Sequentially weighted uniform designs

Abstract

Uniform designs seek to distribute design points uniformly in the experimental domain. Some discrepancies have been developed to measure the uniformity by treating all factors equally. It is reasonable when there exists no prior information about the system or when the potential model is completely unclear. However, in the situation of sequential designs, experimental information, such as the importance of each factor, would be obtained from previous stage experiments. With this fact, the weighted $L_2$-discrepancy is more suitable than the original discrepancy for choosing follow-up designs. In this paper, the sequentially weighted uniform design is proposed, which is obtained by minimizing the weighted $L_2$-discrepancy. The weights, indicating the relative importance of each factor, are estimated through a Bayesian hierarchical Gaussian process method based on serial experimental data. Results from several classic computer simulator examples, as well as a real application in circuit design, demonstrate that the performance of our new method surpasses that of its counterparts.

Keywords:

• Weighted uniform designs
• sequential designs
• weighted discrepancy
• Gaussian process model

Acknowledgments

The authors would like to express our heartfelt appreciation to the Associate Editor and two Referees, especially the Associate Editor, for their constructive suggestions and valuable comments, which have significantly enhanced the quality of this paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is partially supported by the National Natural Science Foundation of China [grant numbers 11871237 and 12001540], the Discipline Coordination Construction Project of Zhongnan University of Economics and Law [grant number XKHJ202125] and the Fundamental Research Funds for the Central Universities of Central China Normal University [grant number CCNU22JC023].