The Kullback-Leibler Divergence as an Estimator of the Statistical Properties of CMB Maps

Abstract

The identification of unsubtracted foreground residuals in the cosmic microwave background maps on large scales is of crucial importance for the analysis of polarization signals. These residuals add a non-Gaussian contribution to the data. We propose the Kullback-Leibler (KL) divergence as an effective, non-parametric test on the one-point probability distribution function of the data. With motivation in information theory, the KL divergence takes into account the entire range of the distribution and is highly non-local. We demonstrate its use by analyzing the large scales of the Planck 2013 SMICA temperature fluctuation map and find it consistent with the expected distribution at a level of 6%. Comparing the results to those obtained using the more popular Kolmogorov-Smirnov test, we find the two methods to be in general agreement.

12 pages, 5 figures, minor change, as published in JCAP

References in corpus (3)

• The non-Gaussian Cold Spot in the 3-year WMAP data
• Power asymmetry in WMAP and Planck temperature sky maps as measured by a local variance estimator
• The Axis of Evil revisited

Cited by in corpus (2)

• The nature of non-Gaussianity and statistical isotropy of the 408 MHz Haslam synchrotron map
• Probing CMB Polarization Gaussianity with the Statistics of Unpolarized Points: Non-Gaussianity of Planck Data and Prospects for Future B-Mode Measurements