On the construction of nested space-filling designs

TL;DR

This paper introduces new algebraic methods for constructing flexible nested space-filling designs with multiple layers, enhancing their application in computer experiments and multi-fidelity modeling.

Contribution

It proposes novel construction techniques for nested space-filling designs using group projection and algebraic methods, allowing arbitrary layers and flexible run sizes.

Findings

Constructed designs support arbitrary nesting layers.

Designs are more flexible in run size than existing methods.

Methods also produce sliced space-filling designs for computer experiments.

Abstract

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 fitting of nonparametric functions, and linking parameters. We propose methods 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 arbitrary number of layers and are more flexible in run size than the existing families of nested space-filling designs. As a byproduct, the proposed methods can also be used to obtain sliced space-filling designs that are appealing for conducting computer experiments with both qualitative and quantitative factors.