Bayesian fMRI models with Spatial Priors Will Penny (1), Nelson Trujillo-Barreto (2) Guillaume...
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Transcript of Bayesian fMRI models with Spatial Priors Will Penny (1), Nelson Trujillo-Barreto (2) Guillaume...
Bayesian fMRI models with Spatial Priors
Will Penny (1), Nelson Trujillo-Barreto (2)Guillaume Flandin (1)
Stefan Kiebel(1), Karl Friston (1)
(1) Wellcome Department of Imaging Neuroscience, UCLhttp://www.fil.ion.ucl.ac.uk/~wpenny
(2) Cuban Neuroscience Center, Havana, Cuba.
Even without applied spatial smoothing, activation maps (and maps of eg. AR coefficients) have spatial structure
Motivation
We can increase the sensitivity of our inferences by smoothing data with Gaussian kernels (SPM2). This is worthwhile, but crude.Can we do better with a spatial model (SPM5) ?
AR(1)
Aim: For SPM5 to remove the need for spatial smoothing just as SPM2 removed the need for temporal smoothing
Contrast
A
q1 q2
W
Y
u1 u2
Y=XW+E[TxN] [TxK] [KxN] [TxN]
r1 r2
The Model
SpatialPriors
SpatialPriors
General Linear ModelLaplacian Prior on regression coefficients W
Time domainSpatial domain
Spatio-Temporal Model for fMRI
General Linear Model:
Data yg
Design matrix XTemporal precision g
Laplacian Prior:
Spatial operator DSpatial precision
Time domain, at voxel gSpatial domain, voxels g=1..G
W
Yg=Xwg+eg
Data yg
Design matrix XTemporal precision g
Spatial operator DSpatial precision
Time domain, at voxel gSpatial domain, voxels g=1..G
))((
)(1
ggT
ggg
ggT
gg
rdiagyXw
DdiagXX
rg
SPATIO-TEMPORAL DECONVOLUTION
Synthetic Data: blobs
True Smoothing
Spatial prior
1-Specificity
Sen
sitiv
ity
Face data
Convolve event-stream with basis functions to account for the hemodynamic response function
Event-related fMRI: Faces versus chequerboard
Smoothing
Spatial Prior
Event-related fMRI: Familiar faces versus unfamiliar faces
Smoothing
Spatial Prior
W. Penny, S. Kiebel and K. Friston (2003) Variational Bayesian Inference for fMRI time series. NeuroImage 19, pp 727-741.
PAPER - 1
• GLMs with voxel-wise AR(p) models
• Model order selection shows p=0,1,2 or 3 is sufficient
• Voxel-wise AR(p) modelling can improve effect size estimation accuracy by 15%
PAPER - 2
W.Penny, N. Trujillo-Barreto and K. Friston (2005). Bayesian fMRI time series analysis with spatial priors. NeuroImage 24(2), pp 350-362.
• Spatial prior for regression coefficients
• Shown to be more sensitive than ‘smoothing the data’
PAPER - 3
W.Penny and G. Flandin (2005). Bayesian analysis of single-subject fMRI: SPM implementation. Technical Report. WDIN, UCL.
• Describes more efficient implementation of algorithm in papers 1 and 2.
• Describes how contrasts are evaluated when specified post-hoc
• Roadmap to code (? Erm, OK, not done yet)
PAPER - 4
W.Penny, G. Flandin and N.Trujillo-Barreto. Bayesian Comparison of Spatially Regularised General Linear Models. Human Brain Mapping, Accepted for publication.
• ROI-based Bayesian model comparison for selecting optimal hemodynamic basis set.
• Above Bayesian approach can be twice as sensitive as the classical F-test method
• Defined spatial priors for AR coefficients
• Bayesian model comparison shows these to be better than (i) global AR value, (ii) tissue-specific AR values
Using model evidence to select hemodynamic basis sets
Nested ModelComparison
Non-nestedmodelcomparison
Optimality of non-nested model comparison
FIR basis (truth) versus Inf-3 basis in low SNR environment
BayesianCluster ofInterest Analysis
Using model evidence to select spatial noise model
TissueSpecificPriors
SpatialSmoothnessPriors
PAPER - 5
W. Penny. Bayesian Analysis of fMRI data with spatial Priors. To appear in Proceedings of the Joint StatisticalMeeting (JSM), 2005.
• Describes Bayesian inference for multivariate contrasts based on chi-squared statistics
• Describes `default thresholds’ for generating PPMs: effect size threshold is 0, probability threshold is 1-1/S where S is the number of voxels in the search volume
• This gives approximately 0, 1 or 2 False Positives per PPM
• Describes a recent bug-fix !!! ?
PAPER - 6
G. Flandin and W. Penny. Bayesian Analysis of fMRI data with spatial basis set priors. Proceedings of Human Brain Mapping Conference, 2005.
• Uses spatial prior based on spatial basis functions eg. wavelets
• This is much faster than previous approach
• And provides yet more sensitivity …… ?!!