Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


Mathematical Sciences

Committee Chair/Advisor

Christopher McMahan

Committee Member

Lior Rennert

Committee Member

Deborah Kunkel

Committee Member

Xinyi Li


More than ever before, technology is evolving at a rapid pace across the broad spectrum of biological sciences. As data collection becomes more precise, efficient, and standardized, a demand for appropriate statistical modeling grows as well. Throughout this dissertation, we examine a variety of new age data arising from modern technology of the 21st century. We begin by employing a suite of existing statistical techniques to address research questions surrounding three medical conditions presenting in public health sciences. Here we describe the techniques used, including generalized linear models and longitudinal models, and we summarize the significant associations identified between research groups and relevant covariates for each setting. These results can better guide treatment and intervention strategies for health care professionals. Next we implement a pipeline of morphometric analyses on 3D image data to compare craniofacial features between people with and without the genetic disorder, Phelan-McDermid Syndrome. The pre-processing steps for morphometric data are described in detail, and a principle component analysis is used to quantify physical deformities of the PMS group. Identification of the physical features associated with PMS can aid health care professionals in the early stages of diagnosis. Additionally, the pipeline of analyses presented may be adapted for similar geometric analyses. Finally, we propose a novel extension to standard genomic prediction models for complex phenotypes. Advances in genome sequencing technology has brought the use of statistical genetics to the forefront of many plant breeding programs. Standard genomic prediction models rely on genetic correlations to enjoy improvements in prediction accuracy. In this work, we propose a multi-level Bayesian prediction model, which uses secondary responses along with a known non-linear relationship to the primary response, capable of more accurately modeling a complex phenotype. We demonstrate the performance gains via a simulation study and also discuss possible extensions.

Available for download on Sunday, December 31, 2023