Studies in Reliability Theory and Survival Analysis and in Markov Chain Monte Carlo Methods

Abstract : The focus of the work has been the development of Markov chain "Monte Carlo" methods in Bayesian analysis, with emphasis on applications to survival or reliability data. We have emphasized the development of methods of dealing with analysis of sensitivity to the prior distribution. In analyzing survival data coming from reliability studies, if we are interested in estimating the distribution of the lifelength of a component, we can use a nonparametric model or a parametric model. A nonparametric model will always give valid estimates, but these are considerably more variable than estimates from a parametric model. On the other hand, parametric models give estimates that may be bad if the model does not conform to the real-world situation. For parametric models, it is necessary to obtain Bayesian parameter estimates, and this can only be done with "Monte Carlo" simulation methods. We have simplified the standard "hyperparameter" method by introducing an importance sampling scheme; this reduces the Monte Carlo estimate to considering only one prior. An interactive parameter control environment was introduced. A detailed example has been worked out involving predictions made in an "interval censored" study on breast cancer and chemotherapy response. Estimates of the heavy-tailed treatment results have been encouraging.