Bayesian fMRI analysis with Spatial Priors

This unfinished web page describes the Variational Bayes (VB) estimation scheme for voxel-specific GLM-AR models that is implemented in SPM-devel.

Both regression coefficients and AR coefficients are spatially regularised. This means that you no longer need to spatially smooth your data an arbitrary amount.

In this model, each regression coefficient has a spatial prior which constrains its value to be similar to the value at nearby voxels. How much it is constrained depends on a spatial regularisation parameter that is estimated automatically. There is a different spatial regularisation parameter for each regressor in your design matrix. This means that different effects can have different spatial regularities. Overall, this means the algorithm should be more sensitive.

Also, the AR coefficients are allowed to be different at each voxel (previously, the same value was used for the whole volume). This also improves parameter estimation.

To use the method first consult the user_guide.pdf

Code

The algorithm is implemented in the development version of SPM (available here if you are off-site devel.zip (178M) - this version from 4 August 2004. I believe I omitted spm_kl_gamma.m from this archive - so please take this too).

A surfable code manifest is available here. The main SPM-embedded routine is spm_spm_vb.m. This calls the function spm_vb_glmar.m which estimates a GLM-AR for a single slice of data. This routine can be accessed from outside of SPM as shown in this example code: test1.m (which uses boxcars.m). This is useful for simulation.

Papers

The algorithm is described in a series of papers. I'd start with Paper VB2.

Paper VB1:
  • W.D. Penny, S. Kiebel, K. Friston (2003) Variational Bayesian Inference for fMRI time series. Neuroimage 19 (3), 727-741.

    Paper VB2:
  • W.Penny, N. Trujillo-Bareto and K. Friston (2004). Bayesian fMRI time series analysis with spatial priors . NeuroImage 24(2), 350-362.

    Paper VB3:
  • W.Penny (2004). Bayesian analysis of single-subject fMRI data: SPM implementation (very unfinished) technical Report. Wellcome Department of Imaging Neuroscience, UCL.

    Paper VB4:
  • W.Penny et al. (2004) Beyond the voxel: Comparing spatially extended fMRI models Manuscript in early stages of preparation.