A SIMULATION STUDY OF BAYESIAN PROPORTIONAL HAZARDS MODELS WITH THE BETA PROCESS PRIOR

  • Lee, Jae-Yong (Department of Statistics, Seoul National University)
  • Published : 2005.09.01

Abstract

In recent years, theoretical properties of Bayesian nonparametric survival models have been studied and the conclusion is that although there are pathological cases the popular prior processes have the desired asymptotic properties, namely, the posterior consistency and the Bernstein-von Mises theorem. In this study, through a simulation experiment, we study the finite sample properties of the Bayes estimator and compare it with the frequentist estimators. To our surprise, we conclude that in most situations except that the prior is highly concentrated at the true parameter value, the Bayes estimator performs worse than the frequentist estimators.

Keywords

References

  1. ANDERSEN, P. K., BORGAN, O., GILL, R. D. AND KEIDING, N. (1993). Statistical models based on counting processes, Springer-Verlag, New York
  2. 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
  3. KIM, S. W. AND IBRAHIM, J. G. (2000). 'On Bayesian inference for proportional hazards models using noninformative priors', Lifetime Data Analysis, 6, 331-341 https://doi.org/10.1023/A:1026505331236
  4. 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
  5. 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
  6. KIM, Y. AND LEE, J. (2004). 'A Bernstein-von Mises theorem in the nonparametric rightcensoring model', The Annals of Statistics, 32, 1492-1512 https://doi.org/10.1214/009053604000000526
  7. KLEIN, J. P. AND MOESCHBERGER, M. L. (2003). Survival analysis: techniques for censored and truncated data, Springer, New York
  8. LAUD, P. W., DAMIEN, P. AND SMITH, A. F. M. (2004) . 'Bayesian nonparametric and covariate analysis of failure time data', In Practical nonparametric and semiparametric Bayesian statistics (D. Dey, P. M'uller and D. Sinha, eds), 213-225
  9. LEE, J. AND KIM, Y. (2004). 'Anew algorithm to generate beta processes', Computational Statistics & Data Analysis, 47, 441-453 https://doi.org/10.1016/j.csda.2003.12.008