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Contour estimation via two fidelity computer simulators under limited resources

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Abstract

The utilization of multiple fidelity simulators for the design and analysis of computer experiments has received increased attention in recent years. In this paper, we study the contour estimation problem for complex systems by considering two fidelity simulators. Our goal is to design a methodology of choosing the best suited simulator and input location for each simulation trial so that the overall estimation of the desired contour can be as good as possible under limited simulation resources. The proposed methodology is sequential and based on the construction of Gaussian process surrogate for the output measure of interest. We illustrate the methodology on a canonical queueing system and evaluate its efficiency via a simulation study.

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References

  • Booker AJ, Dennis JE Jr, Frank PD, Serani DB, Torczon V (1999) A rigorous framework for optimization of expensive functions by surrogates. Struct Optim 17:1–13

    Article  Google Scholar 

  • Chuang SC, Hung YC (2010) Uniform design over general input domains with applications to target region estimation in computer experiments. Comput Stat Data Anal 54:219–232

    Article  MathSciNet  Google Scholar 

  • Currin C, Mitchell TJ, Morris MD, Ylvisaker D (1991) Bayesian prediction of deterministic functions, with applications to the design and analysis of computer experiments. J Am Stat Assoc 86:953–963

    Article  MathSciNet  Google Scholar 

  • Fang K-T, Lin DKJ, Winker P, Zhang Y (2000) Uniform design: theory and application. Technometrics 42:237–248

    Article  MathSciNet  MATH  Google Scholar 

  • Forrester AIJ, Sobester A, Keane AJ (2007) Multi-fidelity optimization via surrogate modelling. Proc R Soc A 463:3251–3269

    Article  MathSciNet  MATH  Google Scholar 

  • Gramacy RB, Lee HH (2008) Bayesian treed gaussian process models with an application to computer modeling. J Am Stat Assoc 103:1119–1130

    Article  MathSciNet  MATH  Google Scholar 

  • Hung YC, Michailidis G (2008) Modeling, scheduling, and simulation of switched processing systems. ACM Trans Model Comput Simul 18:3

    Article  Google Scholar 

  • Jones DR, Schonlau M, Welch WJ (1998) Efficient global optimization of expensive black-box functions. J Glob Optim 13:455–492

    Article  MathSciNet  MATH  Google Scholar 

  • Joseph VR (2006) Limit kriging. Technometrics 48:458–466

    Article  MathSciNet  Google Scholar 

  • Joseph VR, Hung Y, Sudjianto A (2008) Blind kriging: a new method for developing metamodels. J Mech Des 130:0311021-1-8

    Article  Google Scholar 

  • Kennedy MC, O’Hagan A (2000) Predicting the output from a complex computer code when fast approximations are available. Biometrika 87:1–13

    Article  MathSciNet  MATH  Google Scholar 

  • McKay MD, Beckman RJ, Conover WJ (1979) A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 21:239–245

    MathSciNet  MATH  Google Scholar 

  • Mitchell TJ, Morris MD (1992) Bayesian design and analysis of computer experiments: two examples. Stat Sin 2:359–379

    MATH  Google Scholar 

  • Qian PZG, Ai M, Wu CFJ (2009) Construction of nested space-filling designs. Ann Stat 37:3616–3643

    Article  MathSciNet  MATH  Google Scholar 

  • Qian PZG, Wu CFJ (2008) Bayesian hierarchical modeling for integrating low-accuracy and high-accuracy experiments. Technometrics 50:192–204

    Article  MathSciNet  Google Scholar 

  • Qian Z, Seepersad CC, Joseph VR, Allen JK, Wu CFJ (2006) Building surrogate models based on detailed and approximate simulations. J Mech Des 128:668–677

    Article  Google Scholar 

  • Ranjan P, Bingham D, Michailidis G (2008) Sequential experiment design for contour estimation from complex computer codes. Technometrics 50:527–541

    Article  MathSciNet  Google Scholar 

  • Ranjan P, Bingham D, Michailidis G (2011) Errata: Sequential experiment design for contour estimation from complex computer codes. Technometrics 53:109–111

    Article  MathSciNet  Google Scholar 

  • Rennen G, Husslage B, Dam ERV, Hertog DD (2010) Nested maximin Latin hypercube designs. Struct Multidiscip Optim 41:371–395

    Article  MathSciNet  Google Scholar 

  • Sacks J, Schiller SB, Welch WJ (1989a) Design for computer experiments. Technometrics 31:41–47

    Article  MathSciNet  Google Scholar 

  • Sacks J, Welch WJ, Mitchell TJ, Wynn HP (1989b) Design and analysis of computer experiments. Stat Sci 4:409–423

    Article  MathSciNet  MATH  Google Scholar 

  • Welch WJ, Buck RJ, Sacks J, Wynn HP, Mitchell TJ, Morris MD (1992) Screening, predicting, and computer experiments. Technometrics 34:15–25

    Article  Google Scholar 

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Acknowledgments

The authors are grateful to the anonymous reviewers for their suggestions and comments. This work is partially supported by the National Science Council under grant NSC 98-2118-M-390-002-(Chen) and 100-2628-M-002-011-MY4 (Wang), Taida Institute for Mathematical Sciences, National Center for Theoretical Sciences (Taipei Office) and the Mathematics Division of the National Center for Theoretical Sciences (South) in Taiwan.

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Authors and Affiliations

  1. Department of Statistics, National Cheng Kung University, No. 1, Ta-Hsueh Rd., Tainan, 70101, Taiwan

    Ray-Bing Chen

  2. Department of Statistics, National Chengchi University, No. 64, Sec. 2, ZhiNan Rd., Taipei, 11605, Taiwan

    Ying-Chao Hung

  3. Department of Mathematics, National Taiwan University, No. 1, Sec. 4, Roosevelt Rd., Taipei, 10617, Taiwan

    Weichung Wang & Sung-Wei Yen

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  1. Ray-Bing Chen
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  2. Ying-Chao Hung
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  3. Weichung Wang
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  4. Sung-Wei Yen
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Correspondence to Weichung Wang.

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Chen, RB., Hung, YC., Wang, W. et al. Contour estimation via two fidelity computer simulators under limited resources. Comput Stat 28, 1813–1834 (2013). https://doi.org/10.1007/s00180-012-0380-7

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  • DOI: https://doi.org/10.1007/s00180-012-0380-7

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