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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Vydáno v:Technometrics Ročník 51; číslo 4; s. 377 - 388
Hlavní autoři: Cumming, Jonathan A., Goldstein, Michael
Médium: Journal Article
Jazyk:angličtina
Vydáno: Alexandria Taylor & Francis 01.11.2009
The American Society for Quality and The American Statistical Association
American Society for Quality
Témata:
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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