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In neuroscience, functional brain connectivity describes the connectivitybetween brain regions that share functional properties. Neuroscientists oftencharacterize it by a time series of covariance matrices between functionalmeasurements of distributed neuron areas. An effective statistical model forfunctional connectivity and its changes over time is critical for betterunderstanding the mechanisms of brain and various neurological diseases. Tothis end, we propose a matrix-log mean model with an additive heterogeneousnoise for modeling random symmetric positive definite matrices that lie in aRiemannian manifold. The heterogeneity of error terms is introducedspecifically to capture the curved nature of the manifold. We then propose touse the local scan statistics to detect change patterns in the functionalconnectivity. Theoretically, we show that our procedure can recover all changepoints consistently. Simulation studies and an application to the HumanConnectome Project lend further support to the proposed methodology.

Modeling Symmetric Positive Definite Matrices with An Application to Functional Brain Connectivity