On the insufficiency of arbitrarily precise covariance matrices: non-Gaussian weak lensing likelihoods

Abstract

We investigate whether a Gaussian likelihood, as routinely assumed in the analysis of cosmological data, is supported by simulated survey data. We define test statistics, based on a novel method that first destroys Gaussian correlations in a dataset, and then measures the non-Gaussian correlations that remain. This procedure flags pairs of datapoints which depend on each other in a non-Gaussian fashion, and thereby identifies where the assumption of a Gaussian likelihood breaks down. Using this diagnostic, we find that non-Gaussian correlations in the CFHTLenS cosmic shear correlation functions are significant. With a simple exclusion of the most contaminated datapoints, the posterior for $s_8$ is shifted without broadening, but we find no significant reduction in the tension with $s_8$ derived from Planck Cosmic Microwave Background data. However, we also show that the one-point distributions of the correlation statistics are noticeably skewed, such that sound weak lensing data sets are intrinsically likely to lead to a systematically low lensing amplitude being inferred. The detected non-Gaussianities get larger with increasing angular scale such that for future wide-angle surveys such as Euclid or LSST, with their very small statistical errors, the large-scale modes are expected to be increasingly affected. The shifts in posteriors may then not be negligible and we recommend that these diagnostic tests be run as part of future analyses.

arXiv commentReplacement to match accepted MNRAS version

References in corpus (20)

• Efficient Computation of CMB anisotropies in closed FRW models
• Weak Gravitational Lensing
• Stable clustering, the halo model and nonlinear cosmological power spectra
• Revising the Halofit Model for the Nonlinear Matter Power Spectrum
• Why your model parameter confidences might be too optimistic -- unbiased estimation of the inverse covariance matrix
• CFHTLenS: The Canada-France-Hawaii Telescope Lensing Survey
• CFHTLenS tomographic weak lensing cosmological parameter constraints: Mitigating the impact of intrinsic galaxy alignments
• Planck 2015 results. XVII. Constraints on primordial non-Gaussianity
• CosmoSIS: modular cosmological parameter estimation
• CFHTLenS revisited: assessing concordance with Planck including astrophysical systematics
• Parameter inference with estimated covariance matrices
• The Effect of Covariance Estimator Error on Cosmological Parameter Constraints
• Putting the Precision in Precision Cosmology: How accurate should your data covariance matrix be?
• High Performance P3M N-body code: CUBEP3M
• The extended Baryon Oscillation Spectroscopic Survey (eBOSS): a cosmological forecast
• Estimating Cosmological Parameter Covariance
• Breaking the spell of Gaussianity: forecasting with higher order Fisher matrices
• Gravitational Lensing Simulations I : Covariance Matrices and Halo Catalogues
• Quantifying lost information due to covariance matrix estimation in parameter inference
• A fast, always positive definite and normalizable approximation of non-Gaussian likelihoods

Cited by in corpus (45)

• KiDS-1000 Methodology: Modelling and inference for joint weak gravitational lensing and spectroscopic galaxy clustering analysis
• Likelihood-free inference with neural compression of DES SV weak lensing map statistics
• Density split statistics: Cosmological constraints from counts and lensing in cells in DES Y1 and SDSS data
• Scientific Synergy Between LSST and Euclid
• Accurate cosmic shear errors: do we need ensembles of simulations?
• Complete super-sample lensing covariance in the response approach
• Cosmic shear power spectra in practice
• Weak lensing scattering transform: dark energy and neutrino mass sensitivity
• The skewed weak lensing likelihood: why biases arise, despite data and theory being sound
• Cosmic shear with small scales: DES-Y3, KiDS-1000 and HSC-DR1
• Quijote-PNG: Simulations of primordial non-Gaussianity and the information content of the matter field power spectrum and bispectrum
• Beware of commonly used approximations II: estimating systematic biases in the best-fit parameters
• Cosmic Shear: Inference from Forward Models
• DES Y1 Results: Validating cosmological parameter estimation using simulated Dark Energy Surveys
• Dark Energy Survey internal consistency tests of the joint cosmological probes analysis with posterior predictive distributions
• Likelihood Non-Gaussianity in Large-Scale Structure Analyses
• On the accuracy and precision of correlation functions and field-level inference in cosmology
• KiDS-SBI: Simulation-based inference analysis of KiDS-1000 cosmic shear
• Investigating scalar-tensor-gravity with statistics of the cosmic large-scale structure
• Euclid-era cosmology for everyone: Neural net assisted MCMC sampling for the joint 3x2 likelihood
• Non-Gaussianity in the Weak Lensing Correlation Function Likelihood -- Implications for Cosmological Parameter Biases
• Covariance of the galaxy angular power spectrum with the halo model
• EFTofLSS meets simulation-based inference: ${\sigma }_8$ from biased tracers
• Debiasing inference with approximate covariance matrices and other unidentified biases
• A Bayesian method for combining theoretical and simulated covariance matrices for large-scale structure surveys
• Cosmological Inference from Galaxy-Clustering Power Spectrum: Gaussianization and Covariance Decomposition
• Probing massive neutrinos with the Minkowski functionals of the galaxy distribution
• Sufficiency of a Gaussian power spectrum likelihood for accurate cosmology from upcoming weak lensing surveys
• A simulation-based inference pipeline for cosmic shear with the Kilo-Degree Survey
• Analytic marginalization of $N(z)$ uncertainties in tomographic galaxy surveys
• Almanac: Weak Lensing power spectra and map inference on the masked sphere
• Quantification of high dimensional non-Gaussianities and its implication to Fisher analysis in cosmology
• Flow-Based Likelihoods for Non-Gaussian Inference
• Exact joint likelihood of pseudo-$C_{\ell }$ estimates from correlated Gaussian cosmological fields
• Testing the accuracy of likelihoods for cluster abundance cosmology
• Bayesian Control Variates for optimal covariance estimation with pairs of simulations and surrogates
• KiDS-Legacy: Covariance validation and the unified OneCovariance framework for projected large-scale structure observables
• The impact of signal-to-noise, redshift, and angular range on the bias of weak lensing 2-point functions
• Non-parametric Cosmology with Cosmic Shear
• Hybrid summary statistics: neural weak lensing inference beyond the power spectrum
• Weak Gravitational Lensing
• A comparison of shrinkage estimators of the cosmological precision matrix
• Galaxy-Point Spread Function correlations as a probe of weak-lensing systematics with UNIONS data
• Non-Gaussian likelihood of weak lensing power spectra
• The Kaiser-Rocket effect: three decades and counting