Statistical analysis of galaxy surveys – I. Robust error estimation for two-point clustering statistics

By P. Norberg, C. Baugh, Enrique Gaztañaga, Darren J. Croton IfA, University of Edinburgh Icc, University of Durham Ieeccsic UC Berkeley Swinburne University. 2008

287 citations recorded by the source corpus.

We present a test of different error estimators for two-point clustering statistics, appropriate for present and future large galaxy redshift surveys. Using an ensemble of very large dark matter ACDM N-body simulations, we compare internal error estimators (jackknife and bootstrap) to external ones (Monte Carlo realizations). For three-dimensional clustering statistics, we find that none of the internal error methods investigated is able to reproduce either accurately or robustly the errors of external estimators on 1 to 25 h ―1 Mpc scales. The standard bootstrap overestimates the variance of ξ (s) by ∼40 per cent on all scales probed, but recovers, in a robust fashion, the principal eigenvectors of the underlying covariance matrix. The jackknife returns the correct variance on large scales, but significantly overestimates it on smaller scales. This scale dependence in the jackknife affects the recovered eigenvectors, which tend to disagree on small scales with the external estimates. Our results have important implications for fitting models to galaxy clustering measurements. For example, in a two-parameter fit to the projected correlation function, we find that the standard bootstrap systematically overestimates the 95 per cent confidence interval, while the jackknife method remains biased, but to a lesser extent. Ignoring the systematic bias, the scatter between realizations, for Gaussian statistics, implies that a 2σ confidence interval, as inferred from an internal estimator, corresponds in practice to anything from 1σ to 3σ. By oversampling the subvolumes, we find that it is possible, at least for the cases we consider, to obtain robust bootstrap variances and confidence intervals that agree with external error estimates. Our results are applicable to two-point statistics, like ξ(s) and w p (r p ), measured in large redshift surveys, and show that the interpretation of clustering measurements with internally estimated errors should be treated with caution.

Subfields: Artificial Intelligence, Astronomy and Astrophysics, Ecology

View Paper: https://www.semanticscholar.org/paper/ffb12c0ba7f8de60d643bba919d8b33fd2906a71

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Citations in the corpus

• CLUSTERING OF LOW-REDSHIFT (z ⩽ 2.2) QUASARS FROM THE SLOAN DIGITAL SKY SURVEY (2008, background): “…to find values for the real-space correlation length, r0, the best-fit values we find from 9 The interested reader is pointed towards recent work by Norberg et al. (2008), who use large N-body simulations to investigate different error estimators and the 2PCF for galaxy clustering. using the…”
• Cosmological Constraints from a Combination of Galaxy Clustering and Lensing -- III. Application to SDSS Data (2012, background): “…redshift space distortions into account results in systematic errors that can easily exceed 20 percent on large scales (rp >∼ 10h−1 Mpc), causing systematic errors in the inferred galaxy bias (see also Padmanabhan, White & Eisenstein 2007; Norberg et al. 2009; Baldauf et al. 2010; More 2011).”
• Cosmological constraints from a combination of galaxy clustering and lensing – I. Theoretical framework (2012, background): “However, as we demonstrate in §4.5 below, this introduces errors that can easily exceed 40 percent or more on the largest scales probed by the data (∼ 20h−1 Mpc; see also Padmanabhan, White & Eisenstein 2007; Norberg et al. 2009; Baldauf et al. 2010).”
• Cosmological parameter constraints from SDSS luminous red galaxies: a new treatment of large-scale clustering (2009, background): “They found that the jackknife (JK) error, an internal estimate made from the data set itself (see Norberg et al. 2009), gave a reasonable match to the diagonal elements of the covariance matrix obtained directly from the 216 mock catalogues.”
• CFHTLenS tomographic weak lensing cosmological parameter constraints: Mitigating the impact of intrinsic galaxy alignments (2013, methodology): “Bootstrap and Jackknife techniques can be used to estimate the data covariance directly from the survey (Wall & Jenkins 2003), and various de-noising techniques can be applied to reduce the impact of noise bias when the matrix is inverted (see for example Norberg et al. 2009).”
• The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey:a large sample of mock galaxy catalogues (2012, background): “It does however require some arbitrary choices (number of Jack-knife regions, for example) and its performance is far from perfect (see e.g. Norberg et al. 2009).”
• Mock galaxy catalogues using the quick particle mesh method (2013, methodology): “On smaller scales internal estimates of the covariance matrix can be constructed (e.g. via bootstrap or jackknife), however, on large scales these methods do not perform as well (e.g. Norberg et al. 2009, and references therein).”
• Interpreting large-scale redshift-space distortion measurements (2011, background): “Studying the three-dimensional clustering on scales below 25 h−1 Mpc, Norberg et al. (2009) showed that internal methods do recover the principal components of the real covariance matrix in a robust way but can not accurately reproduce the errors themselves, usually overestimating them by as much…”
• GALAXY CLUSTERING IN THE COMPLETED SDSS REDSHIFT SURVEY: THE DEPENDENCE ON COLOR AND LUMINOSITY (2010, methodology): “The tests of Z05 and Norberg et al. (2009) suggest that jackknife error estimates for wp(rp) are typicallly accurate or conservative (see §2.2).”
• GALAXY CLUSTERING IN THE NEWFIRM MEDIUM BAND SURVEY: THE RELATIONSHIP BETWEEN STELLAR MASS AND DARK MATTER HALO MASS AT 1 < z < 2 (2010, methodology): “There is considerable noise in these covariance matrices due to the small number of jackknifes and we mitigate this by restricting the fit to use just 95% of the covariance based on a principle component analysis following the techniques proposed by Porciani & Norberg (2006); Norberg et al. (2009).”
• THE CLUSTERING OF MASSIVE GALAXIES AT z ∼ 0.5 FROM THE FIRST SEMESTER OF BOSS DATA (2010, methodology): “The calculation of errors in clustering measurements can be done in a number of different ways (see Norberg et al. 2009, for discussion).”
• The LABOCA survey of the Extended Chandra Deep Field-South: clustering of submillimetre galaxies (2011, methodology): “…H11, we divide the field into a small number of sub-areas (we choose Nsub = 8), and for each bootstrap sample we randomly draw a total of 3Nsub subareas (with replacement), which has been shown to best approximate the intrinsic uncertainties in the clustering amplitude (Norberg et al. 2009).”