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)
  • 발행 : 2007.06.30

초록

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.

키워드

참고문헌

  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 https://doi.org/10.1214/aop/1176996703
  3. FERGUSON, T. S. (1973). 'A Bayesian analysis of some nonparametric problems', The Annals of Statistics, 1, 209-230 https://doi.org/10.1214/aos/1176342360
  4. FERGUSON, T. S. AND PHADIA, E. G. (1979). 'Bayesian nonparametric estimation based on censored data', The Annals of Statistics, 7, 163-186 https://doi.org/10.1214/aos/1176344562
  5. HJORT, N. L. (1990). 'Nonparametric Bayes estimators based on beta processes in models for life history data', The Annals of Statistics, 18, 1259-1294 https://doi.org/10.1214/aos/1176347749
  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. KIM, Y. AND LEE, J. (2001). 'On posterior consistency of survival models', The Annals of Statistics, 29, 666-686 https://doi.org/10.1214/aos/1009210685
  9. KIM, Y. AND LEE, J. (2003). 'Bayesian analysis of proportional hazard models', The Annals of Statistics, 31, 493-511 https://doi.org/10.1214/aos/1051027878
  10. 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
  11. LEE, J. (2007). 'Sampling methods of neutral to the right process', Journal of Computational and Graphical Statistics, To appear
  12. LEE, J. AND KIM, Y. (2004). 'A new algorithm to generate beta processes', Computational Statistics & Data Analysis, 47, 441-453 https://doi.org/10.1016/j.csda.2003.12.008
  13. 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