Name
Title | ||
|---|---|---|
Asymptotic Behavior of the Likelihood Function of Covariance Matrices of Spatial Gaussian Processes |
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. |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1155/2010/494070 | JOURNAL OF APPLIED MATHEMATICS |
Keywords | Field | DocType |
covariance matrix,gaussian process,condition number,maximum likelihood,covariance function,likelihood function | Mathematical optimization,Covariance function,Likelihood function,Estimation of covariance matrices,Rational quadratic covariance function,Gaussian process,Restricted maximum likelihood,Matérn covariance function,Mathematics,Covariance | Journal |
Volume | ISSN | Citations |
2010 | 1110-757X | 3 |
PageRank | References | Authors |
0.48 | 1 | 1 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Ralf Zimmermann | 1 | 11 | 2.45 |