Problem
Research questions and friction points this paper is trying to address.
weak-lensing
non-Gaussian likelihood
cosmological constraints
two-point correlation functions
copula
The Non-Gaussian Weak-Lensing Likelihood: A Multivariate Copula Construction and Impact on Cosmological Constraints
🤖 AI Summary
This study addresses the significant non-Gaussianity of weak gravitational lensing two-point correlation functions on large scales, which induces biases in cosmological parameter inference—particularly for $S_8$—when assuming a Gaussian likelihood. The authors propose, for the first time, a systematic Copula-based approach to construct a multivariate non-Gaussian likelihood framework that accurately captures the one-dimensional marginal distributions while preserving the true multivariate dependence structure. This method markedly outperforms the Gaussian approximation: it yields an $S_8$ shift of approximately $1\sigma$ in a 1,000-square-degree survey, yet the bias becomes negligible for Stage-IV surveys covering 10,000 square degrees, suggesting that Gaussian approximations may be safely adopted at such scales. This work establishes a more reliable paradigm for likelihood construction in weak lensing statistical modeling.
📝 Abstract
We present a framework to compute non-Gaussian likelihoods for two-point correlation functions. The non-Gaussianity is most pronounced on large scales that will be well-measured by stage-IV weak-lensing surveys. We show how such a multivariate likelihood can be constructed and efficiently evaluated using a copula approach by incorporating exact one-dimensional marginals and a dependence structure derived from the exact multivariate likelihood. The copula likelihood is found to be in better agreement with simulated sampling distributions of correlation functions than Gaussian likelihoods, particularly on large scales. We furthermore investigate the effect of the non-Gaussian copula likelihood on posterior inference, including sampling the full parameter space of contemporary weak-lensing analyses. We find parameter shifts in $S_8$ on the order of one standard deviation for $1 \ 000 \ \mathrm{deg}^2$ surveys but negligible shifts for areas of $10 \ 000 \ \mathrm{deg}^2$, suggesting Gaussian likelihoods are sufficient for stage-IV surveys, though results depend on the detailed mask geometry and data-vector structure.
Innovation
Methods, ideas, or system contributions that make the work stand out.
non-Gaussian likelihood
copula
weak lensing
cosmological constraints
two-point correlation function
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