Kiebel

1
Kiebel Friston 2004 A Framework for discussion

• Random Field Theory reminder
• source reconstruction
• Mass univariate vs. multivariate model
• Peristimulus time 4th dimension vs. factor
• Hierarchal model

2
The problem-Multiple comparisons
reminder

• If n100,000 voxels tested with pu0.05 of
  falsely rejecting Ho...
• then approx n ? pu (eg 5,000) will do so by
  chance (false positives, or type I errors)
• Therefore need to correct p-values for number
  of comparisons
• A severe correction would be a Bonferroni, where
  pc pu /n
• but this is only appropriate when the n tests
  independent
• SPMs are smooth, meaning that nearby voxels
  are correlated
• gt Gaussian Field Theory...

3
Overview
reminder
kernel
4
Random Field Theory-Concepts
reminder

• Statistical map
• Boneforni correction
• Smoothing
• Resel
• Euler characteristic

5
First stage source reconstructed EEG

• Preprocessing stage averaged ERP for each
  subject condition
• Reconstruction of sourcesImage current source
  density or 3 variant image retaining source
  orientation.
• We have 32/64 electrodes EEG no fMRI, should we
  use the 2D or 3D reconstruction? (p 494)

6
Methods for reconstruction

• Distributed source solutions to the inverse
  problem
• Bayesian framework (vs. dipoles)
• anatomically informed basis functions
• imposing priors on the source estimators. (e.g
  source arise from grey matter)
• Source linear mixture of basis func.
• Smaller dimensionality then voxels
• Restricted maximum likelihood (ReML) p 493
• Expectation maximizations (EM) algorithms p494

7
Input to Statistical models source reconstructed
EEG

• Time series of 3D images or 2D scalp surface

8
Multivariate vs. Univariate

• Options available to model spatial correlations
  of the error (nonsphericity) p 495

9
repeated measures

• the same subjects are tested under a number of
  conditions,
• reduces the error variance caused by
  between-group individual differences
• potentially introduce covariation between
  experimental conditions (this is because the same
  people are used in each condition and so there is
  likely to be some consistency in their behaviour
  across conditions).

10
Sphericity

• equality of variances of the differences between
  treatment levels.

11
Multivariate vs. Univariate

12
Temporal dimension

• Treat time as a 4th dimension -gt
• SPM will span 3D anatomical space
  peristimulus time
• Allow anatomical temporal specificity of
  inferences using adjusted P values by RFT.
• Advantage need to estimate temporal smoothness
  at each time bin as opposed to temporal
  correlation over all time bins.
• Time as an experimental factor
• Number of factor levels number of time bines
• Estimate temporal correlations of the error to
  make nonsphericity adjustment for valid
  inference.
• Can be done by ReML based on expectation
  maximization (EM)

13
4th dimension vs. experimental factor

• 4th dimension- disadvantage
• not possible to make inferences about spatial or
  temporal extent of activation foci in SPM -gt
• cant make inferences about differential
  latencies among groups and trial types.
• Contrasts specified for each voxel and time-bin.
• This is OK for the spatial domain, in which we
  are interested in region specific inferences,
  because activation in 1 part of the brain doesnt
  have any quantitative meaning in relation to
  different structures.
• experimental factor-
• compare responses over time explicitly
• Meaningful because it defines the form of the ERP

14
Modeling the correlation

• Separate estimates of the spatial temporal
  correlations.
• Spatial domain mass-univariate-gt spatial corr.
  taken into account in RFT stage and not in
  univariate stage.
• Temporal domain time as a factor, temporal corr.
  between time bins

15
Different models
16
Hierarchical model

• Decompose the data into
• 1st level Within ERP- temporal effect fixed
  effect (single subject)
• SPM manual form at each voxel , weighted
  sums of the data over time (99)
• 2cnd level Between ERP- experimental effect
  (group, condition) random effect (population
  inference)
• Response at 1st level is caused by first level
  parameters that are modeled as random at the 2cnd
  level
• Yx(1)b(1) e(1)
• b(1)x(2)b(2) e(2)
• Variance parameters are estimated by ReML

17
Hierarchical model- advantages

• Enables different transforms (wavelet, Fourier)
  at the 1st level. Since X(1) defines a
  projection onto some subspace of the data.
• 1st level b(1) allows to test subject specific
  effect against its variance (single case
  studies)
• Allows ANOVA on peristimulus time window
  averages.
• Finesse parameterization of nonsphericity 2
  error partitions
• E(1) observation error
• E(2) between subject variability

18
Contrasts and inferences

• Inferences about effects in peristimulus time or
  frequency domain
• Amplitude change in time
• Evoked power in peristimulus time or frequency
  domain

19
More issues

• Temporal basis functions
• Wavelets