Extremely expensive likelihoods: A variational-Bayes solution for precision cosmology
arXiv:2203.05009 · doi:10.1093/mnras/stad638
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 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% 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.
arXiv commentSubmitted to MNRAS, 10 pages, 5 figures
References in corpus (13)
- KiDS-450: Cosmological parameter constraints from tomographic weak gravitational lensing
- Karhunen-Loeve eigenvalue problems in cosmology: how should we tackle large data sets?
- LSST Science Book, Version 2.0
- Dark Energy and Dark Gravity
- The first-year shear catalog of the Subaru Hyper Suprime-Cam SSP Survey
- Cosmology from Cosmic Shear with DES Science Verification Data
- Neutrino masses and cosmological parameters from a Euclid-like survey: Markov Chain Monte Carlo forecasts including theoretical errors
- Breaking the spell of Gaussianity: forecasting with higher order Fisher matrices
- Bounds on light sterile neutrino mass and mixing from cosmology and laboratory searches
- Detecting the cosmological neutrino background in the CMB
- A fast, always positive definite and normalizable approximation of non-Gaussian likelihoods
- Non-Gaussian forecasts of weak lensing with and without priors
- Boosting MonteCarlo sampling with a non-Gaussian fit