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Original Articles

Stochastic Polynomial Interpolation for Uncertainty Quantification With Computer Experiments

Pages 457-467 | Received 01 Nov 2013, Published online: 18 Nov 2015

REFERENCES

  • Agarwal, N., and Aluru, N.R. (2009), “A Domain Adaptive Stochastic Collocation Approach for Analysis of MEMS Under Uncertainties,” Journal of Computational Physics, 228, 7662–7688.
  • Apley, D.W., Liu, J., and Chen, W. (2006), “Understanding the Effects of Model Uncertainty in Robust Design with Computer Experiments,” Journal of Mechanical Design, 128, 945–958.
  • Barthelmann, V., Novak, E., and Ritter, K. (2000), “High Dimensional Polynomial Interpolation on Sparse Grids,” Advances in Computational Mathematics, 12, 273–288.
  • Bates, R.A., Giglio, B., and Wynn, H.P. (2003), “A Global Selection Procedure for Polynomial Interpolators,” Technometrics, 45, 246–255.
  • Bates, R.A., Maruri-Aguilar, H., and Wynn, H.P. (2014), “Smooth Supersaturated Models,” Journal of Statistical Computation and Simulation, 84, 1–12.
  • Box, G.E. P., and Draper, N.R. (2007), Response Surfaces, Mixtures, and Ridge Analyses (2nd ed.), Hoboken, NJ: Wiley.
  • Chen, W., Jin, R., and Sudjianto, A. (2006). “Analytical Global Sensitivity Analysis and Uncertainty Propagation For Robust Design,” Journal of Quality Technology, 38, 333–348.
  • Chung, K.C., and Yao, T.H. (1977), “On Lattices Admitting Unique Lagrange Interpolations,” SIAM Journal on Numerical Analysis, 14, 735–743.
  • Crestaux, T., Le Maître, O.P., and Martinez, J.M. (2009), “Polynomial Chaos Expansion for Sensitivity Analysis,” Reliability Engineering and System Safety, 94, 1161–1172.
  • Currin, C., Mitchell, T., Morris, M., and Ylvisaker, D. (1991), “Bayesian Prediction of Deterministic Functions, With Applications to the Design and Analysis of Computer Experiments,” Journal of the American Statistical Association, 86, 953–963.
  • De Boor, C., and Ron, A. (1990), “On Multivariate Polynomial Interpolation,” Constructive Approximation, 6, 287–302.
  • Dette, H., and Pepelyshev, A. (2010), “Generalized Latin Hypercube Design For Computer Experiments,” Technometrics, 52, 421–429.
  • Gasca, M., and Sauer, T. (2000), “Polynomial Interpolation in Sseveral Variables,” Advances in Computational Mathematics, 12, 377–410.
  • Gautschi, W. (2004), Orthogonal Polynomials: Computation and Approximation, New York: Oxford University Press.
  • Ghanem, R., and Spanos, P.D. (1991), Stochastic Finite Elements: A Spectral Approach, New York: Springer-Verlag.
  • Holliday, T., Pistone, G., Riccomagno, E., and Wynn, H.P. (1999), “The Application of Computational Algebraic Geometry to the Analysis of Designed Experiments: A Case Study,” Computational Statistics, 14, 213–232.
  • Joseph, V.R. (2006), “A Bayesian Approach to the Design and Analysis of Fractionated Experiments,” Technometrics, 48, 219–229.
  • Lazarov, B.S., Schevenels, M., and Sigmund, O. (2012), “Topology Optimization Considering Material and Geometric Uncertainties Using Stochastic Collocation Methods,” Structural and Multidisciplinary Optimization, 46, 597–612.
  • Le Maître, O.P., and Knio, O.M. (2010), Spectral Methods for Uncertainty Quantification: With Applications to Computational Fluid Dynamics, New York: Springer-Verlag.
  • Lemieux, C. (2009), Monte Carlo and Quasi-Monte-Carlo Sampling, New York: Springer-Verlag.
  • Morris, M.D., and Mitchell, T.J. (1995), “Exploratory Designs for Computational Experiments,” Journal of Statistical Planning and Inference, 43, 381–402.
