Presentation #209.03 in the session Cosmology I.
Recently, different probes of the Large Scale Structure (LSS) were highlighted for their ability to constrain the cosmological parameters more precisely than the power spectrum. Some probes, like the bispectrum and the Wavelet Scattering Transform (WST) were highlighted to be especially efficient at constraining the neutrino mass. In this work, we discuss an important assumption of a Fisher analysis, the multivariate Gaussianity of the statistical probe. We evaluate the power spectrum, the bispectrum and the WST on the 3D matter density field from the Quijote Suite (Villaescusa-Navarro et al. 2020) together with a previously published marked power spectrum. We apply the non–Gaussianity test from (Sellentin & Heavens 2017) together with a fast chi square divergence test for high dimensional probes to quantify the non–Gaussianity of these high–dimensional distributions. We find that all of the explored probes of LSS shows some form of non–Gaussianity resulting in a considerable underestimation of the parameter constraints resulting from a Fisher analysis. We develop a correction method to eliminate the non–Gaussian dimensions to get corrected parameter constraints. Our correction method could be applied to multivariate data analysis in general context outside of cosmology. Applying our correction for non–Gaussianity, the parameter constraints increases by (3σ level, 5σ level): (62%, 51%) for the power spectrum, (134%, 84%) for the marked power spectrum, (173%, 111%) for the bispectrum and (90%, 56%) for the reduced RWST, for the maximally affected cosmological parameter. To illustrate this effect, we concatenate the power spectrum and its logarithm to show an extreme example of the Gaussianity being violated. Additionally, we show that an arbitrary, non–linear transformation of the power spectrum can seem to produce tighter confidence ellipses. These examples have a small dimensionality(< 100) and a plausible covariance condition number, while hacking the Gaussianity assumption to report tighter constraints. This suggests that the effect is hard to foresee, and proper Fisher forecast should check for this effect. We briefly discuss our results in the cosmological context.