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arXiv · 1506.07724

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

Assaf Ben-David·Hao Liu·Andrew D. Jackson
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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.

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Assaf Ben-David, Hao Liu, Andrew D. Jackson. 2015-07-03. The Kullback-Leibler Divergence as an Estimator of the Statistical Properties of CMB Maps. https://doi.org/10.1088/1475-7516%2F2015%2F06%2F051

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