Fast Bayesian whole-brain fMRI analysis with spatial 3D priors.
Per Sidén, Anders Eklund, David Bolin, Mattias Villani
Author Information
Per Sidén: Division of Statistics and Machine Learning, Department of Computer and Information Science, Linköping University, SE-581 83 Linköping, Sweden. Electronic address: per.siden@liu.se.
Anders Eklund: Division of Statistics and Machine Learning, Department of Computer and Information Science, Linköping University, SE-581 83 Linköping, Sweden; Division of Medical Informatics, Department of Biomedical Engineering, Linköping University, SE-581 85 Linköping, Sweden; Center for Medical Image Science and Visualization (CMIV), Linköping University, SE-581 85 Linköping, Sweden. Electronic address: anders.eklund@liu.se.
David Bolin: Division of Mathematical Statistics, Department of Mathematical Sciences, Chalmers and University of Gothenburg, SE-412 96 Göteborg, Sweden. Electronic address: david.bolin@chalmers.se.
Mattias Villani: Division of Statistics and Machine Learning, Department of Computer and Information Science, Linköping University, SE-581 83 Linköping, Sweden. Electronic address: mattias.villani@liu.se.
Spatial whole-brain Bayesian modeling of task-related functional magnetic resonance imaging (fMRI) is a great computational challenge. Most of the currently proposed methods therefore do inference in subregions of the brain separately or do approximate inference without comparison to the true posterior distribution. A popular such method, which is now the standard method for Bayesian single subject analysis in the SPM software, is introduced in Penny et al. (2005b). The method processes the data slice-by-slice and uses an approximate variational Bayes (VB) estimation algorithm that enforces posterior independence between activity coefficients in different voxels. We introduce a fast and practical Markov chain Monte Carlo (MCMC) scheme for exact inference in the same model, both slice-wise and for the whole brain using a 3D prior on activity coefficients. The algorithm exploits sparsity and uses modern techniques for efficient sampling from high-dimensional Gaussian distributions, leading to speed-ups without which MCMC would not be a practical option. Using MCMC, we are for the first time able to evaluate the approximate VB posterior against the exact MCMC posterior, and show that VB can lead to spurious activation. In addition, we develop an improved VB method that drops the assumption of independent voxels a posteriori. This algorithm is shown to be much faster than both MCMC and the original VB for large datasets, with negligible error compared to the MCMC posterior.
