Abstract
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.
Original language | English (US) |
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Pages (from-to) | 1251-1278 |
Number of pages | 28 |
Journal | BAYESIAN ANALYSIS |
Volume | 16 |
Issue number | 4 |
DOIs | |
State | Published - 2021 |
Bibliographical note
Funding Information:∗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. †Division of Statistics and Machine Learning, Dept. of Computer and Information Science, Linköping University, SE-581 83 Linköping, Sweden, [email protected] ‡School of Mathematics, The University of Edinburgh, James Clerk Maxwell Building, The King’s Building, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, United Kingdom, [email protected] §CEMSE Division, King Abdullah University of Science and Technology, Saudi Arabia, [email protected] ¶Division of Medical Informatics, Dept. of Biomedical Engineering and Center for Medical Image Science and Visualization (CMIV), Linköping University, SE-581 83 Linköping, Sweden, [email protected] ‖Department of Statistics, Stockholm University, SE-106 91 Stockholm, Sweden, [email protected] ∗∗Corresponding author.
Funding Information:
This work was funded by Swedish Research Council (Vetenskapsr?det) 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 Link?ping University
Publisher Copyright:
© 2021 International Society for Bayesian Analysis
Keywords
- Efficient computation
- Fmri
- Gaussian markov random fields
- Spatial priors
- Spatiotemporal modeling
ASJC Scopus subject areas
- Statistics and Probability
- Applied Mathematics