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On the analysis of event-related potential and electroencephalographic data: Spatio-temporal modeling, variography, and simulation
National awareness of Traumatic Brain Injuries (TBI) has recently increased due to higher incidence among military personnel, as well as to high profile lawsuits and rule-changes in North American professional sports. TBI affect both short-term and long-term brain and behavior mechanisms associated with cognitive deficits which are commonly measured using Event-Related Potential (ERP) data. Unfortunately, sophisticated methodology for ERP data analysis has not yet been established. In this dissertation, I present novel approaches to modeling ERP data in the context of spatio-temporal Gaussian random fields with the purpose of aiding TBI diagnosis in college athletes. First, I employ a flexible, non-separable "sum-metric" spatio-temporal model to represent ERP assessments collected during a working memory task, and utilize the estimated parameters to classify athletes as either being healthy or suffering from TBI. Results indicate that parameter estimates provide a promising basis for accurate ERP classification when applied to the Match condition of the memory task. Next, I develop a novel measure of dissimilarity between two spatio-temporal variogram surfaces. In addition, I detail a method of generating ERP data in the spatio-temporal domain for both healthy subjects and subjecs suffering from TBI. Classification accuracy of the proposed measure is examined for both simulated ERP data and ERP collected from college athletes. Results indicate that the proposed measure of dissimilarity successfully separates two populations of ERP assessments - for both real and simulated data - that are different only according to their variance-covariance matrices. Lastly, I present a method of approximating the ML and REML likelihood functions in the context of parameter estimation for moderately large, non-stationary spatial data. Partial Singular Value Decomposition (SVD) is used to approximate the spatial variance-covariance matrix in order to increase speed of convergence. Approximated parameter estimates are subsequently examined for presence, degree, and direction of estimation bias through the use of a simulation. Results suggest that spatial process parameter estimates are generally downward biased, whereas spatial trend parameter estimates remain unbiased. As expected, partial SVD approximation resulted in a significant increase in speed of computation for both ML and REML-based models.
Chernyavskiy, Pavel, "On the analysis of event-related potential and electroencephalographic data: Spatio-temporal modeling, variography, and simulation" (2015). ETD collection for University of Nebraska - Lincoln. AAI3689706.