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POSTERIOR COMPUTATION OF SURVIVAL MODEL WITH DISCRETE APPROXIMATION  

Lee, Jae-Yong (Department of Statistics, Seoul National University)
Kwon, Yong-Chan (Department of Statistics, Seoul National University)
Publication Information
Journal of the Korean Statistical Society / v.36, no.2, 2007 , pp. 321-333 More about this Journal
Abstract
In the proportional hazard model with the beta process prior, the posterior computation with the discrete approximation is considered. The time period of interest is partitioned by small intervals. On each partitioning interval, the likelihood is approximated by that of a binomial experiment and the beta process prior is by a beta distribution. Consequently, the posterior is approximated by that of many independent binomial model with beta priors. The analysis of the leukemia remission data is given as an example. It is illustrated that the length of the partitioning interval affects the posterior and one needs to be careful in choosing it.
Keywords
Beta process; discrete approximation; Markov chain Monte Carlo; proportional hazard model;
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1 Cox, D. R. (1972). 'Regression models and life-tables', Journal of the Royal Statistical Society, Ser. B, 34, 187-220
2 DOKSUM, K. (1974). 'Tailfree and neutral random probabilities and their posterior distributions', The Annals of Probability, 2, 183-201   DOI   ScienceOn
3 FERGUSON, T. S. AND PHADIA, E. G. (1979). 'Bayesian nonparametric estimation based on censored data', The Annals of Statistics, 7, 163-186   DOI
4 KIM, Y. AND LEE, J. (2001). 'On posterior consistency of survival models', The Annals of Statistics, 29, 666-686   DOI
5 LEE, J. AND KIM, Y. (2004). 'A new algorithm to generate beta processes', Computational Statistics & Data Analysis, 47, 441-453   DOI   ScienceOn
6 IBRAHIM, J. G., CHEN, M.-H. AND SINHA, D. (2001). Bayesian Survival Analysis, SpringerVerlag, New York
7 KALBFLEISCH, J. D. (1978). 'Non-parametric Bayesian analysis of survival time data', Journal of the Royal Statistical Society, Ser. B., 40, 214-221
8 LEE, J. (2007). 'Sampling methods of neutral to the right process', Journal of Computational and Graphical Statistics, To appear
9 LAUD, P. W., DAMIEN, P. AND SMITH, A. F. M. (1998). 'Bayesian nonparametric and covariate analysis of failure time data', In Practical nonparametric and semiparametric Bayesian statistics, volume 133 of Lecture Notes in Statistics (Dey, D. et al. eds.), 213-225, Springer-Verlag, New York
10 WOLPERT, R. L. AND ICKSTADT, K. (1998). 'Simulation of Levy random fields', In Practical nonparametric and semiparametric Bayesian statistics, volume 133 of Lecture Notes in Statistics, (Dey, D. et al. eds.), 227-242, Springer-Verlag, New York
11 KIM, Y. AND LEE, J. (2003). 'Bayesian analysis of proportional hazard models', The Annals of Statistics, 31, 493-511   DOI
12 FERGUSON, T. S. (1973). 'A Bayesian analysis of some nonparametric problems', The Annals of Statistics, 1, 209-230   DOI
13 HJORT, N. L. (1990). 'Nonparametric Bayes estimators based on beta processes in models for life history data', The Annals of Statistics, 18, 1259-1294   DOI