Fast estimation of aperture-mass statistics – II. Detectability of higher order statistics in current and future surveys

Porth, Lucas; Smith, R. E.

doi:10.1093/mnras/stab2819

Cited by 10 publications

(6 citation statements)

References 67 publications

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“…However, a significant amount of the information contained in weak lensing mass maps lies in their non-Gaussian features, and these features are not fully captured by two-point statistics. Many recent studies, using a wide range of tools and statistics, have tried to extract the non-Gaussian information; examples include higherorder moments [19,39,41,83,84,86,[106][107][108], peak counts [4,27,49,60,62,68,77,83,97,111,112], onepoint probability distributions [12,16,100], Minkowski functionals [46,63,81,84,109], Betti numbers [32,82], persistent homology [52,53], scattering transform coefficients [21,102,103], wavelet phase harmonic moments * marcogatti29@gmail.com [5], kNN and CDFs [8,11], map-level inference [15,85], and machine-learning methods [34,35,56,70,89]. Many of these studies, however, are ...…”

Section: Introductionmentioning

confidence: 99%

Dark Energy Survey Year 3 results: cosmology with moments of weak lensing mass maps – validation on simulations

Gatti¹,

Chang²,

Friedrich³

et al. 2020

Monthly Notices of the Royal Astronomical Society

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We present a simulated cosmology analysis using the second and third moments of the weak lensing mass (convergence) maps. The second moment, or variances, of the convergence as a function of smoothing scale contains information similar to standard shear 2-point statistics. The third moment, or the skewness, contains additional non-Gaussian information. The analysis is geared towards the third year (Y3) data from the Dark Energy Survey (DES), but the methodology can be applied to other weak lensing data sets. We present the formalism for obtaining the convergence maps from the measured shear and for obtaining the second and third moments of these maps given partial sky coverage. We estimate the covariance matrix from a large suite of numerical simulations. We test our pipeline through a simulated likelihood analyses varying 5 cosmological parameters and 10 nuisance parameters and identify the scales where systematic or modelling uncertainties are not expected to affect the cosmological analysis. Our simulated likelihood analysis shows that the combination of second and third moments provides a 1.5 percent constraint on S8 ≡ σ8(Ωm/0.3)0.5 for DES Year 3 data. This is 20 percent better than an analysis using a simulated DES Y3 shear 2-point statistics, owing to the non-Gaussian information captured by the inclusion of higher-order statistics. This paper validates our methodology for constraining cosmology with DES Year 3 data, which will be presented in a subsequent paper.

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Section: Introductionmentioning

confidence: 99%

Dark Energy Survey Year 3 results: cosmology with moments of weak lensing mass maps – validation on simulations

Gatti¹,

Chang²,

Friedrich³

et al. 2020

Monthly Notices of the Royal Astronomical Society

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“…This expression can be generalised to higher orders of M n ap with n > 2. Porth & Smith (2021) give the expressions for the variance of M n ap estimated with the so-called direct estimator as a function of the correlation functions of M n ap for a single aperture. We validate Eq.…”

Section: Covariance Estimation From Correlation Functionsmentioning

confidence: 99%

What is the super-sample covariance? A fresh perspective for second-order shear statistics

Linke,

Burger,

Heydenreich

et al. 2024

A&A

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Cosmological analyses of second-order weak lensing statistics require precise and accurate covariance estimates. These covariances are impacted by two sometimes neglected terms: a negative contribution to the Gaussian covariance due to a finite survey area, and the super-sample covariance (SSC), which for the power spectrum contains the impact of Fourier modes larger than the survey window. We show here that these two effects are connected and can be seen as correction terms to the `large-field-approximation', the asymptotic case of an infinitely large survey area. We describe the two terms collectively as `Finite-Field-Terms'. We derive the covariance of second-order shear statistics from first principles. For this, we use an estimator in real space without relying on an estimator for the power spectrum. The resulting covariance does not scale inversely with the survey area, as might naively be assumed. This scaling is only correct under the large-field approximation when the contribution of the finite-field terms tends to zero. Furthermore, all parts of the covariance, not only the SSC, depend on the power spectrum and trispectrum at all modes, including those larger than the survey. We also show that it is generally impossible to transform an estimate of the power spectrum covariance into the covariance of a real-space statistic. Such a transformation is only possible in the asymptotic case of the large-field approximation. Additionally, we find that the total covariance of a real-space statistic can be calculated using correlation function estimates on spatial scales smaller than the survey window. Consequently, estimating covariances of real-space statistics, in principle, does not require information on spatial scales larger than the survey area. We demonstrate that this covariance estimation method is equivalent to the standard sample covariance method.

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“…Assuming a relatively large aperture radius of θ ap = 30 , we would have to cut off a 2 • -strip around every edge or mask in the survey footprint, meaning that we would disregard most of the data. While active research is being conducted to circumvent these problems (Porth et al 2020;Porth & Smith 2021), the arguably best method to estimate third-order aperture statistics from real data is to derive them from the measured 3pcf, as has been introduced in Jarvis et al ( 2004), generalised in Schneider et al (2005) and applied to survey data in Fu et al (2014) and Secco et al (2022). The shear 3pcf can be estimated straightforwardly from a survey with arbitrarily complex geometry, meaning that the converted aperture statistics are not biased by boundary effects.…”

Section: Measuring Aperture Statistics From Three-point Correlation F...mentioning

confidence: 99%

A roadmap to cosmological parameter analysis with third-order shear statistics

Heydenreich¹,

Laila²,

Burger³

et al. 2023

A&A

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In this work, which is the first of a series to prepare a cosmological parameter analysis with third-order cosmic shear statistics, we model both the shear three-point correlation functions Γ(i) and the third-order aperture statistics $ {{\langle{{\mathcal{M}^3_\mathrm{ap}}}\rangle}} $ from the B IHALOFIT bispectrum model and validate these statistics with a series of N-body simulations. We then investigate how to bin the shear three-point correlation functions to achieve an unbiased estimate for third-order aperture statistics in real data. Finally, we perform a cosmological parameter analysis on KiDS1000-like mock data with second- and third-order statistics. In the absence of systematic effects, we recover all cosmological parameters with very little bias. Furthermore, we find that a joint analysis almost doubles the constraining power on S8 and increases the figure of merit in the Ωm-σ8 plane by a factor of 5.9 with respect to an analysis with only second-order shear statistics.

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Fast estimation of aperture-mass statistics – II. Detectability of higher order statistics in current and future surveys

Cited by 10 publications

References 67 publications

Dark Energy Survey Year 3 results: cosmology with moments of weak lensing mass maps – validation on simulations

Dark Energy Survey Year 3 results: cosmology with moments of weak lensing mass maps – validation on simulations

What is the super-sample covariance? A fresh perspective for second-order shear statistics

A roadmap to cosmological parameter analysis with third-order shear statistics

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