Presentation on theme: "Bayesian fMRI models with Spatial Priors Will Penny (1), Nelson Trujillo-Barreto (2) Guillaume Flandin (1) Stefan Kiebel(1), Karl Friston (1) (1) Wellcome."— Presentation transcript:
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, UCL (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 q1q1 q2q2 W Y u1u1 u2u2 Y=XW+E [TxN] [TxK] [KxN] [TxN] r1r1 r2r2 The Model Spatial Priors Spatial Priors
General Linear Model Laplacian Prior on regression coefficients W Time domainSpatial domain Spatio-Temporal Model for fMRI
General Linear Model: Data y g Design matrix X Temporal precision g Laplacian Prior: Spatial operator D Spatial precision Time domain, at voxel g Spatial domain, voxels g=1..G W Y g =Xw g +e g
Data y g Design matrix X Temporal precision g Spatial operator D Spatial precision Time domain, at voxel g Spatial domain, voxels g=1..G rgrg SPATIO-TEMPORAL DECONVOLUTION
W. Penny, S. Kiebel and K. Friston (2003) Variational Bayesian Inference for fMRI time series. NeuroImage 19, pp 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 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 Model Comparison Non-nested model comparison Optimality of non-nested model comparison FIR basis (truth) versus Inf-3 basis in low SNR environment Bayesian Cluster of Interest Analysis
Using model evidence to select spatial noise model Tissue Specific Priors Spatial Smoothness Priors
PAPER - 5 W. Penny. Bayesian Analysis of fMRI data with spatial Priors. To appear in Proceedings of the Joint Statistical Meeting (JSM), 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, Uses spatial prior based on spatial basis functions eg. wavelets This is much faster than previous approach And provides yet more sensitivity …… ?!!