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

TL;DR

This paper introduces the Kullback-Leibler divergence as a non-parametric statistical test to detect residual foreground contamination in cosmic microwave background maps, demonstrating its effectiveness on Planck data.

Contribution

It proposes using the KL divergence for analyzing CMB maps, providing a new tool for identifying non-Gaussian residuals in large-scale data.

Findings

KL divergence effectively detects residuals in CMB maps

Results are consistent with expected distributions at 6% level

KL and Kolmogorov-Smirnov tests generally agree

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.