ann. Statist. 29, 666-686.
22. Kingman, J. F. C. (1993). Poisson Processes. Oxford University Press, Oxford.
23. Lijoi, A., Prünster, I. and Walker, S. G. (2008). Posterior analysis for some classes of nonparametric models. J. Nonpar. Statist. 20, 447-457.
24. Lin, D. Y. and Ying, Z. (1993). A simple nonparametric estimator of the bivariate survival function under univariate censoring. Biometrika 80, 573-581.
25. Lo, A. Y. and Weng, C.-S. (1989). On a class of Bayesian nonparametric estimates. II. Hazard rate estimates. Ann. Inst. Statist. Math. 41, 227-245.
26. MacEachern, S. N. (1999). Dependent nonparametric processes. In ASA Proceedings of the Section on Bayesian Statistical Science. American Statistical Association, Alexandria, VA.
27. MacEachern, S. N. (2000). Dependent Dirichlet processes. Technical Report. Department of Statistics, Ohio State University.
28. MacEachern, S. N. (2001). Decision theoretic aspects of dependent nonparametric processes. In Bayesian methods with applications to science, policy and official statistics (Edited by E. George), 551-560. International Society for Bayesian Analysis, Crete.
29. Nieto-Barajas, L. E. and Walker, S. G. (2007). A Bayesian semi-parametric bivariate failure time model. Computat. Statist. Data Anal. 11, 529-543.
30. Rodríguez, A. Dunson, D. and Gelfand, A. (2008). The nested Dirichlet process. J. Amer. Statist. Assoc. 103, 1131-1144.
31. Tankov, P. (2003). Dependence structure of spectrally positive multidimensional Lévy processes. Unpublished Manuscript.
32. Walker, S. G. and Muliere, P. (2003). A bivariate Dirichlet process. Statist. Probab. Lett. 64, 1-7.
33. Woolson, R. F. and Lachenbruch, P. A. (1980). Rank tests for censored matched pairs, Biometrika 67, 597-606.