New Interpretable Statistics for Large Scale Structure Analysis and
  Generation
  We introduce Wavelet Phase Harmonics (WPH) statistics: interpretable
low-dimensional statistics that describe 2D non-Gaussian fields. These
statistics are built from WPH moments, which were recently introduced in the
data science and machine learning community. We apply WPH statistics to
projected 2D matter density fields from the Quijote N-body simulations of the
large-scale structure of the Universe. By computing Fisher information
matrices, we find that the WPH statistics place more stringent constraints on
four of five cosmological parameters when compared to statistics based on the
combination of the power spectrum and bispectrum. We also use the WPH
statistics with a maximum entropy model to statistically generate new 2D
density fields that accurately reproduce the probability density function, the
mean and standard deviation of the power spectrum, the bispectrum, and
Minkowski functionals of the input density fields. Although other methods are
efficient for either parameter estimates or statistical syntheses of the
large-scale structure, WPH statistics are the first statistics that achieve
state-of-the-art results for both tasks as well as being interpretable.
