Bayesian nonparametric density estimation and sufficient dimension reduction in survival analysis

Shraddha S Mehta, Purdue University

Abstract

Sufficient dimension reduction with logistic Gaussian process priors have been used successfully in a Bayesian nonparametric regression setting. In this thesis, we describe extensions of these methods to handle time-to-event data. We consider both a partial-likelihood approach, where we model the hazard function, and a full-likelihood approach, where we model the density. In both cases, our approach simultaneously estimates the covariate subspace and the conditional density given this subspace. Simulation studies are used to compare these methods with random survival forests and Cox's proportional hazards model in terms of identifying important covariates and predicting survival. These studies show that our two approaches result in more consistent covariate selection and our full-likelihood method results in more accurate predictions.

Degree

Ph.D.

Advisors

Ghosh, Purdue University.

Subject Area

Statistics

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