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Functional brain imaging methods have contributed enormously to our knowledge of the anatomic location of particular brain functions. However, there remains a significant gap in our understanding of how these regions communicate as part of a distributed network. This shortcoming is due in large part to the scarcity of information on the connectivity of the human brain compared to, for example, our knowledge of such anatomy in lower primates. Recently, investigators have undertaken to infer neuroanatomic connectivity from magnetic resonance diffusion imaging, an MRI method which measures the molecular mobility of the endogenous water in tissue. The method is based on the observation that in fibrous tissues such as skeletal muscle and white matter, the diffusion is greater along the direction of the fibers relative to, for example, the perpendicular direction. The direction of greatest diffusion provides an indication of the local white matter fiber direction within each voxel. The connectivity inference problem is then, simply stated, how to infer large-scale neuroanatomic connectivity from such fiber direction maps. Here, we present a physically-motivated, statistical framework for the connectivity inference problem. The particular benefits of the formulation include encapsulation of the unresolved aspects of the problem, and a statistical construction suitable for hypothesis testing of anatomical connectivity differences between groups of subjects.