Optimal design of experiments with quantitative-sequence factors

TL;DR

This paper introduces a new class of optimal experimental designs for experiments involving both quantitative and sequence factors, addressing the challenges of large, semi-discrete input spaces in various scientific fields.

Contribution

It proposes a novel construction method for QS designs using transformations of lattice point sets, achieving desirable properties like space-filling and asymptotic orthogonality.

Findings

Designs are marginally coupled and pair-balanced.

Suitable for high-dimensional experiments.

Flexible in run and factor sizes.

Abstract

A new type of experiment with joint considerations of quantitative and sequence factors is recently drawing much attention in medical science, bio-engineering, and many other disciplines. The input spaces of such experiments are semi-discrete and often very large. Thus, efficient and economical experimental designs are required. Based on the transformations and aggregations of good lattice point sets, we construct a new class of optimal quantitative-sequence (QS) designs that are marginally coupled, pair-balanced, space-filling, and asymptotically orthogonal. The proposed QS designs have a certain flexibility in run and factor sizes and are especially appealing for high-dimensional cases.