Speaker: Zhiling Gu, Ph.D. candidate, Department of Statistics, Iowa State University

Title: Statistical Learning and Inference of Surface-based Functional Data with Applications in Neuroimaging Analysis

Abstract: Surface-based neuroimaging analysis has gained significant attention in recent years due to its ability to capture fine-grained spatial information and provide insights into brain structure and function. In this paper, we present an advanced nonparametric method for learning and inferring for surface-based functional data, facilitating accurate estimation of underlying signals and efficient detection and localization of significant effects. We propose a framework that leverages advanced statistical modeling approaches, including spherical splines on triangulations and next-generation function data analysis, to handle the challenges associated with surface-based data, such as irregular sampling and spatial dependencies. Furthermore, we propose a novel approach for constructing simultaneous confidence corridors (SCCs), which effectively quantify estimation uncertainty. These SCCs provide a comprehensive representation of the uncertainty in the estimated functional patterns and facilitate reliable inference. Furthermore, the procedure is extended to accommodate comparisons between groups of samples, enabling the analysis of group differences or treatment effects. We establish the asymptotic properties of the proposed estimators and SCCs, and provide a computationally efficient procedure for constructing the SCCs. To evaluate the finite-sample performance, we conduct numerical experiments and apply the methods to real-data analysis using the cs-fMRI data provided by the Human Connectome Project Consortium (HCP).