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The influence of correlation functions on stochastic kriging metamodels

Authors:

Wei Xie,

Barry Nelson,

Jeremy StaumAuthors Info & Claims

WSC '10: Proceedings of the Winter Simulation Conference

Pages 1067 - 1078

Published: 05 December 2010 Publication History

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Abstract

The correlation function plays a critical role in both kriging and stochastic kriging metamodels. This paper will compare various correlation functions in both spatial and frequency domains, and analyze the influence of the choice of correlation function on prediction accuracy by experimenting with three tractable examples with differentiable and non-differentiable response surfaces: the M/M/1 queue, multi-product M/G/1 queue and 3-station Jackson network. The twice or higher-order continuously differentiable correlation functions demonstrate a promising capability to fit both differentiable and non-differentiable multi-dimensional response surfaces.

References

[1]

Ankenman, B., B. L. Nelson, and J. Staum. Stochastic kriging for simulation metamodeling. Operations Research 58 (2): 371--382.

Digital Library

Google Scholar

[2]

Borkowski, J. J., and G. F. Piepel. 2009. Uniform designs for highly constrained mixture experiments. Journal of Quality Technology 41 (1): 35--47.

Crossref

Google Scholar

[3]

Cressie, N. A. C. 1993. Statistics for spatial data. New York: John Wiley & Sons.

Google Scholar

[4]

Currin, C, T. Mitchell, M. Morris, and D. Ylvisaker. 1991. Bayesian prediction of deterministic functions, with applications to the design and analysis of computer experiments. Journal of the American Statistical Association 86 (416): 953--963.

Crossref

Google Scholar

[5]

Mitchell, T. J., and M. D. Morris. 1992. The spatial correlation function approach to response surface estimation. In Proceedings of the 1992 Winter Simulation Conference, ed. R. C. Crain, J. R. Wilson, J. J. Swain, and D. Goldsman, 565--571: Piscataway, N. J.: Institute of Electrical and Electronics Engineers.

Digital Library

Google Scholar

[6]

Oppenheim, A. V., R. W. Schafer, and J. R. Buck. 2005. Discrete-time signal processing. Upper Saddle River, NJ: Pearson Education.

Digital Library

Google Scholar

[7]

Sacks, J., S. B. Schiller, and W J. Welch. 1989. Designs for computer experiments. Technometrics 31 (1): 41--47.

Crossref

Google Scholar

[8]

Santner, T. J., B. J. Williams, and W I. Notz. 2003. The design and analysis of computer experiments. New York: Springer.

Google Scholar

[9]

Stein, M. L. 1999. Interpolation of spatial data: Some theory for kriging. New York: Springer-Verlag.

Google Scholar

[10]

van Beers, W. C. M., and J. Kleijnen. 2003. Kriging for interpolation in random simulation. Journal of the Operational Research Society 54:255--262.

Crossref

Google Scholar

[11]

Whitt, W. 1989. Planning queueing simulations. Management Science 35 (11): 1341--1366.

Digital Library

Google Scholar

[12]

Yang, F., J. Liu, M. Tongarlak, B. E. Ankenman, and B. L. Nelson. 2007. Metamodeling for cycle time-throughput-product mix surfaces using progressive model fitting. In Proceedings of the 2007 Winter Simulation Conference, ed. S. G. Henderson, B. Biller, M.-H. Hsieh, J. Shortle, J. D. Tew, and R. R. Barton, 322--330: Piscataway, N. J.: Institute of Electrical and Electronics Engineers.

Digital Library

Google Scholar

Cited By

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Xie WYi YZheng H(2020)Global-local Metamodel-assisted Stochastic Programming via SimulationACM Transactions on Modeling and Computer Simulation10.1145/341108031:1(1-34)Online publication date: 31-Dec-2020
https://dl.acm.org/doi/10.1145/3411080
Xie WYi YHuschka TChick S(2016)A simulation-based prediction framework for two-stage dynamic decision makingProceedings of the 2016 Winter Simulation Conference10.5555/3042094.3042381(2304-2315)Online publication date: 11-Dec-2016
https://dl.acm.org/doi/10.5555/3042094.3042381
Xie WNelson BBarton R(2016)Multivariate Input Uncertainty in Output Analysis for Stochastic SimulationACM Transactions on Modeling and Computer Simulation10.1145/299019027:1(1-22)Online publication date: 23-Oct-2016
https://dl.acm.org/doi/10.1145/2990190
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Index Terms

The influence of correlation functions on stochastic kriging metamodels
1. Computing methodologies
  1. Machine learning
    1. Machine learning approaches
      1. Factorization methods
        Canonical correlation analysis
  2. Modeling and simulation
    1. Model development and analysis
      1. Model verification and validation
2. Mathematics of computing
  1. Probability and statistics
    1. Statistical paradigms
      1. Regression analysis

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Ankenman et al. introduced stochastic kriging as a metamodeling tool for representing stochastic simulation response surfaces, and employed a very simple example to suggest that the use of Common Random Numbers (CRN) degrades the capability of ...

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WSC '10: Proceedings of the Winter Simulation Conference

December 2010

3519 pages

ISBN:9781424498642

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Winter Simulation Conference

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Published: 05 December 2010

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WSC10: Winter Simulation Conference

December 5 - 8, 2010

Maryland, Baltimore

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WSC '10 Paper Acceptance Rate 184 of 281 submissions, 65%;

Overall Acceptance Rate 3,413 of 5,075 submissions, 67%

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Xie WYi YZheng H(2020)Global-local Metamodel-assisted Stochastic Programming via SimulationACM Transactions on Modeling and Computer Simulation10.1145/341108031:1(1-34)Online publication date: 31-Dec-2020
https://dl.acm.org/doi/10.1145/3411080
Xie WYi YHuschka TChick S(2016)A simulation-based prediction framework for two-stage dynamic decision makingProceedings of the 2016 Winter Simulation Conference10.5555/3042094.3042381(2304-2315)Online publication date: 11-Dec-2016
https://dl.acm.org/doi/10.5555/3042094.3042381
Xie WNelson BBarton R(2016)Multivariate Input Uncertainty in Output Analysis for Stochastic SimulationACM Transactions on Modeling and Computer Simulation10.1145/299019027:1(1-22)Online publication date: 23-Oct-2016
https://dl.acm.org/doi/10.1145/2990190
Xie WNelson BBarton RBuckley SMiller J(2014)Statistical uncertainty analysis for stochastic simulation with dependent input modelsProceedings of the 2014 Winter Simulation Conference10.5555/2693848.2693942(674-685)Online publication date: 7-Dec-2014
https://dl.acm.org/doi/10.5555/2693848.2693942
Qu HFu M(2014)Gradient Extrapolated Stochastic KrigingACM Transactions on Modeling and Computer Simulation10.1145/265899524:4(1-25)Online publication date: 18-Nov-2014
https://dl.acm.org/doi/10.1145/2658995

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Enhancing stochastic kriging metamodels for computer simulation

Stochastic Subgradient Method Converges on Tame Functions

The effects of common random numbers on stochastic kriging metamodels

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Enhancing stochastic kriging metamodels for computer simulation

Stochastic Subgradient Method Converges on Tame Functions

The effects of common random numbers on stochastic kriging metamodels

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