Date of Award

2012

Document Type

Campus Access Dissertation

Department

Statistics

First Advisor

Timothy E Hanson

Abstract

My dissertation considers three related topics involving censored or truncated survival data. All three topics utilize a nonparametric family of densities that are centered at a parametric family such as the Weibull, normal, or log-logistic, specifically the Polya tree prior and a novel transformed Bernstein polynomial prior. Both priors start from an initial parametric model, but then allow data to add details that deviate from the parametric family; thus both priors blend the merits of parametric and nonparametric models, such as robustness for density estimation and increased power for hypothesis testing. The three topics are: (i) The formulation of a test statistic that is a Bayes factor constructed from independent marginalized Polya tree priors, where the Polya tree centering distributions are Gaussian with parameters estimated from the data; as the test statistic is very fast to compute, p-values can be obtained through a standard permutation test. (ii) Building a Bayesian nonparametric approach to density estimation based on transformed Bernstein polynomial priors. The smoothness of the prior allows efficient estimation via standard maximization routines. The transformed Bernstein polynomial is then incorporated into the accelerated hazards model and further generalized to accommodate covariates that are time-dependent. (iii) Fleshing out a nonparametric approach to density estimation for truncated data via fully specified Polya trees.

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