1. STATISTICS FOR HIGH DIMENSIONAL BIOLOGICAL RECORDINGS Dr Cyril Pernet, Centre for Clinical Brain Sciences Brain Research Imaging Centre cyril.pernet@ed.ac.uk http://www.sbirc.ed.ac.uk/cyril/

2. Biological Recordings Behavioural / Electrophysiology / MRI images Behavioural / Electrophysiology / MRI images 1D: Single channel (time / freq) 2D: Classification ‘images’ (can actually be spectrograms) 3D: MRI (xyz) and MEEG (channels x time / freq / trials) 4D: fMRI (time * xyz) and MEEG (channels x freq x time x trials)

3. Biological Recordings Often we want:  To ensure data are ok for analyses  high dimensional outliers detection, weighting, etc.  To analyse each ‘cell’ in the data matrix = ‘massive univariate analyses’  multiple comparisons issue  To find features in the data to distinguish conditions / groups  dimension reduction (ICA), classification (MVPA)

4. My toys General linear model (WLS, IRLS) Robust statistics (trimmed means, winsorized variance, skipped correlations, half space/mid-covariance determinant, MAD, S-outliers, etc) Bootstrap and permutations Cross-validation

5. Example 1: EEG outlier detection Weighted least square of MEEG –> weights based on time course similarity: 1. dimension reduction (PCA) 2. outlier detection (MAD) 3. weighting (WLS) OLS – face 1 vs 2 seems a bit differentWLS – face 1 vs 2 seems identical Bias is trial variability in face 2 leads to small diff. in OLS

6. Example 2: MCC Threshold-Free Cluster Enhancement (width e x height h ) Smith and Nichols 2009 - Integrate the cluster mass at multiple thresholds ; used for fMRI/TBSS

7. Example 2: MCC for N dimensions Threshold-Free Cluster Enhancement: Pernet et al 2014 validation for electrophysiology to optimize parameter selection

8. Example 3: ICA – correction factors? Decompose on spatial or temporal patterns to independent sources: Can we test all sources of interest simultaneously and still control the type I error rate?