ACCURATE EMULATORS FOR LARGE-SCALE COMPUTER EXPERIMENTS

• 成果类型: Article
• 署名作者: Haaland, Ben; Qian, Peter Z. G.
• 署名单位: National University of Singapore; National University of Singapore; University of Wisconsin System; University of Wisconsin Madison
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/11-AOS929
• 发表日期: 2011
• 页码: 2974-3002
• 关键词: CENTRAL-LIMIT-THEOREM; gaussian process models; space-filling designs; monte-carlo variance; latin hypercubes; CONSTRUCTION; interpolation; prediction

摘要

Large-scale computer experiments are becoming increasingly important in science. A multi-step procedure is introduced to statisticians for modeling such experiments, which builds an accurate interpolator in multiple steps. In practice, the procedure shows substantial improvements in overall accuracy, but its theoretical properties are not well established. We introduce the terms nominal and numeric error and decompose the overall error of an interpolator into nominal and numeric portions. Bounds on the numeric and nominal error are developed to show theoretically that substantial gains in overall accuracy can be attained with the multi-step approach.