Publication Date

2025

Document Type

Dissertation/Thesis

First Advisor

Ryu, Duchwan

Degree Name

Ph.D. (Doctor of Philosophy)

Legacy Department

Department of Mathematical Sciences

Abstract

Functional Data Analysis (FDA) is a statistical approach used to analyze data that vary across a domain, such as curves or functions. This dissertation investigates Bayesian Functional Data Analysis (BFDA) through three applications. First, we explore the use of BFDA in outcome-dependent follow-up (ODFL) studies. After conducting simulation studies, we apply our model to cardiotoxicity and kidney function data. Second, we extend BFDA to genetic data by modeling DNA methylation levels with a three-parameter skew-normal distribution and an alpha-skew generalized normal distribution. This study also introduces a novel Multistage Markov Chain Monte Carlo (MMCMC) method with the goal of identifying differentially methylated regions. Additionally, our MMCMC model is applied to 450K microarray datasets. Finally, we apply multivariate BFDA to brain data, utilizing multivariate smoothing splines (MSS) to model multi-dimensional responses and proposing a weighted distance matrix for functional clustering analysis (FCw). Two simulation studies are conducted to evaluate the performance of the proposed MSS and FCw methods, which are then applied to classify neural activity in mice.

Extent

165 pages

Language

en

Publisher

Northern Illinois University

Rights Statement

In Copyright

Rights Statement 2

NIU theses are protected by copyright. They may be viewed from Huskie Commons for any purpose, but reproduction or distribution in any format is prohibited without the written permission of the authors.

Media Type

Text

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