  • Morris, M.D., Mitchell, T.J., and Ylvisaker, D. (1993), “Bayesian Design and Analysis of Computer Experiments: Use of Derivatives in Surface Prediction,” Technometrics, 35, 243–255.
  • Muirhead, R.I. (2005), Aspects of Multivariate Statistical Theory (2nd ed.), New York: Wiley.
  • Mullur, A.A., and Messac, A. (2006), “Metamodeling Using Extended Radial Basis Functions: A Comparative Approach,” Engineering with Computers, 21, 203–217.
  • Narayan, A., and Xiu, D. (2012), “Stochastic Collocation Methods on Unstructured Grids in High Dimensions via Interpolation,” SIAM Journal on Scientific Computing, 34, 1729–1752.
  • Narayan, A. (2013), “Constructing Nested Nodal Sets for Multivariate Polynomial Interpolation,” SIAM Journal on Scientific Computing, 35, 2293–2315.
  • Oakley, J.E., and O’Hagan, A. (2004), “Probabilistic Sensitivity Analysis of Complex Models: A Bayesian Approach,” Journal of the Royal Statistical Society, Series B, 66, 751–769.
  • Phillips, G.M. (2003), Interpolation and Approximation by Polynomials, New York: Springer-Verlag.
  • Pistone, G., and Wynn, H.P. (1996), “Generalised Confounding With Gröbner Bases,” Biometrika, 83, 653–666.
  • Rasmussen, C.E., and Williams, C.K. I. (2006), Gaussian Processes for Machine Learning, Cambridge: MIT Press.
  • Robert, C.P. (2007), The Bayesian Choice (2nd ed.), New York: Springer.
  • Sacks, J., Welch, W.J., Mitchell, T.J., and Wynn, H.P. (1989), “Design and Analysis of Computer Experiments,” Statistical Science, 4, 409–423.
  • Saltelli, A. (2000), “What is Sensitivity Analysis,” in Sensitivity Analysis, eds. A. Saltelli, K. Chan, and E.M. Scott, New York: Wiley.
  • Santner, T.J., Williams, B.J., and Notz, W.I. (2003), The Design and Analysis of Computer Experiments, New York: Springer-Verlag.
  • Sauer, T., and Xu, Y. (1995), “On Multivariate Lagrange Interpolation,” Mathematics of Computation, 64, 1147–1170.
  • Simpson, T.W., Mauery, T.M., Korte, J.J., and Mistree, F. (1998), “Comparison of Response Surface and Kriging Models for Multidisciplinary Design Optimization,” AIAA Paper 98, 4758, 1–11.
  • Steinberg, D.M., and Bursztyn, D. (2004), “Data Analytic Tools for Understanding Random Field Regression Models,” Technometrics, 46, 411–420.
  • Sudret, B. (2008), “Global Sensitivity Analysis Using Polynomial Chaos Expansions,” Reliability Engineering and System Safety, 93, 964–979.
  • Tan, M.H. Y., and Wu, C.F. J. (2012), “Robust Design Optimization With Quadratic Loss Derived From Gaussian Process Models,” Technometrics, 54, 51–63.
  • Trefethen, L.N. (2013), Approximation Theory and Approximation Practice, Philadelphia: SIAM.
  • Wang, G.G., and Shan, S. (2007), “Review of Metamodeling Techniques in Support of Engineering Design Optimization,” Journal of Mechanical Design, 129, 370–380.
  • Welch, W., Yu, T., Kang, S.M., and Sacks, J. (1990), “Computer Experiments for Quality Control by Parameter Design,” Journal of Quality Technology, 22, 15–22.
  • Xiu, D. (2010), Numerical Methods for Stochastic Computations: A Spectral Method Approach, Princeton, NJ: Princeton University Press.
  • Xiu, D., and Hesthaven, J.S. (2005), “High-Order Collocation Methods for Differential Equations With Random Inputs,” SIAM Journal on Scientific Computing, 27, 1118–1139.
  • Xiu, D., and Karniadakis, G.E. (2002), “The Wiener-Askey Polynomial Chaos for Stochastic Differential Equations,” SIAM Journal on Scientific Computing, 24, 619–644.

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