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Analysis Methods for Computer Experiments : How to Assess and What Counts? Chen, Hao; Loeppky, Jason L.; Sacks, Jerome, 1931-; Welch, William J.
Abstract
Statistical methods based on a regression model plus a zero-mean Gaussian process (GP) have been widely used for predicting the output of a deterministic computer code. There are many suggestions in the literature for how to choose the regression component and how to model the correlation structure of the GP. This article argues that comprehensive, evidence-based assessment strategies are needed when comparing such modeling options. Otherwise, one is easily misled. Applying the strategies to several computer codes shows that a regression model more complex than a constant mean either has little impact on prediction accuracy or is an impediment. The choice of correlation function has modest effect, but there is little to separate two common choices, the power exponential and the Matérn, if the latter is optimized with respect to its smoothness. The applications presented here also provide no evidence that a composite of GPs provides practical improvement in prediction accuracy. A limited comparison of Bayesian and empirical Bayes methods is similarly inconclusive. In contrast, we find that the effect of experimental design is surprisingly large, even for designs of the same type with the same theoretical properties.
Item Metadata
| Title |
Analysis Methods for Computer Experiments : How to Assess and What Counts?
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| Creator | |
| Date Issued |
2016
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| Description |
Statistical methods based on a regression model plus a zero-mean
Gaussian process (GP) have been widely used for predicting the output of a
deterministic computer code. There are many suggestions in the literature for
how to choose the regression component and how to model the correlation
structure of the GP. This article argues that comprehensive, evidence-based
assessment strategies are needed when comparing such modeling options.
Otherwise, one is easily misled. Applying the strategies to several computer
codes shows that a regression model more complex than a constant mean either
has little impact on prediction accuracy or is an impediment. The choice
of correlation function has modest effect, but there is little to separate two
common choices, the power exponential and the Matérn, if the latter is optimized
with respect to its smoothness. The applications presented here also
provide no evidence that a composite of GPs provides practical improvement
in prediction accuracy. A limited comparison of Bayesian and empirical
Bayes methods is similarly inconclusive. In contrast, we find that the effect of
experimental design is surprisingly large, even for designs of the same type
with the same theoretical properties.
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| Subject | |
| Genre | |
| Type | |
| Language |
eng
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| Date Available |
2016-05-19
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| Provider |
Vancouver : University of British Columbia Library
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| Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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| DOI |
10.14288/1.0302078
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| URI | |
| Affiliation | |
| Citation |
Statistical Science 2016, Vol. 31, No. 1, 40–60
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| Publisher DOI |
10.1214/15-STS531
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| Peer Review Status |
Reviewed
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| Scholarly Level |
Faculty
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| Copyright Holder |
Institute of Mathematical Statistics
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| Rights URI | |
| Aggregated Source Repository |
DSpace
|
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Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International