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arXiv · 1011.4997

Copula Cosmology: Constructing a Likelihood Function

Masanori Sato·Kiyotomo Ichiki·Tsutomu T. Takeuchi
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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.

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Masanori Sato, Kiyotomo Ichiki, Tsutomu T. Takeuchi. 2010-12-27. Copula Cosmology: Constructing a Likelihood Function. https://doi.org/10.1103/physrevd.83.023501

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