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

Abstract

We focus on kernels incorporating different kinds of prior knowledgeon functions to be approximated by Kriging. A recent result on randomfields withpaths invariant under a group action is generalised to combinationsof compositionoperators, and a characterisation of kernels leading to random fieldswith additivepaths is obtained as a corollary. A discussion follows on some implicationson designof experiments, and it is shown in the case of additive kernels thatthe so-calledclass of �axis designs� outperfoms latin hypercubes in terms of theIMSE criterion.