Parameter Inference for Weak Lensing using Gaussian Processes and MOPED
  In this paper, we propose a Gaussian Process (GP) emulator for the
calculation of a) tomographic weak lensing band-power spectra, and b)
coefficients of summary data massively compressed with the MOPED algorithm. In
the former case cosmological parameter inference is accelerated by a factor of
$\sim 10$-$30$ compared to explicit calls to the Boltzmann solver CLASS when
applied to KiDS-450 weak lensing data. Much larger gains will come with future
data, where with MOPED compression, the speed up can be up to a factor of $\sim
10^3$ when the common Limber approximation is used. Furthermore, the GP opens
up the possibility of dropping the Limber approximation, without which the
theoretical calculations may be unfeasibly slow. A potential advantage of GPs
is that an error on the emulated function can be computed and this uncertainty
incorporated into the likelihood. If speed is of the essence, then the mean of
the Gaussian Process can be used and the uncertainty ignored. We compute the
Kullback-Leibler divergence between the emulator likelihood and the CLASS
likelihood, and on the basis of this and from analysing the uncertainties on
the parameters, we find that in this case, the inclusion of the GP uncertainty
does not justify the extra computational expense in the test application. For
future weak lensing surveys such as Euclid and Legacy Survey of Space and
Telescope (LSST), the number of summary statistics will be large, up to $\sim
10^{4}$. The speed of MOPED is determined by the number of parameters, not the
number of summary data, so the gains are very large. In the non-Limber case,
the speed-up can be a factor of $\sim 10^5$, provided that a fast way to
compute the theoretical MOPED coefficients is available. The GP presented here
provides such a fast mechanism and enables MOPED to be employed.
