Parameter inference for weak lensing using Gaussian Processes and MOPED
Abstract
In this paper, we propose a Gaussian Process (GP) emulator for the calculation both of tomographic weak lensing band powers, and of coefficients of summary data massively compressed with the MOPED algorithm. In the former case cosmological parameter inference is accelerated by a factor of ∼1030 compared with Boltzmann solver CLASS applied to KiDS450 weak lensing data. Much larger gains of order 10^{3} will come with future data, and MOPED with GPs will be fast enough to permit the Limber approximation to be dropped, with acceleration in this case of ∼10^{5}. A potential advantage of GPs is that an error on the emulated function can be computed and this uncertainty incorporated into the likelihood. However, it is known that the GP error can be unreliable when applied to deterministic functions, and we find, using the KullbackLeibler divergence between the emulator and CLASS likelihoods, and from the uncertainties on the parameters, that agreement is better when the GP uncertainty is not used. In future, weak lensing surveys such as Euclid, and the Legacy Survey of Space and Time, will have up to ∼10^{4} summary statistics, and inference will be correspondingly more challenging. However, since the speed of MOPED is determined not the number of summary data, but by the number of parameters, MOPED analysis scales almost perfectly, provided that a fast way to compute the theoretical MOPED coefficients is available. The GP provides such a fast mechanism.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 July 2020
 DOI:
 10.1093/mnras/staa2102
 arXiv:
 arXiv:2005.06551
 Bibcode:
 2020MNRAS.497.2213M
 Keywords:

 gravitational lensing: weak;
 methods: data analysis;
 methods: statistical;
 cosmological parameters;
 largescale structure of Universe;
 Astrophysics  Cosmology and Nongalactic Astrophysics
 EPrint:
 16 pages, 11 figures (Accepted for publication in MNRAS)