Date of Award
Doctor of Philosophy (PhD)
School of Mathematical and Statistical Sciences
Dr. Christopher S. McMahan
Dr. Yu-Bo Wang
Dr. Deborah Kunkel
Dr. Xinyi Li
This dissertation focuses on developing high dimensional regression techniques to analyze large scale data using both Bayesian and frequentist approaches, motivated by data sets from various disciplines, such as public health and genetics. More specifically, Chapters 2 and Chapter 4 take a Bayesian approach to achieve modeling and parameter estimation simultaneously while Chapter 3 takes a frequentist approach. The main aspects of these techniques are that they perform variable selection and parameter estimation simultaneously, while also being easily adaptable to large-scale data. In particular, by embedding a logistic model into traditional spike and slab framework and selecting of proper prior distributions, we allow for information injection from side information to guide variable selection. Moreover, we simplify the NP-hard non-convex l0 problem to a weighted LASSO problem by using an approximation to the l0 norm and Generalized Double Pareto (GDP) shrinkage prior collectively. The finite sample performance of our techniques are investigated using extensive numerical simulation studies that are based on the motivating data sets. The methods are then applied to our motivating data sets including human disease surveillance studies, and genetics.
Yang, Yuan, "Advanced High Dimensional Regression Techniques" (2022). All Dissertations. 3144.