Cosmological inference from galaxy-clustering power spectrum: Gaussianization and covariance decomposition

Shengbo Wang, Will J. Percival, Santiago Avila, Robert Crittenden, Davide Bianchi

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Likelihood fitting to two-point clustering statistics made from galaxy surveys usually assumes a multivariate normal distribution for the measurements, with justification based on the central limit theorem given the large number of overdensity modes. However, this assumption cannot hold on the largest scales where the number of modes is low. Whilst more accurate distributions have previously been developed in idealized cases, we derive a procedure suitable for analysing measured monopole power spectra with window effects, stochastic shot noise, and the dependence of the covariance matrix on the model being fitted all taken into account. A data transformation is proposed to give an approximately Gaussian likelihood, with a variance–correlation decomposition of the covariance matrix to account for its cosmological dependence. By comparing with the modified-t likelihood derived under the usual normality assumption, we find in numerical tests that our new procedure gives more accurate constraints on the local non-Gaussianity parameter ƒNL, which is sensitive to the large-scale power. A simple data analysis pipeline is provided for straightforward application of this new approach in preparation for forthcoming large galaxy surveys such as DESI and Euclid.
Original languageEnglish
Pages (from-to)951-965
Number of pages15
JournalMonthly Notices of the Royal Astronomical Society
Issue number1
Early online date20 Mar 2019
Publication statusPublished - 1 Jun 2019


  • astro-ph.CO
  • RCUK
  • STFC
  • ST/N000668/1
  • ST/K00283X/1
  • methods: data analysis
  • methods: statistical
  • large scale structure of Universe


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