Measurement of Conditional Squeezing for non-Gaussian fields

2006 ◽  
Author(s):  
Justin Vines ◽  
Reeta Vyas ◽  
Surendra Singh
Keyword(s):  
Gaussian Fields ◽  
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 Stochastic geometry and topology of non-Gaussian fields

2012 ◽  
Vol 109 (49) ◽  
pp. 19943-19948 ◽  
Author(s):  
T. H. Beuman ◽  
A. M. Turner ◽  
V. Vitelli
Keyword(s):  
Stochastic Geometry ◽  
Gaussian Fields ◽  
And Topology ◽  
Non Gaussian

A two-stage efficient history matching procedure of non-Gaussian fields

2016 ◽  
Vol 138 ◽  
pp. 189-200 ◽  
Author(s):  
Kai Zhang ◽  
Ranran Lu ◽  
Liming Zhang ◽  
Xiaoming Zhang ◽  
Jun Yao ◽  
...  
Keyword(s):  
History Matching ◽  
Gaussian Fields ◽  
Two Stage ◽  
Matching Procedure ◽  
Non Gaussian

scholarly journals Non Gaussian Minkowski functionals and extrema counts for CMB maps

2014 ◽  
Vol 11 (S308) ◽  
pp. 61-66 ◽  
Author(s):  
Dmitri Pogosyan ◽  
Sandrine Codis ◽  
Christophe Pichon
Keyword(s):  
Cosmic Microwave Background ◽  
Orthogonal Polynomials ◽  
Gaussian Fields ◽  
Spherical Space ◽  
Matter Distribution ◽  
Microwave Background ◽  
Minkowski Functionals ◽  
Second Derivatives ◽  
Non Gaussian ◽  
The Universe

AbstractIn the conference presentation we have reviewed the theory of non-Gaussian geometrical measures for 3D Cosmic Web of the matter distribution in the Universe and 2D sky data, such as Cosmic Microwave Background (CMB) maps that was developed in a series of our papers. The theory leverages symmetry of isotropic statistics such as Minkowski functionals and extrema counts to develop post Gaussian expansion of the statistics in orthogonal polynomials of invariant descriptors of the field, its first and second derivatives. The application of the approach to 2D fields defined on a spherical sky was suggested, but never rigorously developed. In this paper we present such development treating the effects of the curvature and finiteness of the spherical space $S_2$ exactly, without relying on flat-sky approximation. We present Minkowski functionals, including Euler characteristic and extrema counts to the first non-Gaussian correction, suitable for weakly non-Gaussian fields on a sphere, of which CMB is the prime example.

Integration of non-Gaussian fields

1996 ◽  
Vol 11 (1) ◽  
pp. 15-23 ◽  
Author(s):  
Ove Ditlevsen ◽  
Gunnar Mohr ◽  
Pernife Hoffmeyer
Keyword(s):  
Gaussian Fields ◽  
Non Gaussian
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