Advisory Committee Chair
Advisory Committee Members
Lloyd J Edwards
Rajesh K Kana
Date of Award
Degree Name by School
Doctor of Philosophy (PhD) School of Public Health
Many applications in neuroscience, psychology, medicine, and public health require collecting and analyzing imaging data. While fine resolution images may appear continuous to the naked eye, they are in fact made up of measurements at discrete locations, either pixels in 2D or voxels in 3D. These data may be treated as the scientific outcomes of interest, or as predictors of outcomes of interest. Here, the concern is with the latter situation, which involves converting images into formats amenable to a linear modeling framework; i.e., each subject’s image is converted into a vector, and used to model the subject’s (scalar) outcome of interest. Imaging data can complicate statistical analyses because using images as predictors can make traditional linear models invalid, or non-identifiable, for two reasons. First, images usually contain as many or more pixels or voxels, i.e., predictors, as subjects. Second, the measurements taken from images are usually highly correlated. Both situations violate the assumptions of traditional linear models. In contrast, Bayesian linear models can circumvent these issues but require principled approaches to selecting prior distributions. The primary goal of this work is to explore and develop a class of priors that is relevant to modeling scalar outcomes using images. The outline of this work is as follows. After a review of literature, the first paper develops and presents an R package, sim2Dpredictr, for simulating data in a situation where images are used to model scalar outcomes; this package is freely available on CRAN. The second paper extends the spike-and-slab lasso prior by generalizing it to the spike-and-slab elastic net, and by incorporating spatial structure explicitly into variable selection using Intrinsic Autoregressions (IAR) as priors; an R package to fit the models, ssnet, is available on github. We evaluate the proposed models with a simulation study by generating data with sim2Dpredictr. The final paper demonstrates the practical utility of the methods by applying them to classification problems using data from the Alzheimer’s Disease Neuroimaging Initiative (ADNI). Finally, we summarize the contributions of the dissertation, and discuss future research directions.
Leach, Justin, "Incorporating Spatial Structure into Bayesian Variable Selection Using Spike-and-Slab Priors with Application to Imaging Data" (2020). All ETDs from UAB. 837.