Spatial 3D Matérn Priors for Fast Whole-Brain fMRI Analysis

Bayesian whole-brain functional magnetic resonance imaging (fMRI) analysis with three-dimensional spatial smoothing priors has been shown to produce state-of-the-art activity maps without pre-smoothing the data. The proposed inference algorithms are computationally demanding however, and used have several less appealing properties, such as being improper having infinite range. We propose a statistical framework for fMRI based on class of Matérn covariance functions. uses Gaussian Markov random field (GMRF) representation possibly anisotropic fields via stochastic partial differential equation (SPDE) approach Lindgren et al. (2011). This allows more flexible interpretable priors, while maintaining sparsity required fast in high-dimensional setting. develop an accelerated gradient descent (SGD) optimization algorithm empirical Bayes (EB) hyperparameters. Conditionally inferred hyperparameters, we make fully treatment brain activity. prior is applied both simulated experimental task-fMRI data clearly demonstrates that it reasonable choice than previously using comparisons maps, simulation cross-validation.