Extremely expensive likelihoods: a variational-Bayes solution for precision cosmology

Monthly Notices of the Royal Astronomical Society, vol. 521, pp. 1152–1161

Abstract

ABSTRACT We present a variational-Bayes solution to compute non-Gaussian posteriors from extremely expensive likelihoods. Our approach is an alternative for parameter inference when Markov chain Monte Carlo (MCMC) sampling is numerically prohibitive or conceptually unfeasible. For example, when either the likelihood or the theoretical model cannot be evaluated at arbitrary parameter values, but only previously selected values, then traditional MCMC sampling is impossible, whereas our variational-Bayes solution still succeeds in estimating the full posterior. In cosmology, this occurs e.g. when the parametric model is based on costly simulations that were run for previously selected input parameters. We demonstrate the applicability of our posterior construction on the KiDS-450 weak lensing analysis, where we reconstruct the original KiDS MCMC posterior at 0.6 per cent of its former numerical posterior evaluations. The reduction in numerical cost implies that systematic effects which formerly exhausted the numerical budget could now be included.

Authors 2

1. Matteo Rizzato corresponding Aachen Leiden Observatory Huygens Laboratory

   Leiden University · Leiden Observatory

   Affiliation as printed

   Leiden Observatory, Leiden University, Huygens Laboratory , Niels Bohrweg 2, NL-2333 CA Leiden, The Netherlands

2. Elena Sellentin Aachen Leiden Observatory Huygens Laboratory Mathematical Institute

   Leiden University · Leiden Observatory

   Affiliation as printed

   Leiden Observatory, Leiden University, Huygens Laboratory , Niels Bohrweg 2, NL-2333 CA Leiden, The Netherlands

   Mathematical Institute, Leiden University, Snellius Building , Niels Bohrweg 1, NL-2333 CA Leiden, The Netherlands