NonGaussianity in the weak lensing correlation function likelihood  implications for cosmological parameter biases
Abstract
We study the significance of nonGaussianity in the likelihood of weak lensing shear twopoint correlation functions, detecting significantly nonzero skewness and kurtosis in 1D marginal distributions of shear twopoint correlation functions in simulated weak lensing data. We examine the implications in the context of future surveys, in particular LSST, with derivations of how the nonGaussianity scales with survey area. We show that there is no significant bias in 1D posteriors of Ω_{m} and σ_{8} due to the nonGaussian likelihood distributions of shear correlations functions using the mock data (100 deg^{2}). We also present a systematic approach to constructing approximate multivariate likelihoods with 1D parametric functions by assuming independence or more flexible nonparametric multivariate methods after decorrelating the data points using principal component analysis (PCA). While the use of PCA does not modify the nonGaussianity of the multivariate likelihood, we find empirically that the 1D marginal sampling distributions of the PCA components exhibit less skewness and kurtosis than the original shear correlation functions. Modelling the likelihood with marginal parametric functions based on the assumption of independence between PCA components thus gives a lower limit for the biases. We further demonstrate that the difference in cosmological parameter constraints between the multivariate Gaussian likelihood model and more complex nonGaussian likelihood models would be even smaller for an LSSTlike survey. In addition, the PCA approach automatically serves as a data compression method, enabling the retention of the majority of the cosmological information while reducing the dimensionality of the data vector by a factor of ~5.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 December 2020
 DOI:
 10.1093/mnras/staa2948
 arXiv:
 arXiv:1905.03779
 Bibcode:
 2020MNRAS.499.2977L
 Keywords:

 gravitational lensing: weak;
 methods: statistical;
 cosmological parameters;
 Astrophysics  Cosmology and Nongalactic Astrophysics
 EPrint:
 16 pages, 10 figures, published MNRAS