Efficient cosmological parameter sampling using sparse grids

TL;DR

This paper introduces a fast and accurate method for cosmological parameter sampling using sparse grid interpolation of the likelihood, outperforming existing approaches in speed and reliability.

Contribution

The authors develop a novel sparse grid interpolation technique for likelihood estimation that is faster, more reliable, and adaptable compared to polynomial and neural network methods.

Findings

Achieves high accuracy in reproducing likelihood projections

Speeds up parameter sampling significantly

Avoids unphysical artifacts common in polynomial fits

Abstract

We present a novel method to significantly speed up cosmological parameter sampling. The method relies on constructing an interpolation of the CMB-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 parallelised 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.