Copula Cosmology: Constructing a Likelihood Function

Details Copula Cosmology: Constructing a Likelihood Function Copula Cosmology: Constructing a Likelihood Function

2010-11-23

arxiv.org/abs/1011.4997v2

Phys.Rev.D83:023501,2011

Astronomy and Astrophysics

Astrophysics

Cosmology and Extragalactic Astrophysics

9 pages, 4 figures. Maches version published by the Physical Review D

Scientific paper

10.1103/PhysRevD.83.023501

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.

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