scholarly journals Generation of arbitrarily non-Gaussian fields with a set correlation structure

2013 ◽  
Vol 2013 (06) ◽  
pp. 003-003
Author(s):  
Iain A Brown
Keyword(s):  
Correlation Structure ◽  
Gaussian Fields ◽  
Non Gaussian ◽  
Set Correlation

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

Fatigue Life Analysis of Vehicle Systems under Non-Gaussian Excitation

2020 ◽  
Vol 17 (2) ◽  
pp. 7956-7966
Author(s):  
Z. Yang ◽  
D. Zhu ◽  
Q. Gao ◽  
L. Gong ◽  
D. Xu
Keyword(s):  
Monte Carlo ◽  
Fatigue Life ◽  
Equations Of Motion ◽  
Principal Component ◽  
Correlation Structure ◽  
Vehicle Systems ◽  
Life Analysis ◽  
Fatigue Life Analysis ◽  
Non Gaussian ◽  
First Four Moments

Fatigue life analysis is an important work in manufacturing of vehicle systems. The traditional method is to assume that stochastic loads are Gaussian type, then fatigue life is calculated by rain-flow counting, S-N curve and Miner linear damage rule. However, it is difficult to acquire accurate results by this means. In this paper, a numerical methodology is used to simulate non-Gaussian loads considering effects of skewness and kurtosis, as well as to estimate fatigue life under non-Gaussian stresses. Firstly, non-Gaussian inputs are represented by polynomial chaos expansion (PCE) and Karhunen-Loeve (KL) expansion when they are characterised using first four moments, i.e. mean, variance, skewness, kurtosis and a given correlation structure. During this process, we propose spectral decomposition to eliminate the influence of potential imaginary numbers, principal component analysis is also proposed to simplify calculating procedure in KL. Besides, original Monte Carlo sampling is replaced by quasi Monte-Carlo (QMC), which could greatly reduce the workload of numerical simulations. In order to get first four moments and correlation structure of outputs, differential equations of motion are numerically integrated by Runge-Kutta method. Meanwhile, response trajectories are represented based on PCE-KL-QMC approach. Eventually, the rain-flow counting is applied into these trajectories to obtain fatigue life variables, and a convenient formula about the saddlepoint approximations (SPA) represented by first four moments is proposed to provide fatigue life PDF. According to the above way, accurate and effective fatigue life estimation results can be presented

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.

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