Kernels and Designs for Modelling Invariant Functions: From Group Invariance to Additivity

Ginsbourger, David; Durrande, Nicolas; Roustant, Oliver (2013). Kernels and Designs for Modelling Invariant Functions: From Group Invariance to Additivity. In: Ucinski, Dariusz; Atkinson, Anthony C; Patan, Maciej (eds.) mODa 10 - Advances in Model-Oriented Design and Analysis. Contributions to Statistics (pp. 107-115). Berlin: Springer 10.1007/978-3-319-00218-7_13

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We focus on kernels incorporating different kinds of prior knowledge on functions to be approximated by Kriging. A recent result on random fields with paths invariant under a group action is generalised to combinations of composition operators, and a characterisation of kernels leading to random fields with additive paths is obtained as a corollary. A discussion follows on some implications on design of experiments, and it is shown in the case of additive kernels that the so-called class of “axis designs” outperforms Latin hypercubes in terms of the IMSE criterion.

Item Type:

Book Section (Book Chapter)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematical Statistics and Actuarial Science

UniBE Contributor:

Ginsbourger, David

Subjects:

500 Science > 510 Mathematics

ISSN:

1431-1968

ISBN:

978-3-319-00218-7

Series:

Contributions to Statistics

Publisher:

Springer

Language:

English

Submitter:

Lutz Dümbgen

Date Deposited:

01 Apr 2014 02:44

Last Modified:

02 Apr 2014 10:49

Publisher DOI:

10.1007/978-3-319-00218-7_13

URI:

https://boris.unibe.ch/id/eprint/41514

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