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Original Articles

Emulation of Numerical Models With Over-Specified Basis Functions

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Pages 153-164 | Received 01 Jan 2014, Published online: 12 Apr 2017

References

  • Chevalier, R. A. (1997), “Type II Supernovae SN 1987A and SN 1993J,” Science, 276, 1374–1378.
  • Eldred, M. S., Webster, C. G., and Constantine, P. (2008), “Evaluation of Non-Intrusive Approaches for Wiener-Askey Generalized Polynomial Chaos,” in Proceedings of the 10th AIAA Non-Deterministic Approaches Conference, Paper No. AIAA 2008-1892.
  • Ernst, O. G., Mugler, A., Starkloff, H. J., and Ullmann, E. (2012), “On the Convergence of Generalized Polynomial Chaos Expansions,” ESAIM: Mathematical Modelling and Numerical Analysis, 46, 317–339.
  • Goh, J., Bingham, D., Holloway, J. P., Grosskopf, M. J., Kuranz, C. C., and Rutter, E. (2013), “Prediction and Computer Model Calibration Using Outputs From Multifidelity Simulators,” Technometrics, 55, 501–512.
  • Gramacy, R. (2007), “tgp: An R Package for Bayesian Nonstationary, Semiparametric Nonlinear Regression and Design by Treed Gaussian Process Models,” Journal of Statistical Software, 19, 1–46.
  • Gramacy, R. B., and Lee, H. K. H. (2008), “Bayesian Treed Gaussian Process Models With an Application to Computer Modeling,” Journal of the American Statistical Association, 103, 1119–1130.
  • ——— (2012), “Cases for the Nugget in Modeling Computer Experiments,” Statistics and Computing, 22, 713–722.
  • Higdon, D., Gattiker, J., Williams, B., and Rightley, M. (2008), “Computer Model Calibration Using High-Dimensional Output,” Journal of the American Statistical Association, 103, 570–583.
  • Kaufman, C. G., Bingham, D., Habib, S., Heitmann, K., and Frieman, J. A. (2011), “Efficient Emulators of Computer Experiments Using Compactly Supported Correlation Functions, With an Application to Cosmology,” The Annals of Applied Statistics, 5, 2470–2492.
  • Kennedy, M. C., and O’Hagan, A. (2001), “Bayesian Calibration of Computer Models,” Journal of the Royal Statistical Society, Series B, 63, 425–464.
  • Kubo, I., Kuo, H. H., and Namli, S. (2007), “The Characterization of a Class of Probability Measures by Multiplicative Renormalization,” Communications on Stochastic Analysis, 1, 455–472.
  • Kuranz, C. C., Drake, R. P., Huntington, C. M., Krauland, C. M., Stefano, C. A., Trantham, M., Grosskopf, M. J., Klein, S. R., and Marion, D. C. (2013), “Early-Time Evolution of a Radiative Shock,” High Energy Density Physics, 9, 315–318.
  • Loéve, M. (1978), Probability Theory ( 4th ed.), New York: Springer-Verlag.
  • Marzouk, Y. M., and Xiu, D. (2009), “A Stochastic Collocation Approach to Bayesian Inference in Inverse Problems,” Communications in Computational Physics, 6, 826–847.
  • McClarren, R. G., Ryu, D., Drake, P., Grosskopf, M., Bingham, D., Chou, C., Fryxell, B., Van der Holst, B., Holloway, J. P., Kuranz, C. C., Mallick, B., Rutter, E., and Torralva, B. R. (2011), “A Physics Informed Emulator for Laser-Driven Radiating Shock Simulations,” Reliability Engineering and System Safety, 96, 1194–1207.
  • McKay, M. D., Beckman, R. J., and Conover, W. J. (1979), “Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output From a Computer Code,” Technometrics, 21, 239–245.
  • Paciorek, C., and Schervish, M. (2004), “Nonstationary Covariance Functions for Gaussian Process Regression,” Advances in Neural Information Processing Systems, 16, 273–280.
  • Qian, P. Z. G., Wu, H., and Wu, C. F. J. (2009), “Gaussian Process Models for Computer Experiments With Qualitative and Quantitative Factors,” Technometrics, 50, 383–396.
  • Reighard, A. B., Drake, R. P., Dannenberg, K. K., Kremer, D. J., Grosskopf, M. J., Harding, E. C., Leibrandt, D. R., Glendinning, S. G., Perry, T. S., Remington, B. A., Greenough, J., Knauer, J., Boehly, T., Bouquet, S., Boireau, L., Koenig, M., and Vinci, T. (2006), “Observation of Collapsing Radiative Shocks in Laboratory Experiments,” Physics of Plasmas, 13, 082901–082901–5.
  • Richardson, S., and Green, P. J. (1997), “On Bayesian Analysis of Mixtures With an Unknown Number of Components,” Journal of the Royal Statistical Society, Series B, 0, 731–792.
  • Sacks, J., Schiller, S., and Welch, W. (1989), “Designs for Computer Experiments,” Technometrics, 31, 41–47.
  • Stripling, H. F., McClarren, R. G., Kuranz, C. C., Grosskopf, M. J., Rutter, E., and Torralva, B. R. (2013), “A Calibration and Data Assimilation Method Using the Bayesian MARS Emulator,” Annals of Nuclear Energy, 52, 103–112.
  • Van der Holst, B., Tóth, G., Sokolov, I. V., Torralva, B. R., Powell, K. G., Drake, R. P., Klapisch, M., Busquet, M., Fryxell, B., and Myra, E. S. (2013), “Simulating Radiative Shocks With the CRASH Laser Package,” High Energy Density Physics, 9, 8–16.
  • Xiu, D. (2007), “Efficient Collocational Approach for Parametric Uncertainty Analysis,” Communications in Computational Physics, 2, 293–309.
  • Xiu, D., and Karniadakis, G. E. (2002), “The Wiener-Askey Polynomial Chaos for Stochastic Differential Equations,” SIAM Journal of Scientific Computing, 24, 619–644.
  • Zhou, Q., Qian, P. Z. G., and Zhou, S. (2011), “A Simple Approach to Emulation for Computer Models With Qualitative and Quantitative Factors,” Technometrics, 53, 266–273.

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