Estimating Covariance Matrices for Two- and Three-Point Correlation Function Moments in Arbitrary Survey Geometries. (arXiv:1910.04764v1 [astro-ph.CO])

<a href="http://arxiv.org/find/astro-ph/1/au:+Philcox_O/0/1/0/all/0/1">Oliver H. E. Philcox</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Eisenstein_D/0/1/0/all/0/1">Daniel J. Eisenstein</a>

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 catalogs, we can estimate model covariances in fractions of the time

required to do so with mocks, obtaining estimates with negligible sampling

noise in $sim 10$ ($sim 100$) CPU-hours for the 2PCF (3PCF) auto-covariance.

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.

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 catalogs, we can estimate model covariances in fractions of the time

required to do so with mocks, obtaining estimates with negligible sampling

noise in $sim 10$ ($sim 100$) CPU-hours for the 2PCF (3PCF) auto-covariance.

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.

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