STATISTICS FOR HIGH DIMENSIONAL BIOLOGICAL RECORDINGS

Dr Cyril Pernet,

Centre for Clinical Brain Sciences

Brain Research Imaging Centre

cyril.pernet@ed.ac.ukhttp://www.sbirc.ed.ac.uk/cyril/

Biological Recordings

• 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)

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)

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

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 different WLS – face 1 vs 2 seems identicalBias is trial variability in face 2 leads to small diff. in OLS

Example 2: MCC• Threshold-Free Cluster Enhancement (widthe x heighth )• Smith and Nichols 2009 - Integrate the cluster mass at

multiple thresholds ; used for fMRI/TBSS

Example 2: MCC for N dimensions• Threshold-Free Cluster Enhancement:• Pernet et al 2014 validation for electrophysiology to

optimize parameter selection

Example 3: ICA – correction factors?

Decompose on spatial or temporalpatterns to independent sources:

Can we test all sources of interest simultaneously and still control the type I error rate?