The exact non-Gaussian weak lensing likelihood: A framework to calculate analytic likelihoods for correlation functions on masked Gaussian random fields

Understand

We present exact non-Gaussian joint likelihoods for auto- and cross-correlation functions on arbitrarily masked spherical Gaussian random fields.

• Our considerations apply to spin-0 as well as spin-2 fields but are demonstrated here 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 for any mask geometry and on a curved sky, as well as jointly for different angular-separation bins and redshift-bin combinations.
• Splitting our calculation into a large- and small-scale part, we apply a computationally efficient approximation for the small scales that does not alter the overall non-Gaussian likelihood shape.