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

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mODa 10 – Advances in Model-Oriented Design and Analysis

Part of the book series: Contributions to Statistics ((CONTRIB.STAT.))

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” outperforms Latin hypercubes in terms of the IMSE criterion.

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Correspondence to David Ginsbourger .

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Ginsbourger, D., Durrande, N., Roustant, O. (2013). Kernels and Designs for Modelling Invariant Functions: From Group Invariance to Additivity. In: Ucinski, D., Atkinson, A., Patan, M. (eds) mODa 10 – Advances in Model-Oriented Design and Analysis. Contributions to Statistics. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00218-7_13

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