Sudoku-based space-filling designs

• 成果类型: Article
• 署名作者: Xu, Xu; Haaland, Ben; Qian, Peter Z. G.
• 署名单位: University of Wisconsin System; University of Wisconsin Madison; National University of Singapore
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asr024
• 发表日期: 2011
• 页码: 711720
• 关键词: computer experiments; latin hypercubes; Input variables

摘要

Sudoku is played by millions of people across the globe. It has simple rules and is very addictive. The game board is a nine-by-nine grid of numbers from one to nine. Several entries within the grid are provided and the remaining entries must be filled in subject to no row, column, or three-by-three subsquare containing duplicate numbers. By exploiting these three types of uniformity, we propose an approach to constructing a new type of design, called a Sudoku-based space-filling design. Such a design can be divided into groups of subdesigns so that the complete design and each subdesign achieve maximum uniformity in univariate and bivariate margins. Examples are given illustrating the proposed construction method. Applications of such designs include computer experiments with qualitative and quantitative factors, linking parameters in engineering and crossvalidation.