2013
DOI: 10.1007/978-3-319-00218-7_13
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Kernels and Designs for Modelling Invariant Functions: From Group Invariance to Additivity

Abstract: 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" outp… Show more

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Cited by 6 publications
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“…In reality the thrust produce by and the endurance of a swimmer are clearly random variables -a slightly different result will be obtained every time they are measured -, but our computer simulations are not -they always return the same result. Nevertheless, Kriging can still provide remarkably good surrogates of such deterministic experiments.5 Other correlation functions are possible and may be more suitable for some problemssee, e.g Ginsbourger, Durrande, and Roustant (2013)…”
mentioning
confidence: 99%
“…In reality the thrust produce by and the endurance of a swimmer are clearly random variables -a slightly different result will be obtained every time they are measured -, but our computer simulations are not -they always return the same result. Nevertheless, Kriging can still provide remarkably good surrogates of such deterministic experiments.5 Other correlation functions are possible and may be more suitable for some problemssee, e.g Ginsbourger, Durrande, and Roustant (2013)…”
mentioning
confidence: 99%