The clustering of Galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: including covariance matrix errors

By Will J. Percival, A. Ross, Ariel G. Sánchez, L. Samushia, A. Burden, Robert G. Crittenden, A. Cuesta, M. V. Magaña, Marc Manera, F. Beutler and 12 more. 2013

207 citations recorded by the source corpus.

We present improved methodology for including covariance matrices in the error budget of Baryon Oscillation Spectroscopic Survey (BOSS) galaxy clustering measurements, revisiting Data Release 9 (DR9) analyses, and describing a method that is used in DR10/11 analyses presented in companion papers. The precise analysis method adopted is becoming increasingly important, due to the precision that BOSS can now reach: even using as many as 600 mock catalogues to estimate covariance of two-point clustering measurements can still lead to an increase in the errors of ∼20 per cent, depending on how the cosmological parameters of interest are measured. In this paper, we extend previous work on this contribution to the error budget, deriving formulae for errors measured by integrating over the likelihood, and to the distribution of recovered best-fitting parameters fitting the simulations also used to estimate the covariance matrix. Both are situations that previous analyses of BOSS have considered. We apply the formulae derived to baryon acoustic oscillation (BAO) and redshift-space distortion (RSD) measurements from BOSS in our companion papers. To further aid these analyses, we consider the optimum number of bins to use for two-point measurements using the monopole power spectrum or correlation function for BAO, and the monopole and quadrupole moments of the correlation function for anisotropic-BAO and RSD measurements.

Subfields: Astronomy and Astrophysics, Instrumentation

View Paper: https://www.semanticscholar.org/paper/f533618855513b662176a91100a210dcd78a432e

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Citations in the corpus

The SDSS-IV Extended Baryon Oscillation Spectroscopic Survey: Baryon Acoustic Oscillations at Redshift of 0.72 with the DR14 Luminous Red Galaxy Sample (2017, methodology): “…order to account for the finite number of mock measurements used to derive Ĉ, the unbiased estimator for the precision matrix (Hartlap et al. 2007; Percival et al. 2014; Taylor et al. 2014) should be written as W n N C1 1 , 16 mocks 1= - - -⎛ ⎝⎜ ⎞ ⎠⎟ˆ ˆ ( ) where n is the number of elements in…”
The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: baryon acoustic oscillations in the Fourier space (2016, methodology): “…propagate the error in the covariance matrix to the error on the estimated parameters; this is done by scaling the variance for each parameter by (Percival et al. 2014) M1 = √ 1 + B(nb − np) 1 + A + B(np + 1) , (54) MNRAS 464, 3409–3430 (2017) where np is the number of parameters and A = 2 (Ns −…”
The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: mock galaxy catalogues for the BOSS Final Data Release (2015, methodology): “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).”
The clustering of the SDSS main galaxy sample – II. Mock galaxy catalogues and a measurement of the growth of structure from redshift space distortions at z = 0.15 (2014, background): “Of order 1000 mock galaxy catalogues (mocks) are necessary to ensure noise in the covariance matrix does not add significant noise to our measurements (Percival et al. 2014).”
The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: baryon acoustic oscillations in the correlation function of LOWZ and CMASS galaxies in Data Release 12 (2015, methodology): “We measure ξ (s, μ) using the Landy & Szalay (1993) estimator, with radial bins of width 8 h−1 Mpc and angular bins of μ = 0.01 (see VargasMagana et al. 2013; Percival et al. 2014 for the effect of bin-sizes on the measurement).”
The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: Cosmological implications of the configuration-space clustering wedges (2016, methodology): “They demonstrated that, to account for this extra uncertainty, the recovered parameter constraints must be rescaled by a factor that depends on Nb, Nm and the number of parameters included in the analysis, Np (see equation 18 in Percival et al. 2014).”
The clustering of the SDSS-IV extended Baryon Oscillation Spectroscopic Survey DR14 quasar sample: First measurement of baryon acoustic oscillations between redshift 0.8 and 2.2 (2017, methodology): “These factors are defined in Hartlap, Simon & Schneider (2007), Dodelson & Schneider (2013) and Percival et al. (2014); we apply the factors in the same way as in, e.g. Anderson et al. (2014).”
The VIMOS Public Extragalactic Redshift Survey (VIPERS): The growth of structure at $0.5 < z < 1.2$ from redshift-space distortions in the clustering of the PDR-2 final sample (2016, methodology): “We follow Percival et al. (2014) and correct for these e ﬀ ects by applying two correction factors.”
The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: cosmological analysis of the DR12 galaxy sample (2016, methodology): “The full procedure for estimating the covariance matrices is described in Percival et al. (2014), which includes the uncertainties in the covariance matrix when derived from a finite sample of simulations.”
The clustering of the SDSS DR7 Main Galaxy Sample I: a 4 per cent distance measure at z=0.15 (2014, background): “Percival et al. (2014) derived factors that correct uncertainties determined using a covariance matrix that is constructed from mock realisations and to standard deviations determined from those realisations so that they account biases that result from the finite number of realisations employed.”
The power spectrum and bispectrum of SDSS DR11 BOSS galaxies – I. Bias and gravity (2014, background): “In particular, for DR11 the full southern area is contained in the NGC (see section 6.1 of Percival et al. 2014 for more details).”
The clustering of the SDSS-IV extended Baryon Oscillation Spectroscopic Survey DR14 quasar sample: measurement of the growth rate of structure from the anisotropic correlation function between redshift 0.8 and 2.2 (2018, methodology): “The inverse of the covariance matrices used to fit the cosmological parameters include the correction procedure described in Hartlap et al. (2007) and Percival et al. (2014) due to finite number of mocks and number of bins in the analysis.”
The DESI Experiment Part I: Science,Targeting, and Survey Design (2016, background): “Efficient information compression is necessary when the covariance matrix of the observables are estimated from a finite number of mock surveys [88].”
Elucidating ΛCDM: Impact of Baryon Acoustic Oscillation Measurements on the Hubble Constant Discrepancy (2017, background): “…more galaxies, notably the Baryon Oscillation Spectroscopic Survey (BOSS5), have led to both improved precision in the BAO scale measurements over a range of redshifts, and improved analysis methodologies (e.g., Percival et al. 2014; Anderson et al. 2014; Kazin et al. 2014; Reid et al. 2016).”
Combining full-shape and BAO analyses of galaxy power spectra: a 1.6% CMB-independent constraint on H0 (2020, background): “[94], noting that this contributes only a small ∼ 2% error on the derived parameter errors.”
The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: tomographic BAO analysis of DR12 combined sample in Fourier space (2016, methodology): “To correct for this, we follow Percival et al. (2014) and rescale the variance of each parameter by M = √ 1 + B(Nb − Np) 1 + A + B(Np + 1) , (34) where Np and Nb are the number of parameters and number of k bins, respectively, and A = 2 (Nmock − Nb − 1)(N − Nb − 4) , B = Nmock − Nb − 2 (Nmock − Nb…”
The completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: BAO and RSD measurements from anisotropic clustering analysis of the quasar sample in configuration space between redshift 0.8 and 2.2 (2020, background): “(11) Therefore the final parameter matrix needs to be rescaled MNRAS 000, 1–22 (2020) following Percival et al. (2014) M = 1 + B ( Nb − Np ) 1 + A + B ( Np + 1 ) , (12) where such a correction is suitable under the assumption of a Gaussian likelihood.”