© Institute of Mathematical Statistics, 2014 ON THE CONSTRUCTION OF NESTED SPACE-FILLING DESIGNS

Nested space-filling designs are nested designs with attractive low-dimensional stratification. Such designs are gaining popularity in statistics, applied mathematics and engineering. Their applications include multi-fidelity computer models, stochastic optimization problems, multi-level fit-ting of nonparametric functions, and linking parameters. We propose meth-ods for constructing several new classes of nested space-filling designs. These methods are based on a new group projection and other algebraic techniques. The constructed designs can accommodate a nested structure with an arbi-trary number of layers and are more flexible in run size than the existing families of nested space-filling designs. As a byproduct, the proposed meth-ods can also be used to obtain sliced space-filling designs that are appealing for conducting computer experiments with both qualitative and quantitative factors