Modern technologies for imaging brain activity, such as functional MRI, are very useful in studying mechanisms for human brain. In this thesis, statistical methods and computational techniques are developed to investigate brain function through fMRI. In particular, we are interested in the activation of human brain networks and learning patterns. In the first component of the work, we developed a new group ICA approach, Homotopic Group ICA (;;H-gICA”), which seeks to identify networks of correlated regions across subjects and measures the degree of synchrony in spontaneous activity between geometrically corresponding interhemispheric brain regions. H-gICA is able to increase the potential for network discovery and facilitate the investigation of functional homotopy via ICA based networks. In the second part of the work, we develop methodology for an investigation of motor learning using activation distributions. We investigate tests of dimension for detect- ing learning-based changes, particularly motor learning. Our investigation includes a large scale simulation study of brain activation maps, motivated by a study of motor learning in healthy adults. In the third part of the work, we devise an approach to phenotype classification from gene expression profiling. We propose a new high dimensional discriminant analysis method called group Nearest Shrunken Centroids (gNSC), which enables us to use gene pathway information. We also apply our method on a novel context analysis of association between pathways and certain medical words to improve the power of feature selection.
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STATISTICAL METHODS FOR BRAIN IMAGING AND GENOMIC DATA ANALYSIS
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