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:	05 Dec 2022 14:28
Publisher DOI:	10.1007/978-3-319-00218-7_13
URI:	https://boris.unibe.ch/id/eprint/41514