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

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

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

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

Cosmology and Nongalactic Astrophysics · Submitted 25 Jun 2015

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The authors' main claim 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%.

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arXiv ID1506.07724 (version 2)

Pith ID5IOM6D6B, Pith's permanent record of this paper and its review

CitationAndrew D. Jackson, Assaf Ben-David, Hao Liu. "The Kullback-Leibler Divergence as an Estimator of the Statistical Properties of CMB Maps." arXiv:1506.07724 (2015). https://pith.science/paper/5IOM6D6B

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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.21 · human participants 0.01 · controlled comparison 0.22 · randomized assignment 0.01 · states quantitative result 0.97 · compares with prior results 0.96 · mentions code or data availability 0.02.

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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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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	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.	background 1.00	0.06	0.05	asserted 1.00
s1	These residuals add a non-Gaussian contribution to the data.	background 1.00	0.10	0.02	asserted 1.00
s2	We propose the Kullback-Leibler (KL) divergence as an effective, non-parametric test on the one-point probability distribution function of the data.	contribution 0.70	0.84	0.25	asserted 0.90
s3	With motivation in information theory, the KL divergence takes into account the entire range of the distribution and is highly non-local.	method 0.84	0.14	0.04	asserted 1.00
s4	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%.	result 0.98	0.98	0.48	asserted 0.76
s5	Comparing the results to those obtained using the more popular Kolmogorov-Smirnov test, we find the two methods to be in general agreement.	result 0.95	0.95	0.12	asserted 0.98

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Original 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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5 arXiv papers cite this in 8 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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Cites it as support 1 paper

This provides confirmation that the SMICA map is indeed consistent with our ensemble of realizations and provides further support for the conclusion of [ref] that the more complicated FFP simulations are not essential for analyzing the statistical properties of the SMICA map; simple Gaussian appear to be sufficient.

Skewness and Kurtosis as Indicators of Non-Gaussianity in Galactic Foreground Maps · The SMICA Map · 0.99

Cites it as background 1 paper

Among them Minkowski functionals [ref] , high-order correlations [ref] , kurtosis and skewness [ref] , statistics of local extrema (maxima, minima and saddle points) [ref] , clusterization of peaks [ref] , the Kullback-Leibler divergence [ref] , percolation [ref] and neural-network approach [ref] .

Gaussianity test of Planck CMB polarization data using the statistics of unpolarized points (Part I) · Introduction · 0.91

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Uses the method or tool of 2 papers

Since we are interested in the statistical properties of the CMB map on large scales, we first degrade the map from its native HEALPix [ref] resolution of $=2048$ to $=32$.

HEALPix -- a Framework for High Resolution Discretization, and Fast Analysis of Data Distributed on the Sphere · Preliminary remarks: Planck data · 0.92
Our data analysis made use of the GLESP package[<http://www.glesp.nbi.dk/>] [ref] , and of HEALPix [ref] .

Gauss--Legendre Sky Pixelization (GLESP) for CMB maps · Discussion · 1.00

Uses data or values from 1 paper

We have performed the KL divergence test on the CMB map obtained by the Planck collaboration [ref] using the SMICA method.

Planck 2013 results. XVI. Cosmological parameters · Preliminary remarks: Planck data · 0.99

Cites as background 7 papers

The Planck 2013 and 2015 data releases open new directions in precision cosmology with regard to a more advanced investigation of the statistical isotropy and non-Gaussianity of the cosmic microwave background (CMB) [ref] .

Planck 2013 results. I. Overview of products and scientific results · Introduction · 0.88
The Planck 2013 and 2015 data releases open new directions in precision cosmology with regard to a more advanced investigation of the statistical isotropy and non-Gaussianity of the cosmic microwave background (CMB) [ref] .

Planck 2013 results. XXIII. Isotropy and statistics of the CMB · Introduction · 0.88
The Planck 2013 and 2015 data releases open new directions in precision cosmology with regard to a more advanced investigation of the statistical isotropy and non-Gaussianity of the cosmic microwave background (CMB) [ref] .

Planck 2013 Results. XXIV. Constraints on primordial non-Gaussianity · Introduction · 0.88

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