A Bayesian method for combining theoretical and simulated covariance matrices for largescale structure surveys
Abstract
Accurate and precise covariance matrices will be important in enabling planned cosmological surveys to detect new physics. Standard methods imply either the need for many Nbody simulations in order to obtain an accurate estimate, or a precise theoretical model. We combine these approaches by constructing a likelihood function conditioned on simulated and theoretical covariances, consistently propagating noise from the finite number of simulations and uncertainty in the theoretical model itself using an informative InverseWishart prior. Unlike standard methods, our approach allows the required number of simulations to be less than the number of summary statistics. We recover the linear `shrinkage' covariance estimator in the context of a Bayesian data model, and test our marginal likelihood on simulated mock power spectrum estimates. We conduct a thorough investigation into the impact of prior confidence in different choices of covariance models on the quality of model fits and parameter variances. In a simplified setting, we find that the number of simulations required can be reduced if one is willing to accept a mild degradation in the quality of model fits, finding that even weakly informative priors can help to reduce the simulation requirements. We identify the correlation matrix of the summary statistics as a key quantity requiring careful modelling. Our approach can be easily generalized to any covariance model or set of summary statistics, and elucidates the role of hybrid estimators in cosmological inference.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 February 2019
 DOI:
 10.1093/mnras/sty3102
 arXiv:
 arXiv:1807.06875
 Bibcode:
 2019MNRAS.483..189H
 Keywords:

 methods: data analysis;
 methods: statistical;
 largescale structure of Universe;
 cosmology: observations;
 Astrophysics  Cosmology and Nongalactic Astrophysics
 EPrint:
 21 pages, 11 figures. Minor changes to match the version published in MNRAS