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Abstract:
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In Neurosciences, magnetic resonance imaging (MRI) is a primary modality for studying brain structure and activity. Modeling spatial dependence of MRI data at different scales is one of the main challenges of contemporary neuroimaging. Methods that account for spatial correlation often require very cumbersome matrix evaluations which are prohibitive for data of this size, and thus current methods typically reduce dimensionality by modeling covariance among regions of interest rather than among voxels. However, ignoring spatial dependence at different scales could drastically reduce our ability to detect important activation patterns in the brain. To overcome these problems, we introduce a novel Bayesian Tensor approach, treating the brain image as response and having a vector of predictors. Our method provides estimates of the parameters of interest using a generalized sparsity principle. We demonstrate posterior consistency and develop a computational efficient algorithm. The effectiveness of our approach is illustrated through simulation studies and the analysis of the effects of cocaine addiction on the brain structure.
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