Functional magnetic resonance imaging (fMRI) provides rich measurements of brain activity and has become an important tool for studying brain organization, individual variation, and brain-covariate associations. However, fMRI data are often high-dimensional, structurally complex, and heterogeneous across subjects, which poses challenges for statistical analysis. This dissertation develops flexible and interpretable statistical methodologies for analyzing complex fMRI data.

The first part of this dissertation focuses on higher-order relationships in the brain. We introduce centered edge functional connectivity (ceFC) as an unbiased measure of covariation between brain edges, study its estimation under both classical and high-dimensional regimes, and develop a multiple hypothesis testing framework to identify nonzero edge-level associations while controlling the false discovery rate.

The second part investigates whether the proposed ceFC provides additional predictive information for phenotypic traits beyond conventional node-centric functional connectivity (nFC) within a brain-wide association study framework. The empirical results show that when a sufficient set of information from nFC is included, features extracted from ceFC provide limited additional predictive benefit.

The third part studies image response regression under dynamic naturalistic stimuli. We propose a flexible spatio-temporal image response regression via neural networks (ST-IRRNN) to estimate dynamic coefficient functions. We also introduce several ST-IRRNN variants designed to accommodate different forms of spatio-temporal dependence. Numerical studies demonstrate improved estimation accuracy and temporal stability compared to fixed-window spatial baselines. Additionally, an application to a naturalistic movie-watching fMRI dataset shows that the proposed methods effectively recover scene-dependent effects of stimuli across large-scale brain systems.

Overall, this dissertation contributes new statistical methods for studying both connectivity structure and dynamic effects in fMRI data. These tools provide new perspectives for understanding brain organizations and brain associations with phenotypes, behaviors, and continuous naturalistic stimuli.