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

Citation:

Philcox OHE, Eisenstein DJ. Estimating covariance matrices for two- and three-point correlation function moments in Arbitrary Survey Geometries. Monthly Notices of the Royal Astronomical Society [Internet]. 2019;490 :5931-5951.

Date Published:

December 01, 201

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 arbitrarynon-linear 2PCFs (which may be estimated from the survey itself), with ashot-noise rescaling parameter included to capture non-Gaussianity. Wegeneralize previous approaches to include Legendre moments via ageometry-correction function calibrated from measured pair and triplecounts. Making use of importance sampling and random particlecatalogues, we can estimate model covariances in fractions of the timerequired to do so with mocks, obtaining estimates with negligiblesampling noise in ̃10 (̃100) CPU-hours for the 2PCF (3PCF)autocovariance. We compare results to sample covariances from a suite ofBOSS DR12 mocks and find the matrices to be in good agreement, assuminga shot-noise rescaling parameter of 1.03 (1.20) for the 2PCF (3PCF). Toobtain strongest constraints on cosmological parameters, we must usemultiple statistics in concert; having robust methods to measure theircovariances at low computational cost is thus of great relevance toupcoming surveys.

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