Anja Zgodic

Date of Award

Spring 2023

Document Type

Open Access Dissertation



First Advisor

Alexander C. McLain


Variable selection methods in both the frequentist and Bayesian frameworks are powerful techniques that provide prediction and inference in high-dimensional linear regression models. These methods often assume independence between observations and normally distributed errors with the same variance. In practice, these two assumptions are often violated. To mitigate this, we develop efficient and powerful Bayesian approaches for linear mixed modeling and heteroscedastic linear regression. These method offers increased flexibility through the development of empirical Bayes estimators for hyperparameters, with computationally efficient estimation through the Expectation Conditional-Minimization (ECM) algorithm. The novelty of these approaches lies in the partitioning and parameter expansion, which allows maximum a posteriori probability (MAP) estimation of parameters. We illustrate Linear Mixed Modeling and Heteroscedastic Linear Regression with a PaRtitiOned empirical Bayes ECM algorithms. We term these methods LMM-PROBE and H-PROBE, respectively. We examine the empirical properties of LMM-PROBE and H-PROBE through simulation studies and data analysis using real-world datasets. An example for LMM-PROBE is provided using the riboflavin dataset, where we identify genes associated with the decline of riboflavin production in recombinant Bacillus subtilis bacteria and predict production rate over time. An example for H-PROBE is provided using data from a neuroscience study of the brain, where we predict the aphasia quotient, a measure of severity of language impairment, and model its variance using relevant clinical predictors.


© 2023, Anja Zgodic

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