Date of Award

6-30-2016

Document Type

Open Access Dissertation

Department

Statistics

First Advisor

Timothy E. Hanson

Abstract

Dependent data are very common in many research fields, such as medicine (repeated measures), finance (time series), traffic (clustered), etc. Effective control/modeling of the dependency among data can enhance the performance of the models and result in better prediction. In many cases, the correlation itself may be of great interest. In this dissertation, we develop novel Bayesian semi-/nonparametric regression models to analyze data with various dependence structures. In Chapter 2, a Bayesian non- parametric multivariate ordinal regression model is proposed to fit drinking behavior survey data from DWI offenders. The responses are two-dimensional ordinal data, drinking frequency and drinking quantity at each occasion. In Chapter 3, we develop a hierarchical Gaussian process model to analyze repeated hearing test data of pe- diatric cancer patients. A penalized B-spline is used to capture the overall trend of the curve. Individual intercepts and slopes as random effects are allowed to model individual deviation from the population mean. Since the curves are theoretically smooth, a hierarchical Gaussian process is assumed on top of the individual-specific mean function. In Chapter 4, we propose a constructive approach to imposing a mean constraint in a finite mixture of multivariate normal densities. Implemented in a linear mixed model, the effectiveness of the constraint is verified by both simulation and data analysis using longitudinal cholesterol data.

Rights

© 2016, Junshu Bao

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