The exact non-Gaussian weak lensing likelihood: A framework to calculate analytic likelihoods for correlation functions on masked Gaussian random fields
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2025-09-10
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Journal Article
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Abstract
We present exact non-Gaussian joint likelihoods for auto- and cross-correlation functions on arbitrarily maskedspherical Gaussian random fields. Our considerations apply to spin-0 as well as spin-2 fields but are demonstratedhere for the spin-2 weak-lensing correlation function.We motivate that this likelihood cannot be Gaussian and show how it can nevertheless be calculated exactly forany mask geometry and on a curved sky, as well as jointly for different angular-separation bins and redshift-bincombinations. Splitting our calculation into a large- and small-scale part, we apply a computationally efficientapproximation for the small scales that does not alter the overall non-Gaussian likelihood shape.To compare our exact likelihoods to correlation-function sampling distributions, we simulated a large numberof weak-lensing maps, including shape noise, and find excellent agreement for one-dimensional as well astwo-dimensional distributions. Furthermore, we compare the exact likelihood to the widely employed Gaussianlikelihood and find significant levels of skewness at angular separations ≳ 1◦, such that the mode of the exactdistributions is shifted away from the mean towards lower values of the correlation function. We find that theassumption of a Gaussian random field for the weak-lensing field is well valid at these angular separations.Considering the skewness of the non-Gaussian likelihood, we evaluate its impact on the posterior constraintson 𝑆₈. On a simplified weak-lensing-survey setup with an area of 10 000 deg², we find that the posterior meanof 𝑆₈ is around 2.5% higher when using the non-Gaussian likelihood, a shift comparable to the precision ofcurrent stage-III surveys.
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published
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Journal / series
Volume
8
Pages / Article No.
Publisher
Maynooth Academic Publishing
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Subject
Likelihood; Non Gaussian; Bayesian statistics; Gaussian random field; Correlation function; Weak lensing
Organisational unit
03928 - Refregier, Alexandre / Refregier, Alexandre
02010 - Dep. Physik / Dep. of Physics
Notes
Funding
193352 - Cosmology in the non-linear and baryonic Universe (SNF)