Journal Article

Efficient cosmological parameter sampling using sparse grids

M. Frommert, D. Pflüger, T. Riller, M. Reinecke, H.-J. Bungartz and T. A. Enßlin

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 406, issue 2, pages 1177-1189
Published in print August 2010 | ISSN: 0035-8711
Published online July 2010 | e-ISSN: 1365-2966 | DOI: http://dx.doi.org/10.1111/j.1365-2966.2010.16788.x
Efficient cosmological parameter sampling using sparse grids

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We present a novel method to significantly speed up cosmological parameter sampling. The method relies on constructing an interpolation of the cosmic microwave background log-likelihood based on sparse grids, which is used as a shortcut for the likelihood evaluation. We obtain excellent results over a large region in parameter space, comprising about 25 log-likelihoods around the peak, and we reproduce the one-dimensional projections of the likelihood almost perfectly. In speed and accuracy, our technique is competitive to existing approaches to accelerate parameter estimation based on polynomial interpolation or neural networks, while having some advantages over them. In our method, there is no danger of creating unphysical wiggles as it can be the case for polynomial fits of a high degree. Furthermore, we do not require a long training time as for neural networks, but the construction of the interpolation is determined by the time it takes to evaluate the likelihood at the sampling points, which can be parallelized to an arbitrary degree. Our approach is completely general, and it can adaptively exploit the properties of the underlying function. We can thus apply it to any problem where an accurate interpolation of a function is needed.

Keywords: methods: data analysis; cosmological parameters

Journal Article.  9433 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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