Szapudi´s talk – False Detection Rate ltaneous hypothesis testing - Setting the statistical signifi ections of Non-Gaussianity in CMB observatio Brief review of detections/methods used to set the statistic significance. Application of FDR to individual statistical methods. Application of FDR to a combination of statistical methods?. What is the appropriate method for assessing the statistical significance of localized detections?.
Szapudi´s talk – F alse D etection R ate. Simultaneous hypothesis testing - Setting the statistical significance. Detections of Non-Gaussianity in CMB observations. Brief review of detections/methods used to set the statistical significance. - PowerPoint PPT Presentation
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Szapudi´s talk – False Detection Rate
Simultaneous hypothesis testing - Setting the statistical significance
Detections of Non-Gaussianity in CMB observations
•Brief review of detections/methods used to set the statistical significance. •Application of FDR to individual statistical methods.•Application of FDR to a combination of statistical methods?.•What is the appropriate method for assessing the statistical significance of localized detections?.
CMB: Non-Gaussianity tests
Non-Gaussianity tests
Real spaceSpherical Harmonic
space
Wavelet space
Blind tests – The alternative to the null hypothesis is not specified.
Non-Gaussianity tests: Real Space
Courtesy of WMAP Science Team
Based on the temperature fluctuationobserved at each pixel i, ΔT(i)
Tests (detections):
•Genus (Park 2003).
•N-point correlation function (Eriksen et al. 2003, Eriksen et al. 2004).
•Minkowski functionals and length of skeleton (Eriksen et al. 2004).
•Extrema (Larson & Wandelt 2004)
•2-point correlation function of maxima and minima (Tojeiro et al. 2005, Larson & Wandelt 2005)
Non-Gaussianity Tests: Spherical Harmonic Space
),(),( l m
lmlmYaT
Based on the complex coefficients
lma
Tests (detections):
•Power spectrum distribution (Eriksen et al. 2003, Hansen et al. 2004).
•Correlations between adjacent multipoles (Prunet et al. 2004).
Non-Gaussianity Tests: Wavelet Space
Based on wavelet coefficients calculated at each pixel i, at a given scale R,wv(i,R) .
Tests (detections):
•Kurtosis – Spherical Mexican HatWavelet (Vielva et al. 2003, Mukherjee & Wang 2004, McEwen et al. 2004, Liu & Zhang 2005, Cruz et al. 2006).
•Skewness – Real Morlet Wavelet(McEwen et al. 2004, Liu & Zhang 2005).
•Number and area and volume of spots – SMHW (Cruz et al. 2004, Cruz et al. 2006).
•Higher Criticism – SMHW (Cayon et al. 2005, Cruz et al. 2006).
Testing the null hypothesis through Monte Carlo simulations
),(),( l m
lmlmYaT
Simulating a CMB map:
At each pixel (i – θ,ψ) 1)
)2/,0()Im(),Re( lllmlm CBNaa
Bl – Antenna Cl - Cosmology
2) Add Noise - dispersion given by simulated experiment.
Mask – Galaxy plus point sources (zeros to the pixel in the mask).
Monopole and dipole removal.
Testing the null hypothesis through Monte Carlo simulations