All ETDs from UAB

Advisory Committee Chair

Nengjun Yi

Advisory Committee Members

Byron C Jaeger

Dorothy Leann Long

Akm F Rahman

Michael E Seifert

Document Type


Date of Award


Degree Name by School

Doctor of Philosophy (PhD) School of Public Health


There are proposals that extend classical additive models (AMs) to accommodate high-dimensional data (p >> n) using group sparse regularization. However, the sparse regularization may induce excess shrinkage when estimating smooth functions, damaging predictive performance. Moreover, most of these AMs consider an “all-in-allout” approach for functional selection, rendering them difficult to answer if nonlinear effects are necessary. While some Bayesian models can address these shortcomings, model fitting can create a new challenge, scalability. In this dissertation, we propose Bayesian hierarchical additive models to address the previous shortcomings: we consider the smoothing penalty for proper shrinkage of curve interpolation via reparameterization. A novel two-part spike-and-slab LASSO prior for smooth functions is developed to address the sparsity of signals while providing extra flexibility to select the linear or nonlinear components of smooth functions. The proposed prior applies to both the generalized additive model framework and the Cox proportional hazards framework. Computational-wise, we develop scalable and deterministic algorithms, including the EM-coordinate Descent algorithm, to alleviate the computational burden of fitting Bayesian models. Via Monte Carlo studies and real-world data applications, we demonstrate improved predictive and computational performance of the proposed Bayesian hierarchical additive model against state-ofthe- art models. To improve the accessibility of the proposed models, we offer a freely available software BHAM that implements Bayesian hierarchical additive models in the R programming environment. Specifically, the package includes functions to fit geniii eralized additive models and additive Cox proportional hazards models with the two-part spike-and-slab LASSO prior. In addition, it supplies other utility functions to construct additive function formulas in high-dimensional settings, select optimal models, summarize bi-level variable selection results, and visualize nonlinear effects. Interested readers can access the software BHAM via the public GitHub repository at In conclusion, the dissertation contributes to the current literature on flexible modeling of complex signals for high-dimensional data analysis. The proposed models can be widely applied in molecular and clinical data analysis to inform biomedical research.

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