Bayesian survival analysis using Bernstein polynomials

Scandinavian Journal of Statistics

Volumn 32, Issue 3, 2005, Pages 447-466

  Chang, I Shou ^a   Hsiung, Chao A ^a   Yuh Jenn, W U ^a   Yang, Che Chi ^b  

^a NATIONAL HEALTH RESEARCH INSTITUTES   (Taiwan)

^b LUNGHWA UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Taiwan)

Author keywords

Beta process prior; Geometric prior; Markov chain Monte Carlo; Random Bernstein polynomials; Right censored data

Indexed keywords

EID: 24344484769     PISSN: 03036898     EISSN: None     Source Type: Journal    
DOI: 10.1111/j.1467-9469.2005.00451.x     Document Type: Review

References (31)

1. Altomare, F. & Campiti, M. (1994). Korovkin-type approximation theory and its application. W. de Gruyter, Berlin.
2. Arjas, E. & Gasbarra, D. (1994). Nonparametric Bayesian inference from right censored survival data using the Gibbs sampler. Statist. Sinica 4, 505-524.
3. Berk, R. H. (1966). Limiting behavior of posterior distributions when the model is incorrect. Ann. Math. Statist. 37, 51-58.
4. Berk, R. H. (1970). Consistency of a posteriori. Ann. Math. Statist. 41, 894-906.
5. Billingsley, P. (1968). Convergence of probability measures. Wiley, New York.
6. Bunke, O. & Milhaud, X. (1998). Asymptotic behavior of Bayes estimates under possibly incorrect models. Ann. Statist. 26, 617-644.
7. Chang, I. S., Wu, Y. J., Wen, C. C. & Hsiung, C. A. (2004). Isotonic regression and concave regression with random Bernstein polynomials (Preprint).
8. De Boor, C. (1978). A practical guide to splines. Springer-Verlag, New York.
9. 1 view. John Wiley & Sons, New York.
10. Gammerman, D. (1991). Dynamic Bayesian models for survival data. Appl. Statist. 40, 63-79.
11. Ghosh, J. K. & Ramamoorthi, R. V. (1995). Consistency of Bayesian inference for survival analysis with or without censoring. In Analysis of Censored Data (eds H. L. Koul & J. V. Deshpande), 27, 95-103. IMS, Hayward, CA.
12. Green, P. G. (1995). Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika 82, 711-732.
13. Hall, P., Huang, L. S., Gifford, J. A. & Gijbels, I. (2001). Nonparametric estimation of hazard rate under the constraint of monotonicity. J. Comput. Graph. Statist. 10, 592-614.
14. Hjort, N. L. (1990). Nonparametric Bayes estimators based on beta process in models for life history data. Ann. Statist. 18, 1259-1294.
15. Ibrahim, J. G., Chen, M. H. & Sinha, D. (2001). Bayesian survival analysis. Springer-Verlag, New York.
16. Kim, Y. & Lee, J. (2001). On posterior consistency of survival models. Ann. Statist. 29, 666-686.
17. Lorentz, C. G. (1986). Bernstein polynomials. Chelsea, New York.
18. McKeague, I. W. & Tighiouart, M. (2000). Bayesian estimators for conditional hazard functions. Biometrics 56, 1007-1015.
19. McKeague, I. W. & Tighiouart, M. (2002). Nonparametric Bayes estimators for hazard functions based on right censored data. Tamkang J. Math. 33, 173-189.
20. Nair, V. N. (1984). Confidence bands for survival functions with censored data: a comparative study. Technometrics 26, 265-275.
21. Petrone, S. (1999). Random Bernstein polynomials. Scand. J. Statist. 26, 373-393.
22. Petrone, S. & Wasserman, L. (2002). Consistency of Bernstein polynomial posteriors. J. Roy. Statist. Soc. Ser. B 64, 79-100.
23. Prautzsch, H., Boehm, W. & Paluszny, M. (2002). Bezier and B-spline techniques. Springer-Verlag, Berlin, Heidelberg.
24. Robert, C. P. & Casella, G. (1999). Monte Carlo statistical methods. Springer-Verlag, New York.
25. Rudin, W. (1976). Principles of mathematical analysis, 3rd edn. McGraw-Hill, New York.
26. Sinha, D. & Dey, D. K. (1997). Semiparametric Bayesian analysis of survival data. J. Amer. Statist. Assoc. 92, 1195-1212.
27. Sinha, D. & Dey, D. K. (1998). Survival analysis using semiparametric Bayesian methods. In Practical nonparametric and semiparametric Bayesian statistics (eds D. K. Dey, P. Müller & D. Sinha), 195-211. Springer-Verlag, New York.
28. Tierney, L. (1994). Markov chains for exploring posterior distributions. Ann. Statist. 22, 1701-1728 (discussion: 1728-1762).
29. van der Vaart, A. W. & Wellner, J. A. (1996). Weak convergence and empirical processes. Springer-Verlag, New York.
30. van der Vaart, A.W. (1998). Asymptotic statistics. Cambridge University Press, Cambridge.
31. Walker, S. & Muliere, P. (1997). Beta-Stacy processes and a generalization of Polya-urn scheme. Ann. Statist. 25, 1762-1780.