Jittering and Clustering: Strategies for the Construction of Robust Designs

TL;DR

This paper explores methods for constructing robust experimental designs using jittering and clustering, which improve resilience to model inaccuracies by incorporating randomness and space partitioning techniques.

Contribution

It introduces novel randomized strategies for robust design construction, extending existing methods to higher dimensions and demonstrating their effectiveness against worst-case model deviations.

Findings

Randomized robust designs have bounded maximum loss.

Voronoi tessellation-based sampling improves design robustness.

Extensions to higher dimensions are feasible and effective.

Abstract

We discuss, and give examples of, methods for randomly implementing some minimax robust designs from the literature. These have the advantage, over their deterministic counterparts, of having bounded maximum loss in large and very rich neighbourhoods of the, almost certainly inexact, response model fitted by the experimenter. Their maximum loss rivals that of the theoretically best possible, but not implementable, minimax designs. The procedures are then extended to more general robust designs. For two-dimensional designs we sample from contractions of Voronoi tessellations, generated by selected basis points, which partition the design space. These ideas are then extended to $k$-dimensional designs for general k.