New results in the geometry of random fields, with applications to CMB and galaxy density Keith Worsley, Hugo Drouin, Pauline Klein Department of Mathematics.

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Presentation transcript:

New results in the geometry of random fields, with applications to CMB and galaxy density Keith Worsley, Hugo Drouin, Pauline Klein Department of Mathematics and Statistics, McConnell Brain Imaging Centre, Montreal Neurological Institute, McGill University

Milky way

The 2dF Galaxy Redshift Survey: spectra and redshifts Mon. Not. R. Astron. Soc. 328, 1039–1063 (2001) Milky way

fMRI data: 120 scans, 3 scans each of hot, rest, warm, rest, hot, rest, … T = (hot – warm effect) / S.d. ~ t 110 if no effect

Gaussianized χ 2 field? Gaussian threshold EC

Gaussianized T field? Gaussian threshold EC

EC for WMAP, unsmoothed, FWHM = 1.6 o Gaussian threshold EC Observed Expected

Observed – Expected EC, with Poisson sd in tails EC Gaussian threshold

EC for WMAP smoothed to FWHM o (expected) no smoothing scale space

Simulation (expected) no smoothing scale space

Scale space WMAP data o  20.5 o Gaussian threshold EC Observed Expected