TY - JOUR

T1 - Non-Gaussianity in the weak lensing correlation function likelihood-implications for cosmological parameter biases

AU - Lin, Chien Hao

AU - Harnois-Déraps, Joachim

AU - Eifler, Tim

AU - Pospisil, Taylor

AU - Mandelbaum, Rachel

AU - Lee, Ann B.

AU - Singh, Sukhdeep

N1 - Publisher Copyright:
© 2020 The Author(s) Published by Oxford University Press on behalf of the Royal Astronomical Society.
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020/12/1

Y1 - 2020/12/1

N2 - 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 ωm 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. 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.

AB - 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 ωm 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. 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.

KW - cosmological parameters

KW - gravitational lensing: Weak

KW - methods: Statistical

UR - http://www.scopus.com/inward/record.url?scp=85096142275&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85096142275&partnerID=8YFLogxK

U2 - 10.1093/mnras/staa2948

DO - 10.1093/mnras/staa2948

M3 - Article

AN - SCOPUS:85096142275

VL - 499

SP - 2977

EP - 2993

JO - Monthly Notices of the Royal Astronomical Society

JF - Monthly Notices of the Royal Astronomical Society

SN - 0035-8711

IS - 2

ER -