scholarly journals Impact of the non-Gaussian covariance of the weak lensing power spectrum and bispectrum on cosmological parameter estimation

2013 ◽  
Vol 87 (12) ◽  
Author(s):  
Masanori Sato ◽  
Takahiro Nishimichi
Keyword(s):  
Parameter Estimation ◽  
Power Spectrum ◽  
Cosmological Parameter ◽  
Weak Lensing ◽  
Non Gaussian

scholarly journals Sufficiency of a Gaussian power spectrum likelihood for accurate cosmology from upcoming weak lensing surveys

2021 ◽  
Author(s):  
Robin E Upham ◽  
Michael L Brown ◽  
Lee Whittaker
Keyword(s):  
Power Spectrum ◽  
Random Noise ◽  
Power Spectra ◽  
Stage Iv ◽  
Wishart Distribution ◽  
Weak Lensing ◽  
Dependence Structure ◽  
Gaussian Fields ◽  
Non Gaussian ◽  
Parameter Constraints

Abstract We investigate whether a Gaussian likelihood is sufficient to obtain accurate parameter constraints from a Euclid-like combined tomographic power spectrum analysis of weak lensing, galaxy clustering and their cross-correlation. Testing its performance on the full sky against the Wishart distribution, which is the exact likelihood under the assumption of Gaussian fields, we find that the Gaussian likelihood returns accurate parameter constraints. This accuracy is robust to the choices made in the likelihood analysis, including the choice of fiducial cosmology, the range of scales included, and the random noise level. We extend our results to the cut sky by evaluating the additional non-Gaussianity of the joint cut-sky likelihood in both its marginal distributions and dependence structure. We find that the cut-sky likelihood is more non-Gaussian than the full-sky likelihood, but at a level insufficient to introduce significant inaccuracy into parameter constraints obtained using the Gaussian likelihood. Our results should not be affected by the assumption of Gaussian fields, as this approximation only becomes inaccurate on small scales, which in turn corresponds to the limit in which any non-Gaussianity of the likelihood becomes negligible. We nevertheless compare against N-body weak lensing simulations and find no evidence of significant additional non-Gaussianity in the likelihood. Our results indicate that a Gaussian likelihood will be sufficient for robust parameter constraints with power spectra from Stage IV weak lensing surveys.

scholarly journals Weak lensing cosmology with convolutional neural networks on noisy data

2019 ◽  
Vol 490 (2) ◽  
pp. 1843-1860 ◽  
Author(s):  
Dezső Ribli ◽  
Bálint Ármin Pataki ◽  
José Manuel Zorrilla Matilla ◽  
Daniel Hsu ◽  
Zoltán Haiman ◽  
...  
Keyword(s):  
Neural Networks ◽  
Correlation Function ◽  
Power Spectrum ◽  
Convolutional Neural Networks ◽  
Higher Order ◽  
Weak Lensing ◽  
Noise Levels ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Non Gaussian

ABSTRACT Weak gravitational lensing is one of the most promising cosmological probes of the late universe. Several large ongoing (DES, KiDS, HSC) and planned (LSST, Euclid, WFIRST) astronomical surveys attempt to collect even deeper and larger scale data on weak lensing. Due to gravitational collapse, the distribution of dark matter is non-Gaussian on small scales. However, observations are typically evaluated through the two-point correlation function of galaxy shear, which does not capture non-Gaussian features of the lensing maps. Previous studies attempted to extract non-Gaussian information from weak lensing observations through several higher order statistics such as the three-point correlation function, peak counts, or Minkowski functionals. Deep convolutional neural networks (CNN) emerged in the field of computer vision with tremendous success, and they offer a new and very promising framework to extract information from 2D or 3D astronomical data sets, confirmed by recent studies on weak lensing. We show that a CNN is able to yield significantly stricter constraints of (σ8, Ωm) cosmological parameters than the power spectrum using convergence maps generated by full N-body simulations and ray-tracing, at angular scales and shape noise levels relevant for future observations. In a scenario mimicking LSST or Euclid, the CNN yields 2.4–2.8 times smaller credible contours than the power spectrum, and 3.5–4.2 times smaller at noise levels corresponding to a deep space survey such as WFIRST. We also show that at shape noise levels achievable in future space surveys the CNN yields 1.4–2.1 times smaller contours than peak counts, a higher order statistic capable of extracting non-Gaussian information from weak lensing maps.

scholarly journals Weak lensing minima and peaks: Cosmological constraints and the impact of baryons

