Global Fitting of the Response Surface via Estimating Multiple Contours of a Simulator
Computer simulators are widely used to understand complex physical systems in many areas such as aerospace, renewable energy, climate modelling, and manufacturing. One fundamental aspect of the study of computer simulators is known as experimental design, that is, how to select the input settings wh...
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| Published in: | Journal of statistical theory and practice Vol. 14; no. 1 |
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| Language: | English |
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01.03.2020
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| ISSN: | 1559-8608, 1559-8616 |
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| Abstract | Computer simulators are widely used to understand complex physical systems in many areas such as aerospace, renewable energy, climate modelling, and manufacturing. One fundamental aspect of the study of computer simulators is known as experimental design, that is, how to select the input settings where the computer simulator is run and the corresponding response is collected. Extra care should be taken in the selection process because computer simulators can be computationally expensive to run. The selection should acknowledge and achieve the goal of the analysis. This article focuses on the goal of producing more accurate prediction which is important for risk assessment and decision making. We propose two new methods of design approaches that sequentially select input settings to achieve this goal. The approaches make novel applications of simultaneous and sequential contour estimations. Numerical examples are employed to demonstrate the effectiveness of the proposed approaches. |
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| AbstractList | Computer simulators are widely used to understand complex physical systems in many areas such as aerospace, renewable energy, climate modelling, and manufacturing. One fundamental aspect of the study of computer simulators is known as experimental design, that is, how to select the input settings where the computer simulator is run and the corresponding response is collected. Extra care should be taken in the selection process because computer simulators can be computationally expensive to run. The selection should acknowledge and achieve the goal of the analysis. This article focuses on the goal of producing more accurate prediction which is important for risk assessment and decision making. We propose two new methods of design approaches that sequentially select input settings to achieve this goal. The approaches make novel applications of simultaneous and sequential contour estimations. Numerical examples are employed to demonstrate the effectiveness of the proposed approaches. |
| ArticleNumber | 9 |
| Author | Ranjan, P. Yang, F. Lin, C. Devon |
| Author_xml | – sequence: 1 givenname: F. surname: Yang fullname: Yang, F. organization: College of Mathematics, Sichuan University – sequence: 2 givenname: C. Devon orcidid: 0000-0002-5027-7361 surname: Lin fullname: Lin, C. Devon email: devon.lin@queensu.ca organization: Department of Mathematics and Statistics, Queen’s University – sequence: 3 givenname: P. surname: Ranjan fullname: Ranjan, P. organization: OM&QT Area, Indian Institute of Management Indore |
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| Keywords | Computer experiment Gaussian process Sequential design Maximin design Contour estimation Latin hypercube Space-filling |
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| References | Dancik G (2018) mlegp: maximum likelihood estimates of Gaussian processes. 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R package version 2.1-1 GramacyRBLeeHKHAdaptive design and analysis of supercomputer experimentsTechnometrics2009512130145266817010.1198/TECH.2009.0015 ChipmanHRanjanPWangWSequential design for computer experiments with a flexible Bayesian additive modelCan J Stat2012404663678299885510.1002/cjs.11156 LoeppkyJLMooreLMWilliamsBJBatch sequential designs for computer experimentsJ Stat Plan Inference2010140614521464259222410.1016/j.jspi.2009.12.004 McKayMDBeckmanRJConoverWJA comparison of three methods for selecting values of input variables in the analysis of output from a computer codeTechnometrics197921239455332520415.62011 GramacyRBLeeHKCases for the nugget in modeling computer experimentsStat Comput2012223713722290961710.1007/s11222-010-9224-x JosephVRDasguptaTTuoRWuCJSequential exploration of complex surfaces using minimum energy designsTechnometrics2015576474331835010.1080/00401706.2014.881749 SacksJWelchWJMitchellTJWynnHPDesign and analysis of computer experimentsStat Sci19894409423104176510.1214/ss/1177012413 DetteHPepelyshevAGeneralized Latin hypercube design for computer experimentsTechnometrics201052421429278924910.1198/TECH.2010.09157 GreenbergDA numerical model investigation of tidal phenomena in the Bay of Fundy and Gulf of MaineMar Geod1979216118710.1080/15210607909379345 Gramacy RB, Taddy MA (2016) tgp: Bayesian treed Gaussian process models. 