ACCURATE EMULATORS FOR LARGE-SCALE COMPUTER EXPERIMENTS

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...

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Bibliographic Details
Published in:The Annals of statistics 2011-12, Vol.39 (6), p.2974-3002
Main Authors: Haaland, Ben, Qian, Peter Z. G.
Format: Article
Language:English
Subjects:
41A17
65G50
65M12
Accuracy
Applied mathematics
Computer analysis
Computer experiment
Computers
Datasets
Emulation
Error rates
Exact sciences and technology
Experiment design
Experiments
Fourier transformations
Gaussian process
General practice
General topics
Interpolation
large-scale problem
Mathematical foundations
Mathematical functions
Mathematics
multi-step procedure
numerical technique
Probability and statistics
radial basis function
reproducing kernel Hilbert space
Sample size
Sciences and techniques of general use
Statistics
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Summary: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.
ISSN:0090-5364
2168-8966
DOI:10.1214/11-AOS929