STATISTICAL METHODS IN HIGH-DIMENSIONAL STRUCTURED DATA

Modern data pose several challenges to statistical analysis. They are not only big in size, high in dimensionality but also complex in structure. For example, diffusion tensor imaging (DTI) measures water diffusion within white matter. A 3D DTI of the brain consists of millions of voxels with a complex structure induced by the anatomical shape of the human brain. The first project is dedicated to studying the association between DTI images, which are a proxy of effective connectivity in the brain, and clinical outcomes. To account for the spatial structure and to reduce the dimensionality, we propose a hierarchical Bayesian "scalar-on-image'' regression method designed specially for aribitary-shaped image data. The second project is concerned with defining and implementing the methodology for fitting populations of separable spatio-temporal processes. Methods were motivated by and applied to functional magnetic imaging (fMRI) studies where large spatial images of the brain are observed at a dense grid of points over time. We show that separability combined with principal component analysis of latent processes provide a fast and feasible tool for dimensionality reduction and model-driven discovery. The third project is dedicated to modeling matrix-valued data observed repeatedly over time. The project was motivated by an accelerometry study which collected minute-level activity intensity data 24 hours a day and 7 days a week. Considering the week as a unit of measurement, the basic measurement unit is a 1440 (minutes within a day) by 7 (days within a week) dimensional matrix. As data are observed for many weeks for the same subject this induces a natural within-subject clustering structure. We use a linear mixed effect model to account for the multilevel design, while the 2D structure is handled via normal matrix-variate distribution. All three proposed methods are scalable and software is available