Bayesian emulator optimisation for cosmology: application to the Lymanalpha forest
Abstract
The Lymanalpha forest provides strong constraints on both cosmological parameters and intergalactic medium astrophysics, which are forecast to improve further with the next generation of surveys including eBOSS and DESI. As is generic in cosmological inference, extracting this information requires a likelihood to be computed throughout a highdimensional parameter space. Evaluating the likelihood requires a robust and accurate mapping between the parameters and observables, in this case the 1D flux power spectrum. Cosmological simulations enable such a mapping, but due to computational time constraints can only be evaluated at a handful of sample points; "emulators" are designed to interpolate between these. The problem then reduces to placing the sample points such that an accurate mapping is obtained while minimising the number of expensive simulations required. To address this, we introduce an emulation procedure that employs Bayesian optimisation of the training set for a Gaussian process interpolation scheme. Starting with a Latin hypercube sampling (other schemes with good spacefilling properties can be used), we iteratively augment the training set with extra simulations at new parameter positions which balance the need to reduce interpolation error while focussing on regions of high likelihood. We show that smaller emulator error from the Bayesian optimisation propagates to smaller widths on the posterior distribution. Even with fewer simulations than a Latin hypercube, Bayesian optimisation shrinks the 95% credible volume by 90% and, e.g., the 1σ error on the amplitude of smallscale primordial fluctuations by 38%. This is the first demonstration of Bayesian optimisation applied to largescale structure emulation, and we anticipate the technique will generalise to many other probes such as galaxy clustering, weak lensing and 21cm.
 Publication:

Journal of Cosmology and Astroparticle Physics
 Pub Date:
 February 2019
 DOI:
 10.1088/14757516/2019/02/031
 arXiv:
 arXiv:1812.04631
 Bibcode:
 2019JCAP...02..031R
 Keywords:

 Astrophysics  Cosmology and Nongalactic Astrophysics
 EPrint:
 23 pages, 4 figures. Minor changes to match version published in JCAP