Speaker
Description
The two-point correlation function is a widely used summary statistic for extracting information from cosmological fields. Even when these fields are perfectly Gaussian, the likelihood of two-point function estimators is inherently non-Gaussian, particularly on the large angular scales that will be probed by upcoming stage-IV weak lensing surveys. Despite this, weak lensing analyses have so far relied on Gaussian likelihood approximations.
As stage-IV surveys push to larger scales with higher precision, these Gaussian approximations will become increasingly inaccurate—an issue already hinted at by indications of non-Gaussianity in correlation functions from stage-III surveys. Revisiting these statistical modeling choices is especially relevant given the ongoing "S8 tension," the discrepancy in clustering amplitudes inferred from high- and low-redshift probes.
We present a framework specifically designed to compute the exact likelihood for correlation functions of spin-0 and spin-2 fields, with the latter being directly relevant for cosmic shear. Our results reveal significant skewness in the likelihood, leading to a systematic shift in its mode toward lower values. Initial tests indicate that this effect can shift the posterior mean of S8 by up to two percent, comparable to the precision of current stage-III surveys.
To efficiently model non-Gaussian likelihoods in high dimensions, we implement a Gaussian copula approach, enabling feasible evaluations beyond the exact low-dimensional likelihood. First results from this method will be presented, along with comparisons to simulated distributions and standard Gaussian likelihoods for noisy weak lensing maps.
