UC Berkeley

The dissertation makes contributions to two critical inferential problems in brain science.

The first problem is detecting effective connectivity from time series measurements of brain activity. Chapter 2 studies effective connectivity inference for a specific subject. We develop both global and simultaneous testing procedures to connectivity pattern, and establish their asymptotic guarantees. We show the finite-sample performance of tests through intensive simulations, and illustrate with a neuroimaging based brain connectivity analysis. Chapter 3 extends the scenario to multi-subject effective connectivity inference. The motivation originates from elucidating subject covariate effects on brain effective connectivity in multi-subject function resonance imaging experiments. We propose a new model to explain how covariates change connectivity patterns among subjects. We develop a testing procedure on the model parameters of covariate effects with false discovery rate (FDR) control. Thorough numerical experiments and a HCP fMRI data analysis demonstrate the superior performance of the method.

The second problem is recovering strong association between brain cognitive function and regional cortical physiological features. Such an association is complex and nonlinear that existing solutions in linear models are inadequate to capture. Chapter 4 studies detecting the strong association, equivalently variable selection, in nonparametric additive model. We show that the proposed method is guaranteed to control FDR even the sample size does not tend to infinity, and achieves a power that approaches one as the sample size tends to infinity. We demonstrate the efficacy of the method through intensive simulations and comparisons with the alternative solutions.