Fast Bayesian whole-brain fMRI analysis with spatial 3D priors

TL;DR

This paper introduces a fast MCMC-based Bayesian analysis method for whole-brain fMRI data, enabling exact inference with spatial 3D priors and revealing limitations of previous variational approaches.

Contribution

It presents a novel MCMC scheme for exact Bayesian inference in whole-brain fMRI analysis, outperforming existing variational methods in speed and accuracy.

Findings

MCMC provides more accurate posterior estimates than VB.

VB can produce spurious activations compared to MCMC.

The improved VB method is significantly faster with minimal error.

Abstract

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.