Validation of semi-analytical, semi-empirical covariance matrices for two-point correlation function for Early DESI data

Michael Rashkovetskyi, Daniel J. Eisenstein, Jessica Nicole Aguilar, David Brooks, Todd Claybaugh, Shaun Cole, Kyle Dawson, Axel de la Macorra, Peter Doel, Kevin Fanning, Andreu Font-Ribera, Jaime E. Forero-Romero, Satya Gontcho A Gontcho, ChangHoon Hahn, Klaus Honscheid, Robert Kehoe, Theodore Kisner, Martin Landriau, Michael Levi, Marc ManeraRamon Miquel, Jeongin Moon, Seshadri Nadathur, Jundan Nie, Claire Poppett, Ashley J. Ross, Graziano Rossi, Eusebio Sanchez, Christoph Saulder, Michael Schubnell, Hee-Jong Seo, Gregory Tarle, David Valcin, Benjamin Alan Weaver, Cheng Zhao, Zhimin Zhou, Hu Zou

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We present an extended validation of semi-analytical, semi-empirical covariance matrices for the two-point correlation function (2PCF) on simulated catalogs representative of luminous red galaxies (LRGs) data collected during the initial 2 months of operations of the Stage-IV ground-based Dark Energy Spectroscopic Instrument (DESI). We run the pipeline on multiple effective Zel’dovich (EZ) mock galaxy catalogs with the corresponding cuts applied and compare the results with the mock sample covariance to assess the accuracy and its fluctuations. We propose an extension of the previously developed formalism for catalogs processed with standard reconstruction algorithms. We consider methods for comparing covariance matrices in detail, highlighting their interpretation and statistical properties caused by sample variance, in particular, non-trivial expectation values of certain metrics even when the external covariance estimate is perfect. With improved mocks and validation techniques, we confirm a good agreement between our predictions and sample covariance. This allows one to generate covariance matrices for comparable data sets without the need to create numerous mock galaxy catalogs with matching clustering, only requiring 2PCF measurements from the data itself. The code used in this paper is publicly available at
Original languageEnglish
Pages (from-to)3894–3911
JournalMonthly Notices of the Royal Astronomical Society
Issue number3
Early online date13 Jul 2023
Publication statusPublished - 1 Sept 2023


  • astro-ph.CO
  • math.ST
  • stat.TH
  • methods: statistical
  • surveys
  • software: data analysis
  • galaxies: statistics
  • Large-scale structure of universe
  • cosmology: theory

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