Small Sample Bayesian Designs for Complex High-Dimensional Models Based on Information Gained Using Fast Approximations

We consider the problem of designing for complex high-dimensional computer models that can be evaluated at different levels of accuracy. Ordinarily, this requires performing many expensive evaluations of the most accurate version of the computer model to obtain a reasonable coverage of the design sp...

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Published in:	Technometrics Vol. 51; no. 4; pp. 377 - 388
Main Authors:	Cumming, Jonathan A., Goldstein, Michael
Format:	Journal Article
Language:	English
Published:	Alexandria Taylor & Francis 01.11.2009 The American Society for Quality and The American Statistical Association American Society for Quality
Subjects:	Approximation Bayes linear methods Bayesian analysis Computer analysis Computer experiments Computer modeling Computer simulation Design Design analysis Design evaluation Experiment design Experimental design Hydrocarbon reservoir Least squares Mathematical functions Mathematical vectors Modeling Multiscale emulation Simulation Simulations Statistical methods
ISSN:	0040-1706, 1537-2723
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Abstract	We consider the problem of designing for complex high-dimensional computer models that can be evaluated at different levels of accuracy. Ordinarily, this requires performing many expensive evaluations of the most accurate version of the computer model to obtain a reasonable coverage of the design space. In some cases, it is possible to supplement the information from the accurate model evaluations with a large number of evaluations of a cheap, approximate version of the computer model to enable a more informed design choice. We describe an approach that combines the information from both the approximate model and the accurate model into a single multiscale emulator for the computer model. We then propose a design strategy for selecting a small number of expensive evaluations of the accurate computer model based on our multiscale emulator and a decomposition of the input parameter space. We illustrate our methodology with an example concerning a computer simulation of a hydrocarbon reservoir.
AbstractList	We consider the problem of designing for complex high-dimensional computer models that can be evaluated at different levels of accuracy. Ordinarily, this requires performing many expensive evaluations of the most accurate version of the computer model to obtain a reasonable coverage of the design space. In some cases, it is possible to supplement the information from the accurate model evaluations with a large number of evaluations of a cheap, approximate version of the computer model to enable a more informed design choice. We describe an approach that combines the information from both the approximate model and the accurate model into a single muniscale emulator for the computer model. We then propose a design strategy for selecting a small number of expensive evaluations of the accurate computer model based on our multiscale emulator and a decomposition of the input parameter space. We illustrate our methodology with an example concerning a computer simulation of a hydrocarbon reservoir. [PUBLICATION ABSTRACT] We consider the problem of designing for complex high-dimensional computer models that can be evaluated at different levels of accuracy. Ordinarily, this requires performing many expensive evaluations of the most accurate version of the computer model to obtain a reasonable coverage of the design space. In some cases, it is possible to supplement the information from the accurate model evaluations with a large number of evaluations of a cheap, approximate version of the computer model to enable a more informed design choice. We describe an approach that combines the information from both the approximate model and the accurate model into a single multiscale emulator for the computer model. We then propose a design strategy for selecting a small number of expensive evaluations of the accurate computer model based on our multiscale emulator and a decomposition of the input parameter space. We illustrate our methodology with an example concerning a computer simulation of a hydrocarbon reservoir.
Author	Cumming, Jonathan A. Goldstein, Michael
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SubjectTerms	Approximation Bayes linear methods Bayesian analysis Computer analysis Computer experiments Computer modeling Computer simulation Design Design analysis Design evaluation Experiment design Experimental design Hydrocarbon reservoir Least squares Mathematical functions Mathematical vectors Modeling Multiscale emulation Simulation Simulations Statistical methods
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Title	Small Sample Bayesian Designs for Complex High-Dimensional Models Based on Information Gained Using Fast Approximations
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