Publication Date

Spring 3-28-2017

Abstract

1. "Parametric Bootstrap (PB) and Objective Bayesian (OB) Testing with Applications to Heteroscedastic ANOVA": For one-way heteroscedastic ANOVA, we show a close relationship between the PB and OB approaches to significance testing, demonstrating the conditions for which the two approaches are equivalent. Using a simulation study, PB and OB performance is compared to a test based on the predictive distribution as well as the unweighted test of Akritas & Papadatos (2004). We extend this work to the RCBD with subsampling model, and prove a repeated sampling property and large sample property for general OB significance testing.

2. "Early Identification of Binswanger's Disease Patients Using Random Forests": We use cross validation to compare several methods for predicting if vascular dementia patients are of the Binswanger type or if they more likely suffer from some other small vessel disease. We investigate which biomarkers are most important for classification, and see that a random forest algorithm accurately identifies Binswanger's patients years before a clinical diagnosis can be ascertained.

3. "High-Throughput Gene Expression Analysis Under the Case-Cohort Study Design": The case-cohort study design blends the efficiency of case control studies with the philosophical soundness of full cohort studies, and presents an efficient way to analyze survival data, particularly for large cohorts with low failure rates. Using a tandem of real data examples and simulation studies, we investigate the performance of the most popular case-cohort analysis approaches in the context of high-dimensional biomarker evaluation.

Degree Name

Statistics

Level of Degree

Doctoral

Department Name

Mathematics & Statistics

First Committee Member (Chair)

Guoyi Zhang

Second Committee Member

Ronald Christensen

Third Committee Member

Huining Kang

Fourth Committee Member

Yan Lu

Language

English

Keywords

Parametric Bootstrap, Bayesian Significance Testing, Random Forests, Binswanger's Disease, Case-Cohort Design, High-Throughput Gene Expression

Document Type

Dissertation

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