NOVEL APPROACHES TO ANALYZING TIME SERIES OF OBJECTS WITH APPLICATIONS TO BRAIN CONNECTIVITY

This project is motivated by the problem of characterizing “brain connectivity” networks. This is a significant problem because the variation in the organization of brain functional networks is linked to behavior, psychological traits, and clinical pathophysiology. One challenge here is that there is no unique characterization of brain connectivity and consequently there is no coherent rigorous procedure for conducting formal statistical inference. This proposal will address these limitations by developing a statistical framework for analyzing complex "objects" such as the time-evolving higher-order spectral matrices; topological features from these high-dimensional spectral matrices; and frequency-specific time-evolving communities derived from graphical networks. We will develop novel statistical approaches that will address the new challenges to analyzing these objects which include (a.) characterizing distributions of these objects; (b.) characterizing temporal dynamics of these objects; (c.) extracting differences in these objects across various populations (control vs disease); (d.) finding associations between these physiologically-derived objects and outcomes such as behavior.