Contents

## R in addition to om Field Theory Overview 1. Terminology 2. R in addition to om Field Theory 3. Imaging Data

Fu, Joseph, Health & Medicine Reporter has reference to this Academic Journal, PHwiki organized this Journal R in addition to om Field Theory Will Penny SPM short course, London, May 2005 realignment & motion correction smoothing normalisation General Linear Model model fitting statistic image corrected p-values image data parameter estimates design matrix anatomical reference kernel Statistical Parametric Map R in addition to om Field Theory

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Overview 1. Terminology 2. R in addition to om Field Theory 3. Imaging Data 4. Cluster level inference SPM Results FDR Overview 1. Terminology 2. R in addition to om Field Theory 3. Imaging Data 4. Cluster level inference SPM Results FDR Inference at a single voxel a = p(t>uH) NULL hypothesis, H: activation is zero u=2 t-distribution p-value: probability of getting a value of t at least as extreme as u. If a is small we reject the null hypothesis. u=(effect size)/std(effect size)

Sensitivity in addition to Specificity Sensitivity in addition to Specificity Eg. t-scores from regions that truly do in addition to do not activate o o o o o o o x x x o o x x x o x x x x u1 Sensitivity in addition to Specificity Eg. t-scores from regions that truly do in addition to do not activate o o o o o o o x x x o o x x x o x x x x u2

Inference at a single voxel a = p(t>uH) NULL hypothesis, H: activation is zero u=2 t-distribution We can choose u to ensure a voxel-wise significance level of a. This is called an uncorrected p-value, as long as reasons well see later. We can then plot a map of above threshold voxels. Inference as long as Images Signal+Noise Noise Using an uncorrected p-value of 0.1 will lead us to conclude on average that 10% of voxels are active when they are not. This is clearly undesirable. To correct as long as this we can define a null hypothesis as long as images of statistics.

Family-wise Null Hypothesis Family-Wise Error (FWE) rate = corrected p-value Use of uncorrected p-value, a=0.1 FWE Use of corrected p-value, a=0.1 The Bonferroni correction The Family-Wise Error rate (FWE), a, as long as a family of N independent voxels is = Nv where v is the voxel-wise error rate. There as long as e, to ensure a particular FWE set v = / N BUT

The Bonferroni correction Independent Voxels Spatially Correlated Voxels Bonferroni is too conservative as long as brain images Overview 1. Terminology 2. R in addition to om Field Theory 3. Imaging Data 4. Cluster level inference SPM Results FDR R in addition to om Field Theory Consider a statistic image as a discretisation of a continuous underlying r in addition to om field Use results from continuous r in addition to om field theory Discretisation

Euler Characteristic (EC) Topological measure threshold an image at u EC = blobs at high u: Prob blob = avg (EC) So FWE, a = avg (EC) Example 2D Gaussian images = R (4 ln 2) (2) -3/2 u exp (-u2/2) Voxel-wise threshold, u Number of Resolution Elements (RESELS), R N=100×100 voxels, Smoothness FWHM=10, gives R=10×10=100 Example 2D Gaussian images = R (4 ln 2) (2) -3/2 u exp (-u2/2) For R=100 in addition to =0.05 RFT gives u=3.8

Resel Counts as long as Brain Structures FWHM=20mm (1) Threshold depends on Search Volume (2) Surface area makes a large contribution Overview 1. Terminology 2. Theory 3. Imaging Data 4. Levels of Inference 5. SPM Results Functional Imaging Data The R in addition to om Fields are the component fields, Y = Xw +E, e=E/ We can only estimate the component fields, using estimates of w in addition to To apply RFT we need the RESEL count which requires smoothness estimates

Estimated component fields data matrix design matrix parameters errors + = voxels scans estimate residuals estimated component fields parameter estimates estimated variance = Each row is an estimated component field Applied Smoothing Smoothness smoothness » voxel size practically FWHM 3 VoxDim Typical applied smoothing: Single Subj fMRI: 6mm PET: 12mm Multi Subj fMRI: 8-12mm PET: 16mm Overview 1. Terminology 2. Theory 3. Imaging Data 4. Levels of Inference 5. SPM Results

Cluster Level Inference We can increase sensitivity by trading off anatomical specificity Given a voxel level threshold u, we can compute the likelihood (under the null hypothesis) of getting a cluster containing at least n voxels CLUSTER-LEVEL INFERENCE Similarly, we can compute the likelihood of getting c clusters each having at least n voxels SET-LEVEL INFERENCE Levels of inference set-level P(c 3 n 12, u 3.09) = 0.019 cluster-level P(c 1 n 82, t 3.09) = 0.029 (corrected) voxel-level P(c 1 n > 0, t 4.37) = 0.048 (corrected) At least one cluster with unspecified number of voxels above threshold At least one cluster with at least 82 voxels above threshold At least 3 clusters above threshold Overview 1. Terminology 2. Theory 3. Imaging Data 4. Levels of Inference 5. SPM Results

False Discovery Rate Signal+Noise Noise Summary We should not use uncorrected p-values We can use R in addition to om Field Theory (RFT) to correct p-values RFT requires FWHM > 3 voxels We only need to correct as long as the volume of interest Cluster-level inference False Discovery Rate is a viable alternative

## Fu, Joseph Health & Medicine Reporter

Fu, Joseph is from United States and they belong to Asian American Times, The and they are from Mesa, United States got related to this Particular Journal. and Fu, Joseph deal with the subjects like Health and Wellness; Medical

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