Putting the precision in precision cosmology: How accurate should your data covariance matrix be?

By A. Taylor, B. Joachimi, Thomas D. Kitching. 2012

171 citations recorded by the source corpus.

Cosmological parameter estimation requires that the likelihood function of the data is accurately known. Assuming that cosmological large-scale structure power spectra data are multivariate Gaussian-distributed, we show the accuracy of parameter estimation is limited by the accuracy of the inverse data covariance matrix - the precision matrix. If the data covariance and precision matrices are estimated by sampling independent realisations of the data, their statistical properties are described by the Wishart and Inverse-Wishart distributions, respectively. Independent of any details of the survey, we show that the fractional error on a parameter variance, or a Figure-of-Merit, is equal to the fractional variance of the precision matrix. In addition, for the only unbiased estimator of the precision matrix, we find that the fractional accuracy of the parameter error depends only on the difference between the number of independent realisations and the number of data points, and so can easily diverge. For a 5% error on a parameter error and N_D >100 we need N_S > N_D realisations and a fractional accuracy of 10^4 -10^6 this approach will be problematic. We discuss possible ways to relax these conditions: improved theoretical modelling; shrinkage methods; data-compression; simulation and data resampling methods.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/295742e7b02c72540915d3607252d28bbbaeb03d

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Citations in the corpus

COSMOLIKE - cosmological likelihood analyses for photometric galaxy surveys (2016, background): “The number of total bins in the joint data vector can also be limited by the number of independent realizations that can be generated for covariance estimation (Hartlap et al. 2007; Dodelson & Schneider 2013; Taylor et al. 2013).”
The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: mock galaxy catalogues for the BOSS Final Data Release (2015, background): “The impact of the uncertainties in the covariance matrix on the derived cosmological constraints has been subject of several recent analyses (Dodelson & Schneider 2013; Taylor et al. 2013; Percival et al. 2014).”