Kernels and Designs for Modelling Invariant Functions: From Group Invariance to Additivity
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.
- Carnell, R.: lhs: Latin Hypercube Samples. R package version 0.5 (2009) Google Scholar