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The permutation test is an often used test procedure in brain imaging.Unfortunately, generating every possible permutation for large-scale brainimage datasets such as HCP and ADNI with hundreds images is not practical. Manyprevious attempts at speeding up the permutation test rely on variousapproximation strategies such as estimating the tail distribution with knownparametric distributions. In this study, we show how to rapidly accelerate thepermutation test without any type of approximate strategies by exploiting theunderlying algebraic structure of the permutation group. The method is appliedto large number of MRIs in two applications: (1) localizing the male and femaledifferences and (2) localizing the regions of high genetic heritability in thesulcal and gyral pattern of the human cortical brain.

Rapid Acceleration of the Permutation Test via Slow Random Walks in the Permutation Group