New Interpretable Statistics for Large-Scale Structure Analysis and Generation

We introduce Wavelet Phase Harmonics (WPH) statistics: interpretablelow-dimensional statistics that describe 2D non-Gaussian fields. Thesestatistics are built from WPH moments, which were recently introduced in thedata science and machine learning community. We apply WPH statistics toprojected 2D matter density fields from the Quijote N-body simulations of thelarge-scale structure of the Universe. By computing Fisher informationmatrices, we find that the WPH statistics place more stringent constraints onfour of five cosmological parameters when compared to statistics based on thecombination of the power spectrum and bispectrum. We also use the WPHstatistics with a maximum entropy model to statistically generate new 2Ddensity fields that accurately reproduce the probability density function, themean and standard deviation of the power spectrum, the bispectrum, andMinkowski functionals of the input density fields. Although other methods areefficient for either parameter estimates or statistical syntheses of thelarge-scale structure, WPH statistics are the first statistics that achievestate-of-the-art results for both tasks as well as being interpretable.