Zimmermann, Ralf (2010) Asymptotic Behavior of the Likelihood Function of Covariance Matrices of Spatial Gaussian Processes. Journal of Applied Mathematics, 2010, pp. 1-17. Hindawi Publishing Corporation. doi: 10.1155/2010/494070. ISSN 1110-757X.
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Official URL: http://dx.doi.org/10.1155/2010/494070
Abstract
The covariance structure of spatial Gaussian predictors (aka Kriging predictors) is generally modeled by parameterized covariance functions; the associated hyperparameters in turn are estimated via the method of maximum likelihood. In this work, the asymptotic behavior of the maximum likelihood of spatial Gaussian predictor models as a function of its hyperparameters is investigated theoretically. Asymptotic sandwich bounds for the maximum likelihood function in terms of the condition number of the associated covariance matrix are established. As a consequence, the main result is obtained: optimally trained nondegenerate spatial Gaussian processes cannot feature arbitrary ill-conditioned correlation matrices. The implication of this theorem on Kriging hyperparameter optimization is exposed. A nonartificial example is presented, where maximum likelihood-based Kriging model training is necessarily bound to fail.
Item URL in elib: | https://elib.dlr.de/68506/ | ||||||||
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Document Type: | Article | ||||||||
Additional Information: | Article ID: 494070 | ||||||||
Title: | Asymptotic Behavior of the Likelihood Function of Covariance Matrices of Spatial Gaussian Processes | ||||||||
Authors: |
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Date: | December 2010 | ||||||||
Journal or Publication Title: | Journal of Applied Mathematics | ||||||||
Refereed publication: | Yes | ||||||||
Open Access: | Yes | ||||||||
Gold Open Access: | Yes | ||||||||
In SCOPUS: | Yes | ||||||||
In ISI Web of Science: | Yes | ||||||||
Volume: | 2010 | ||||||||
DOI: | 10.1155/2010/494070 | ||||||||
Page Range: | pp. 1-17 | ||||||||
Editors: |
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Publisher: | Hindawi Publishing Corporation | ||||||||
ISSN: | 1110-757X | ||||||||
Status: | Published | ||||||||
Keywords: | spatial Gaussian process · Kriging interpolation · design and analysis of computer experiments · best linear unbiased estimator · hyper-parameter training · maximum likelihood estimation · condition number | ||||||||
HGF - Research field: | Aeronautics, Space and Transport | ||||||||
HGF - Program: | Aeronautics | ||||||||
HGF - Program Themes: | Aircraft Research (old) | ||||||||
DLR - Research area: | Aeronautics | ||||||||
DLR - Program: | L AR - Aircraft Research | ||||||||
DLR - Research theme (Project): | L - Simulation & Validation (old) | ||||||||
Location: | Braunschweig | ||||||||
Institutes and Institutions: | Institute of Aerodynamics and Flow Technology > C²A²S²E - Center for Computer Applications in AeroSpace Science and Engineering | ||||||||
Deposited By: | Zimmermann, Dr. Ralf | ||||||||
Deposited On: | 19 Jan 2011 11:46 | ||||||||
Last Modified: | 11 Jun 2021 04:13 |
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