On Baxter Type Theorems for Generalized Random Gaussian Fields

Author(s):  
Sergey Krasnitskiy ◽  
Oleksandr Kurchenko
1999 ◽  
Vol 4 (1) ◽  
pp. 153-162
Author(s):  
J. Šaltyte ◽  
K. Dučinskas

The problem of classification of objects located in domain D ⊂ R2 based on observations of random Gaussian fields with a factorized covariance function is considered. The first‐order asymptotic expansion for the expected error regret is presented. Obtained numerical results allow us to compare suggested expansion for some widely applicable models of spatial covariance function.


Author(s):  
Robin E Upham ◽  
Michael L Brown ◽  
Lee Whittaker

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.


2021 ◽  
Vol 172 ◽  
pp. 109063
Author(s):  
Minhao Hong ◽  
Fangjun Xu

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