Maximum One-Factor-At-A-Time Designs for Screening in Computer Experiments

Abstract

Identifying important factors from a large number of potentially important factors of a highly nonlinear and computationally expensive black box model is a difficult problem. Morris screening and Sobol’ design are two commonly used model-free methods for doing this. In this article, we establish a connection between these two seemingly different methods in terms of their underlying experimental design structure and further exploit this connection to develop an improved design for screening called Maximum One-Factor-At-A-Time (MOFAT) design. We also develop efficient methods for constructing MOFAT designs with a large number of factors. Several examples are presented to demonstrate the advantages of MOFAT designs compared to Morris screening and Sobol’ design methods.

KEYWORDS:

• Experimental design
• Morris screening
• Sensitivity analysis
• Sobol’ indices

Supplementary Materials

The supplementary materials contain technical proofs of the theoretical results, details of the algorithm for constructing MOFAT designs, and codes for reproducing Figure 4. The R package MOFAT (Xiao and Joseph 2022) available through CRAN can be used for generating MOFAT designs.

Acknowledgments

We would like to thank the Editor (Robert B. Gramacy), an AE, and two referees for their valuable comments.

Disclosure Statement

The authors report that there are no competing interests to declare.

Additional information

Funding

This research is supported by a U.S. Army Research Office grant W911NF-17-1-0007 and a U.S. National Science Foundation grant CMMI-1921646.