Bayesian Estimation for Censored Data: An Experiment in Sensitivity Analysis

Abstract

We consider the problem of estimating an unknown distribution function F in the presence of censoring under the conditions that a parametric model is believed to hold approximately. We use a Bayesian approach, in which a mixture of Dirichlet priors is put on the unknown F. A hyperparameter of the prior dictates the extent to which this prior concentrates its mass around the parametric family. The output of a successive substitution sampling algorithm is used to estimate the posterior distributions of the parameters of interest. We develop an importance sampling scheme that enables us to use the output of the successive substitution sampling algorithm to very quickly recalculate the posterior when we change the prior. The calculations can be done sufficiently fast to enable the dynamic display of the changing posterior as the prior is varied.

Research supported by Air Force Office of Scientific Research Grant 90-0202. I thank Shau-Ming Wu for his help in the development of the Xlisp-Stat programs used to analyze the prostate cancer data in Sect. 4.