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 the spatial priors used have several less appealing properties, such as being improper and having infinite spatial range. We propose a statistical inference framework for whole-brain fMRI analysis based on the class of Matérn covariance functions. The framework uses the Gaussian Markov random field (GMRF) representation of possibly anisotropic spatial Matérn fields via the stochastic partial differential equation (SPDE) approach of Lindgren et al. (2011). 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) optimization algorithm for empirical Bayes (EB) inference of the spatial hyperparameters. Conditionally on the inferred hyperparameters, we make a fully Bayesian treatment of the brain activity. The Matérn prior is applied to both simulated and experimental task-fMRI data and clearly demonstrates that it is a more reasonable choice than the previously used priors, using comparisons of activity maps, prior simulation and cross-validation.
This work was funded by Swedish Research Council (Vetenskapsrådet) grant no 2013-5229 and grant no 2016-04187. Finn Lindgren was funded by the European Union’s Horizon 2020 Programme for Research and Innovation, no 640171, EUSTACE. Anders Eklund was funded by Center for Industrial Information Technology (CENIIT) at Linköping University.
"Spatial 3D Matérn Priors for Fast Whole-Brain fMRI Analysis." Bayesian Anal. Advance Publication 1 - 28, 2021. https://doi.org/10.1214/21-BA1283