Searching for non-gaussianity: Statistical tests

Abstract

Non-gaussianity represents the statistical signature of physical processes such as turbulence. It can also be used as a powerful tool to discriminate between competing cosmological scenarios. A canonical analysis of non-gaussianity is based on the study of the distribution of the signal in the real (or direct) space (e.g. brightness, temperature). This work presents an image processing method in which we propose statistical tests to indicate and quantify the non-gaussian nature of a signal. Our method is based on a wavelet analysis of a signal. Because the temperature or brightness distribution is a rather weak discriminator, the search for the statistical signature of non-gaussianity relies on the study of the coefficient distribution of an image in the wavelet decomposition basis which is much more sensitive. We develop two statistical tests for non-gaussianity. In order to test their reliability, we apply them to sets of test maps representing a combination of gaussian and non-gaussian signals. We deliberately choose a signal with a weak non-gaussian signature and we find that such a non-gaussian signature is easily detected using our statistical discriminators. In a second paper, we apply the tests in a cosmological context.

14 pages, 7 figures, in press in Astronomy & Astrophysics Supplement Series

Cited by in corpus (13)

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• Secondary anisotropies of the CMB
• Detection and discrimination of cosmological non-Gaussian signatures by multi-scale methods
• Cosmic microwave background bispectrum and slow roll inflation
• The discriminating power of wavelets to detect non-Gaussianity in the CMB
• Cosmological non-Gaussian Signature Detection: Comparing Performance of Different Statistical Tests
• Primordial non-Gaussianity: local curvature method and statistical significance of constraints on f_NL from WMAP data
• Non-Gaussianity: Comparing wavelet and Fourier based methods
• A full sky prediction of the SZ effect from diffuse hot gas in the local universe and the upper limit from the WMAP data
• Full-sky correlations of peaks in the microwave background
• Using the COBE/DMR data as a test-bed for normality assessments
• Effect of component separation on the temperature distribution of the CMB
• Separating the kinetic SZ effect from primary CMB fluctuations