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| References_xml | – reference: Dancik G (2018) mlegp: maximum likelihood estimates of Gaussian processes. R package version 3.1.7 – reference: PalomoJPauloRGarcia-DonatoGSAVE: an r package for the statistical analysis of computer modelsJ Stat Softw2015641312310.18637/jss.v064.i13 – reference: BowerRGBensonAJThe broken hierarchy of galaxy formationMon Not R Astron Soc200637064565510.1111/j.1365-2966.2006.10519.x – reference: DengXLinCDLiuKWRoweRKAdditive Gaussian process for computer models with qualitative and quantitative factorsTechnometrics201759283292367796010.1080/00401706.2016.1211554 – reference: GreenbergDA numerical model investigation of tidal phenomena in the Bay of Fundy and Gulf of MaineMar Geod1979216118710.1080/15210607909379345 – reference: DixonLCWSzegoGPThe global optimization problem: an introductionTowards Glob Optim19782115 – reference: Gu M, Palomo J, Berger J (2018) RobustGaSP: robust Gaussian stochastic process emulation. R package version 0.5.6 – reference: MorrisMDMitchellTJExploratory designs for computer experimentsJ Stat Plan Inference19954338140210.1016/0378-3758(94)00035-T – reference: Park JS (1991) Tuning complex computer codes to data and optimal designs. Unpublished Ph.D. thesis, University of Illinois, Champaign-Urbana – reference: LoeppkyJLMooreLMWilliamsBJBatch sequential designs for computer experimentsJ Stat Plan Inference2010140614521464259222410.1016/j.jspi.2009.12.004 – reference: JosephVRGulEBaSMaximum projection designs for computer experimentsBiometrika2015102371380337101010.1093/biomet/asv002 – reference: GramacyRBLeeHKCases for the nugget in modeling computer experimentsStat Comput2012223713722290961710.1007/s11222-010-9224-x – reference: Roustant O, Ginsbourger D, Deville Y (2018) DiceKriging: kriging methods for computer experiments. R package version 1.5.6 – reference: ImanRLConoverWJA distribution-free approach to inducing rank correlation among input variablesCommun Stat Part B Simul Comput19821131133410.1080/03610918208812265 – reference: JosephVRDasguptaTTuoRWuCJSequential exploration of complex surfaces using minimum energy designsTechnometrics2015576474331835010.1080/00401706.2014.881749 – reference: TangBOrthogonal array-based Latin hypercubesJ Am Stat Assoc19938813921397124537510.1080/01621459.1993.10476423 – reference: OwenABOrthogonal arrays for computer experiments, integration and visualizationStat Sin1992243945211879520822.62064 – reference: GramacyRBLeeHKHBayesian treed Gaussian process models with an application to computer modelingJ Am Stat Assoc200810348311191130252883010.1198/016214508000000689 – reference: SantnerTJWilliamsBJNotzWIThe design and analysis of computer experiments2003New YorkSpringer10.1007/978-1-4757-3799-8 – reference: BayarriMJBergerJOCalderESDalbeyKLunagomezSPatraAKPitmanEBSpillerETWolpertRLUsing statistical and computer models to quantify volcanic hazardsTechnometrics200951402413275647610.1198/TECH.2009.08018 – reference: GramacyRBLeeHKHAdaptive design and analysis of supercomputer experimentsTechnometrics2009512130145266817010.1198/TECH.2009.0015 – reference: ZhangRLinCDRanjanPLocal approximate Gaussian process model for large-scale dynamic computer experimentsJ Comput Graph Stat20182779880710.1080/10618600.2018.1473778 – reference: RanjanPBinghamDMichailidisGSequential experiment design for contour estimation from complex computer codesTechnometrics2008504527541265565110.1198/004017008000000541(Errata (2011), Technometrics, 53:1, 109–110) – reference: Gramacy RB, Taddy MA (2016) tgp: Bayesian treed Gaussian process models. R package version 2-4-14 – reference: JohnsonMMooreLYlvisakerDMinimax and maximin distance designJ Stat Plan Inference199026131148107925810.1016/0378-3758(90)90122-B – reference: LamCQNotzWISequential adaptive designs in computer experiments for response surface model fitStat Appl20086207233 – reference: SacksJSchillerSGuptaBergerSpatial designsStatistical decision theory and related topics IV1988New YorkSpringer38539910.1007/978-1-4612-3818-8_32 – reference: SacksJWelchWJMitchellTJWynnHPDesign and analysis of computer experimentsStat Sci19894409423104176510.1214/ss/1177012413 – reference: CurrinCMitchellTMorrisMYlvisakerDBayesian prediction of deterministic functions, with applications to the design and analysis of computer experimentsJ Am Stat Assoc199186416953963114634310.1080/01621459.1991.10475138 – reference: MacDonald B, Ranjan P, Chipman H (2015) GPfit: an R package for Gaussian process model fitting using a new optimization algorithm. R package version 1.0-1 – reference: RasmussenCEWilliamsCKIGaussian processes for machine learning2006Cambridge, MAThe MIT Press1177.68165 – reference: DetteHPepelyshevAGeneralized Latin hypercube design for computer experimentsTechnometrics201052421429278924910.1198/TECH.2010.09157 – reference: Ba S (2015) SLHD: maximin-distance (sliced) Latin hypercube designs. R package version 2.1-1 – reference: JosephVRHungYOrthogonal-maximin Latin hypercube designsStat Sin20081817118624169071137.62050 – reference: McKayMDBeckmanRJConoverWJA comparison of three methods for selecting values of input variables in the analysis of output from a computer codeTechnometrics197921239455332520415.62011 – reference: LinkletterCBinghamDHengartnerNHigdonDYeKQVariable selection for Gaussian process models in computer experimentsTechnometrics2006484478490232861710.1198/004017006000000228 – reference: LoeppkyJLSacksJWelchWJChoosing the sample size of a computer experiment: a practical guideTechnometrics2009514366376275647310.1198/TECH.2009.08040 – reference: SacksJSchillerSBWelchWJDesigns for computer experimentsTechnometrics198931414799766910.1080/00401706.1989.10488474 – reference: ChipmanHRanjanPWangWSequential design for computer experiments with a flexible Bayesian additive modelCan J Stat2012404663678299885510.1002/cjs.11156 – reference: FangKTLiRSudjiantoADesign 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| SubjectTerms | Algorithms Analysis and Advanced Methodologies in the Design of Experiments Mathematics and Statistics Original Article Probability Theory and Stochastic Processes Statistical Theory and Methods Statistics |
| Title | Global Fitting of the Response Surface via Estimating Multiple Contours of a Simulator |
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