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Abstract:
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Brain connectivity analysis is now at the foreground of neuroscience research. A connectivity network is characterized by a graph, where nodes represent brain regions, and links represent statistical dependence that is often encoded by partial correlation. Such a graph is inferred from the matrix-valued neuroimaging data such as electroencephalography and functional magnetic resonance imaging. There have been a good number of successful proposals for sparse precision matrix estimation under normal or matrix normal distribution; however, this family of solutions does not offer a direct statistical significance quantification for the estimated links. We adopt a matrix normal distribution framework and formulate the brain connectivity inference as a precision matrix hypothesis testing problem. Based on the separable spatial-temporal dependence structure, we develop oracle and data-driven procedures to test both the global and marginal hypotheses with false discovery rate control. We study the one-sample and two-sample cases, establish the theoretical properties of our tests, and demonstrate the empirical performance through both simulations and real neuroimaging data analysis.
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