2020 ◽  
Vol 495 (3) ◽  
pp. 2531-2542 ◽  
Author(s):  
William R Coulton ◽  
Jia Liu ◽  
Ian G McCarthy ◽  
Ken Osato
Keyword(s):  
Power Spectrum ◽  
Neutrino Mass ◽  
Matter Density ◽  
Weak Lensing ◽  
Cosmological Constraints ◽  
Credible Intervals ◽  
Hydrodynamical Simulations ◽  
Non Gaussian ◽  
The Impact

ABSTRACT We present a novel statistic to extract cosmological information in weak lensing data: the lensing minima. We also investigate the effect of baryons on cosmological constraints from peak and minimum counts. Using the MassiveNuS simulations, we find that lensing minima are sensitive to non-Gaussian cosmological information and are complementary to the lensing power spectrum and peak counts. For an LSST-like survey, we obtain $95{{\ \rm per\ cent}}$ credible intervals from a combination of lensing minima and peaks that are significantly stronger than from the power spectrum alone, by $44{{\ \rm per\ cent}}$, $11{{\ \rm per\ cent}}$, and $63{{\ \rm per\ cent}}$ for the neutrino mass sum ∑mν, matter density Ωm, and amplitude of fluctuation As, respectively. We explore the effect of baryonic processes on lensing minima and peaks using the hydrodynamical simulations BAHAMAS and Osato15. We find that ignoring baryonic effects would lead to strong (≈4σ) biases in inferences from peak counts, but negligible (≈0.5σ) for minimum counts, suggesting lensing minima are a potentially more robust tool against baryonic effects. Finally, we demonstrate that the biases can in principle be mitigated without significantly degrading cosmological constraints when we model and marginalize the baryonic effects.

scholarly journals Tomographic weak lensing bispectrum: a thorough analysis towards the next generation of galaxy surveys

2019 ◽  
Vol 490 (4) ◽  
pp. 4688-4714 ◽  
Author(s):  
Matteo Rizzato ◽  
Karim Benabed ◽  
Francis Bernardeau ◽  
Fabien Lacasa
Keyword(s):  
Power Spectrum ◽  
High Performance ◽  
Large Scale ◽  
Signal To Noise Ratio ◽  
Principal Component ◽  
Weak Lensing ◽  
Galaxy Surveys ◽  
Point Correlation ◽  
Non Gaussian ◽  
The Impact

ABSTRACT We address key points for an efficient implementation of likelihood codes for modern weak lensing large-scale structure surveys. Specifically, we focus on the joint weak lensing convergence power spectrum–bispectrum probe and we tackle the numerical challenges required by a realistic analysis. Under the assumption of (multivariate) Gaussian likelihoods, we have developed a high performance code that allows highly parallelized prediction of the binned tomographic observables and of their joint non-Gaussian covariance matrix accounting for terms up to the six-point correlation function and supersample effects. This performance allows us to qualitatively address several interesting scientific questions. We find that the bispectrum provides an improvement in terms of signal-to-noise ratio (S/N) of about 10 per cent on top of the power spectrum, making it a non-negligible source of information for future surveys. Furthermore, we are capable to test the impact of theoretical uncertainties in the halo model used to build our observables; with presently allowed variations we conclude that the impact is negligible on the S/N. Finally, we consider data compression possibilities to optimize future analyses of the weak lensing bispectrum. We find that, ignoring systematics, five equipopulated redshift bins are enough to recover the information content of a Euclid-like survey, with negligible improvement when increasing to 10 bins. We also explore principal component analysis and dependence on the triangle shapes as ways to reduce the numerical complexity of the problem.

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

2020 ◽  
Vol 499 (2) ◽  
pp. 2977-2993
Author(s):  
Chien-Hao Lin ◽  
Joachim Harnois-Déraps ◽  
Tim Eifler ◽  
Taylor Pospisil ◽  
Rachel Mandelbaum ◽  
...  
Keyword(s):  
Correlation Functions ◽  
Principal Component ◽  
Cosmological Parameter ◽  
Weak Lensing ◽  
Likelihood Model ◽  
Point Correlation ◽  
Parametric Functions ◽  
Non Gaussian ◽  
Parameter Constraints ◽  
Skewness And Kurtosis

ABSTRACT 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.

scholarly journals Cosmological Parameter Estimation from the Two-dimensional Genus Topology: Measuring the Shape of the Matter Power Spectrum

2020 ◽  
Vol 896 (2) ◽  
pp. 145
Author(s):  
Stephen Appleby ◽  
Changbom Park ◽  
Sungwook E. Hong ◽  
Ho Seong Hwang ◽  
Juhan Kim
Keyword(s):  
Parameter Estimation ◽  
Power Spectrum ◽  
Cosmological Parameter ◽  
Two Dimensional ◽  
Matter Power Spectrum
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