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Quantifying lost information due to covariance matrix estimation in parameter inference

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Title: Quantifying lost information due to covariance matrix estimation in parameter inference
Authors: Sellentin, E
Heavens, AF
Item Type: Journal Article
Abstract: Parameter inference with an estimated covariance matrix systematically loses information due to the remaining uncertainty of the covariance matrix. Here, we quantify this loss of precision and develop a framework to hypothetically restore it, which allows to judge how far away a given analysis is from the ideal case of a known covariance matrix. We point out that it is insufficient to estimate this loss by debiasing the Fisher matrix as previously done, due to a fundamental inequality that describes how biases arise in non-linear functions. We therefore develop direct estimators for parameter credibility contours and the figure of merit, finding that significantly fewer simulations than previously thought are sufficient to reach satisfactory precisions. We apply our results to DES Science Verification weak lensing data, detecting a 10 per cent loss of information that increases their credibility contours. No significant loss of information is found for KiDS. For a Euclid-like survey, with about 10 nuisance parameters we find that 2900 simulations are sufficient to limit the systematically lost information to 1 per cent, with an additional uncertainty of about 2 per cent. Without any nuisance parameters, 1900 simulations are sufficient to only lose 1 per cent of information. We further derive estimators for all quantities needed for forecasting with estimated covariance matrices. Our formalism allows to determine the sweetspot between running sophisticated simulations to reduce the number of nuisance parameters, and running as many fast simulations as possible.
Issue Date: 19-Oct-2016
Date of Acceptance: 17-Oct-2016
URI: http://hdl.handle.net/10044/1/48807
DOI: https://dx.doi.org/10.1093/mnras/stw2697
ISSN: 0035-8711
Publisher: Oxford University Press
Start Page: 4658
End Page: 4665
Journal / Book Title: Monthly Notices of the Royal Astronomical Society
Volume: 464
Issue: 4
Copyright Statement: © 2016 The Authors. Published by Oxford University Press on behalf of the Royal Astronomical Society. This is a pre-copy-editing, author-produced version of an article accepted for publication in Monthly Notices of the Royal Astronomical Society following peer review. The definitive publisher-authenticated version Elena Sellentin, Alan F. Heavens; Quantifying lost information due to covariance matrix estimation in parameter inference. Mon Not R Astron Soc 2017; 464 (4): 4658-4665. doi: 10.1093/mnras/stw2697 is available online at: https://dx.doi.org/10.1093/mnras/stw2697
Sponsor/Funder: Imperial College Trust
Science and Technology Facilities Council
Science and Technology Facilities Council (STFC)
Funder's Grant Number: N/A
ST-N000838
ST/N000838/1
Keywords: Science & Technology
Physical Sciences
Astronomy & Astrophysics
methods: data analysis
methods: statistical
cosmology: observations
SIMULATIONS
COSMOLOGY
0201 Astronomical And Space Sciences
Publication Status: Published
Open Access location: https://arxiv.org/pdf/1609.00504.pdf
Appears in Collections:Physics
Astrophysics



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