On probability of high extremes of Gaussian fields with a smooth random trend

2019 ◽  
Vol 147 ◽  
pp. 29-35
Author(s):  
Goran Popivoda ◽  
Siniša Stamatović
Keyword(s):  
Gaussian Fields ◽  
Extremes Of Gaussian Fields

Extremes of Gaussian fields with a smooth random variance

2016 ◽  
Vol 110 ◽  
pp. 185-190 ◽  
Author(s):  
Goran Popivoda ◽  
Siniša Stamatović
Keyword(s):  
Gaussian Fields ◽  
Extremes Of Gaussian Fields ◽  
Random Variance

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 Derivatives of local times for some Gaussian fields II

2021 ◽  
Vol 172 ◽  
pp. 109063
Author(s):  
Minhao Hong ◽  
Fangjun Xu
Keyword(s):  
Local Times ◽  
Gaussian Fields ◽  
Derivatives Of

On Level Crossings by Gaussian Fields

Statistics ◽  
1985 ◽  
Vol 16 (4) ◽  
pp. 581-596
Author(s):  
U. Zähle
Keyword(s):  
Gaussian Fields ◽  
Level Crossings
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