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Title: Estimating covariance matrices for two- and three-point correlation function moments in Arbitrary Survey Geometries

Abstract

ABSTRACT We present configuration-space estimators for the auto- and cross-covariance of two- and three-point correlation functions (2PCF and 3PCF) in general survey geometries. These are derived in the Gaussian limit (setting higher order correlation functions to zero), but for arbitrary non-linear 2PCFs (which may be estimated from the survey itself), with a shot-noise rescaling parameter included to capture non-Gaussianity. We generalize previous approaches to include Legendre moments via a geometry-correction function calibrated from measured pair and triple counts. Making use of importance sampling and random particle catalogues, we can estimate model covariances in fractions of the time required to do so with mocks, obtaining estimates with negligible sampling noise in ∼10 (∼100) CPU-hours for the 2PCF (3PCF) autocovariance. We compare results to sample covariances from a suite of BOSS DR12 mocks and find the matrices to be in good agreement, assuming a shot-noise rescaling parameter of 1.03 (1.20) for the 2PCF (3PCF). To obtain strongest constraints on cosmological parameters, we must use multiple statistics in concert; having robust methods to measure their covariances at low computational cost is thus of great relevance to upcoming surveys.

Authors:
ORCiD logo [1];  [2]
  1. Center for Astrophysics | Harvard & Smithsonian, 60 Garden St., Cambridge, MA 02138, USA, Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544, USA
  2. Center for Astrophysics | Harvard & Smithsonian, 60 Garden St., Cambridge, MA 02138, USA
Publication Date:
Sponsoring Org.:
USDOE
OSTI Identifier:
1574553
Grant/Contract Number:  
SC0013718
Resource Type:
Published Article
Journal Name:
Monthly Notices of the Royal Astronomical Society
Additional Journal Information:
Journal Name: Monthly Notices of the Royal Astronomical Society Journal Volume: 490 Journal Issue: 4; Journal ID: ISSN 0035-8711
Publisher:
Oxford University Press
Country of Publication:
United Kingdom
Language:
English

Citation Formats

Philcox, Oliver H. E., and Eisenstein, Daniel J. Estimating covariance matrices for two- and three-point correlation function moments in Arbitrary Survey Geometries. United Kingdom: N. p., 2019. Web. doi:10.1093/mnras/stz2896.
Philcox, Oliver H. E., & Eisenstein, Daniel J. Estimating covariance matrices for two- and three-point correlation function moments in Arbitrary Survey Geometries. United Kingdom. doi:10.1093/mnras/stz2896.
Philcox, Oliver H. E., and Eisenstein, Daniel J. Wed . "Estimating covariance matrices for two- and three-point correlation function moments in Arbitrary Survey Geometries". United Kingdom. doi:10.1093/mnras/stz2896.
@article{osti_1574553,
title = {Estimating covariance matrices for two- and three-point correlation function moments in Arbitrary Survey Geometries},
author = {Philcox, Oliver H. E. and Eisenstein, Daniel J.},
abstractNote = {ABSTRACT We present configuration-space estimators for the auto- and cross-covariance of two- and three-point correlation functions (2PCF and 3PCF) in general survey geometries. These are derived in the Gaussian limit (setting higher order correlation functions to zero), but for arbitrary non-linear 2PCFs (which may be estimated from the survey itself), with a shot-noise rescaling parameter included to capture non-Gaussianity. We generalize previous approaches to include Legendre moments via a geometry-correction function calibrated from measured pair and triple counts. Making use of importance sampling and random particle catalogues, we can estimate model covariances in fractions of the time required to do so with mocks, obtaining estimates with negligible sampling noise in ∼10 (∼100) CPU-hours for the 2PCF (3PCF) autocovariance. We compare results to sample covariances from a suite of BOSS DR12 mocks and find the matrices to be in good agreement, assuming a shot-noise rescaling parameter of 1.03 (1.20) for the 2PCF (3PCF). To obtain strongest constraints on cosmological parameters, we must use multiple statistics in concert; having robust methods to measure their covariances at low computational cost is thus of great relevance to upcoming surveys.},
doi = {10.1093/mnras/stz2896},
journal = {Monthly Notices of the Royal Astronomical Society},
number = 4,
volume = 490,
place = {United Kingdom},
year = {2019},
month = {10}
}

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