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Title: Spatial 3D Matern priors for fast whole-brain fMRI analysis Authors:  Finn Lindgren - University of Bath (United Kingdom)
David Bolin - Chalmers (Sweden)
Anders Eklund - Linköping university (Sweden)
Mattias Villani - Stockholm University (Sweden)
Per Siden - Linköping University (Sweden) [presenting]
Abstract: Bayesian whole-brain functional magnetic resonance imaging (fMRI) analysis with three-dimensional spatial smoothing priors have been shown to produce state-of-the-art activity maps without pre-smoothing the data. The proposed inference algorithms are computationally demanding however, and the proposed spatial priors have several less appealing properties, such as being improper and having infinite spatial range. We propose a statistical inference framework for functional magnetic resonance imaging (fMRI) analysis based on the class of Matern covariance functions. The framework uses the Gaussian Markov random field (GMRF) representation of Matern fields via the stochastic partial differential equation (SPDE) approach. This allows for more flexible and interpretable spatial priors, while maintaining the sparsity required for fast inference in the high-dimensional whole-brain setting. We develop an accelerated stochastic gradient descent (SGD) optimisation algorithm for empirical Bayes (EB) inference of the spatial hyperparameters. Conditional on the inferred hyperparameters, we make a fully Bayesian treatment of the main parameters of interest, that is, the brain activity coefficients. We apply the Matern prior to both experimental and simulated task-fMRI data and clearly demonstrate that this is a more reasonable choice than the previously used priors, by using prior simulation, cross validation and visual inspection of the resulting activation maps.