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

Per Sidén1, Anders Eklund2, David Bolin3

  • 1Division of Statistics and Machine Learning, Department of Computer and Information Science, Linköping University, SE-581 83 Linköping, Sweden.

Neuroimage
|November 24, 2016
PubMed
Summary

We present a fast Markov chain Monte Carlo (MCMC) scheme for exact Bayesian whole-brain modeling in functional magnetic resonance imaging (fMRI). This method allows direct comparison with approximate variational Bayes (VB) methods, revealing potential inaccuracies in VB. An improved VB approach is also introduced, offering speed and accuracy.

Keywords:
Gaussian Markov random fieldsGeneral linear modelMarkov chain Monte CarloSpatial priorsVariational BayesfMRI

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Area of Science:

  • Neuroimaging
  • Computational Neuroscience
  • Statistical Modeling

Background:

  • Task-related functional magnetic resonance imaging (fMRI) analysis presents significant computational challenges for whole-brain Bayesian modeling.
  • Current methods often analyze brain subregions separately or use approximate inference, lacking comparison to true posterior distributions.
  • The standard Bayesian single-subject analysis in SPM software employs a slice-by-slice variational Bayes (VB) approach with enforced posterior independence between voxel activity coefficients.

Purpose of the Study:

  • To introduce a computationally efficient Markov chain Monte Carlo (MCMC) scheme for exact Bayesian inference in whole-brain fMRI models.
  • To enable direct comparison between approximate VB methods and exact MCMC inference.
  • To develop an improved VB method that relaxes the posterior independence assumption for enhanced accuracy and speed.

Main Methods:

  • Development of a fast and practical MCMC scheme for exact inference in Bayesian fMRI models, applicable both slice-wise and whole-brain.
  • Exploitation of data sparsity and modern techniques for efficient sampling from high-dimensional Gaussian distributions to make MCMC feasible.
  • Introduction of an improved VB algorithm that removes the a posteriori voxel independence assumption.

Main Results:

  • The MCMC scheme provides the first opportunity to evaluate approximate VB posteriors against exact MCMC posteriors.
  • Demonstration that the standard VB method can lead to spurious activation findings.
  • The improved VB method shows significantly faster performance than both MCMC and the original VB for large datasets, with minimal error compared to the MCMC posterior.

Conclusions:

  • Exact Bayesian inference for whole-brain fMRI is now computationally feasible using the developed MCMC scheme.
  • Approximate VB methods, while faster, may introduce inaccuracies such as spurious activations.
  • The newly developed VB method offers a superior balance of speed and accuracy for large-scale fMRI data analysis.