The Non-Gaussian Weak-Lensing Likelihood: A Multivariate Copula Construction and Impact on Cosmological Constraints

TL;DR

This paper develops a copula-based framework to accurately model non-Gaussian likelihoods in weak-lensing surveys, improving parameter inference especially on large scales.

Contribution

It introduces a multivariate copula approach for non-Gaussian likelihoods, enhancing the modeling of large-scale correlations in weak-lensing data.

Findings

Copula likelihood aligns better with simulated distributions than Gaussian models.

Parameter shifts of about one standard deviation in $S_8$ for 1,000 deg² surveys.

Gaussian likelihoods are adequate for 10,000 deg² surveys, depending on survey specifics.

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.