Abstract: Autism spectrum disorder is a neurodevelopmental condition characterized by difficulties with social interactions, communication, and restricted or repetitive behaviors. In this talk, I discuss how my lab is developing statistical methods to better characterize resting-state and task-based functional connectivity in autistic children. In the first part, we review current approaches to address motion artifacts in resting-state fMRI data. These approaches use nuisance regression of motion-alignment parameters combined with scrubbing of high-motion volumes. Participants with insufficient low-motion data are removed from the study. We show this leads to selection bias, as children with more severe autism symptoms tend to move more. We use ensemble learning without scrubbing or participant removal to reduce motion artifacts. We develop a causal inference framework to estimate the effect of stimulant medication on the correlations between brain regions. In the second part of the talk, we analyze task-based fMRI and formulate covariance regression using generalized estimating equations (GEE). We review the basic formulation of the general linear model for task activation in fMRI. We then extend this framework to model the effect of task predictors on the time-varying covariance of the fMRI signal. The framework uses a log-Euclidean link function with sandwich variance estimators for inference. We apply this method to examine the impact of movie watching on brain connectivity.