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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