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Sparse Partitioned Empirical Bayes Ecm Algorithms For High-Dimensional Linear Mixed Effects And Heteroscedastic Regression, Anja Zgodic

Theses and Dissertations

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, …