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