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Survival and Reliability Analysis Under Polya Tree Processes Priors

The thesis consists of three components, which are related to survival and lifetime data analysis. We propose a Bayesian nonparametric approach to testing treatment effects and estimating regression coefficients in the Cox proportional hazards model by considering not only the rank statistics, but also the spacings between rank statistics. The Bayesian solution of our approach has a closed form even with censored data, which can be calculated extremely fast and has a ready interpretation. Simulation studies are carried out and the method is applied to analyze a real data set. Finally, we propose a nonparametric estimator for reliability, which degenerates to the well-known Mann Whitney U statistic in special cases.

The thesis consists of three components, which are related to survival and lifetime data analysis.