Statistics Colloquium : Dr. Dulal Bhaumik

Abstract: In this article we develop a cluster of models for high dimensional time dependent data with a hierarchical structure. Such data are observed in many research areas, such as neuroimaging, microbiome, and omics. Addressing some of the existing fundamental concerns, we incorporate a flexible spatio type covariance matrix for when distance based space is absent and ensure its positive definiteness property by implementing a special type of Bessel function. Furthermore, we reduce the dimension using Moran basis functions for easing the burden of computation while guaranteeing the convergence and robustness of our estimates. This is achieved through the development of a spatio type weighting matrix utilizing the empirical semivariogram. In multiple ways, we can count the benefits of our approach. First, the hierarchical nature of the proposed spatiotemporal model reduces the noise at different levels, leading to better power in signal detection. Second, our approach decorrelates the temporal association for proper inferential properties and explores the input-output relation, focusing on only spatial correlations. Third, it provides better interpretations of the overall relationship between outcome measures and associated covariates controlling the false discovery rate (FDR). Methodologies developed in this article are then used to detect disrupted connectivity for targeting interventions while comparing autism spectrum disorder to controls using resting state functional magnetic resonance imaging data. A network is built using disrupted connectivity and interpretation of key links in the network is provided in terms of neurobehavioral functions.