Non-Gaussianity in the weak lensing correlation function likelihood – implications for cosmological parameter biases

Journal Article · Thu Oct 01 00:00:00 EDT 2020 · Monthly Notices of the Royal Astronomical Society

DOI:https://doi.org/10.1093/mnras/staa2948· OSTI ID:1686190

Lin, Chien-Hao  ^[1]; Harnois-Déraps, Joachim  ^[2]; Eifler, Tim  ^[3]; Pospisil, Taylor ^[4]; Mandelbaum, Rachel  ^[1]; Lee, Ann B. ^[4]; Singh, Sukhdeep ^[5]

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1. McWilliams Center for Cosmology, Department of Physics, Carnegie Mellon University, Pittsburgh, PA 15213, USA
2. Scottish Universities Physics Alliance, Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh EH9 3HJ, UK
3. Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109 USA, Steward Observatory/Department of Astronomy, University of Arizona, 933 North Cherry Avenue, Tucson, AZ 85721, USA
4. Department of Statistics & Data Science, Carnegie Mellon University, Pittsburgh, PA 15213, USA
5. Berkeley Center for Cosmological Physics, Department of Physics, and Lawrence Berkeley National Laboratory, University of California, Berkeley, CA 94720, USA

We study the significance of non-Gaussianity in the likelihood of weak lensing shear two-point correlation functions, detecting significantly non-zero skewness and kurtosis in 1D marginal distributions of shear two-point correlation functions in simulated weak lensing data. We examine the implications in the context of future surveys, in particular LSST, with derivations of how the non-Gaussianity scales with survey area. We show that there is no significant bias in 1D posteriors of Ω_m and σ₈ due to the non-Gaussian likelihood distributions of shear correlations functions using the mock data (100 deg²). We also present a systematic approach to constructing approximate multivariate likelihoods with 1D parametric functions by assuming independence or more flexible non-parametric multivariate methods after decorrelating the data points using principal component analysis (PCA). While the use of PCA does not modify the non-Gaussianity of the multivariate likelihood, we find empirically that the 1D marginal sampling distributions of the PCA components exhibit less skewness and kurtosis than the original shear correlation functions. Modelling the likelihood with marginal parametric functions based on the assumption of independence between PCA components thus gives a lower limit for the biases. Here, we further demonstrate that the difference in cosmological parameter constraints between the multivariate Gaussian likelihood model and more complex non-Gaussian likelihood models would be even smaller for an LSST-like survey. In addition, the PCA approach automatically serves as a data compression method, enabling the retention of the majority of the cosmological information while reducing the dimensionality of the data vector by a factor of ~5.

• Research Organization: Carnegie Mellon Univ., Pittsburgh, PA (United States)
• Sponsoring Organization: USDOE Office of Science (SC), High Energy Physics (HEP)
• Contributing Organization: The LSST Dark Energy Science Collaboration
• Grant/Contract Number: SC0011114; SC0010118
• OSTI ID: 1686190
• Alternate ID(s): OSTI ID: 1755489
• Journal Information: Monthly Notices of the Royal Astronomical Society, Journal Name: Monthly Notices of the Royal Astronomical Society Vol. 499 Journal Issue: 2; ISSN 0035-8711
• Publisher: Royal Astronomical Society
• Country of Publication: United Kingdom
• Language: English

Related Subjects

79 ASTRONOMY AND ASTROPHYSICS
gravitational lensing: weak
methods: statistical
cosmological parameters