Montse Fuentes - Colloquium Speaker
Imaging data with thousands of spatially-correlated data points are common in many fields. 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, and it could allow for accurate testing for significance in neural activity. The high dimensionality of this type of data (millions of voxels) presents modeling challenges and serious computational constraints. 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 – coarser or larger spatial units – rather than among voxels. However, ignoring spatial dependence at different scales could drastically reduce our ability to detect important activation patterns in the brain and hence produce misleading results. To overcome these problems, we introduce a novel Bayesian tensor approach modelling the data at the voxel level, treating the brain image as a tensor response and having a vector of predictors with a high dimensional set of risk parameters varying across the different dimensions of the tensor response. Our tensor regression method characterizes dependency in the data and provides estimates of the parameters of interest using a generalized sparsity principle. This method is implemented using a fully Bayesian approach to characterize different sources of uncertainty. We demonstrate posterior consistency of the parameters of interest and develop a computational efficient algorithm. The effectiveness of our approach is illustrated through simulation studies and the analysis of the effects of drug addiction on the brain structure. We implement this method to identify the effects of cocaine addiction on the functioning of the brain.