Copula Cosmology: Constructing a Likelihood Function

TL;DR

This paper introduces the copula as a flexible mathematical tool to construct likelihood functions for cosmological data, demonstrating its effectiveness in modeling complex distributions like cosmic shear power spectra.

Contribution

It presents a novel application of the Gaussian copula to build likelihood functions that better capture the true distribution of cosmological measurements.

Findings

Gaussian copula reproduces the n-dimensional distribution accurately

Copula likelihood outperforms traditional Gaussian likelihood in modeling cosmic shear data

Potentially improves future weak lensing analyses

Abstract

To estimate cosmological parameters from a given dataset, we need to construct a likelihood function, which sometimes has a complicated functional form. We introduce the copula, a mathematical tool to construct an arbitrary multivariate distribution function from one-dimensional marginal distribution functions with any given dependence structure. It is shown that a likelihood function constructed by the so-called Gaussian copula can reproduce very well the n-dimensional probability distribution of the cosmic shear power spectrum obtained from a large number of ray-tracing simulations. This suggests that the Copula likelihood will be a powerful tool for future weak lensing analyses, instead of the conventional multivariate Gaussian likelihood.