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Volumn 231, Issue 17, 2012, Pages 5718-5746

Multi-output local Gaussian process regression: Applications to uncertainty quantification

Author keywords

Adaptivity; Bayesian; Gaussian process; Multi element; Multi output; Stochastic partial differential equations; Uncertainty quantification

Indexed keywords

ERROR STATISTICS; GAUSSIAN DISTRIBUTION; STOCHASTIC SYSTEMS; TREES (MATHEMATICS); UNCERTAINTY ANALYSIS;

EID: 84862859211     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2012.04.047     Document Type: Article
Times cited : (194)

References (46)
  • 1
    • 84900847494 scopus 로고
    • Small sample sensitivity analysis techniques for computer models with an application to risk assessment
    • Iman R.L., Conover W.J. Small sample sensitivity analysis techniques for computer models with an application to risk assessment. Communications in Statistics - Theory and Methods 1980, 9(17):1749-1842.
    • (1980) Communications in Statistics - Theory and Methods , vol.9 , Issue.17 , pp. 1749-1842
    • Iman, R.L.1    Conover, W.J.2
  • 2
    • 55349113698 scopus 로고    scopus 로고
    • Multilevel Monte Carlo path simulation
    • Oxford University Computing Laboratory
    • M.B. Giles, Multilevel Monte Carlo path simulation, Tech. rep., Oxford University Computing Laboratory, 2006.
    • (2006) Tech. rep.
    • Giles, M.B.1
  • 3
    • 84892272601 scopus 로고    scopus 로고
    • Improved multilevel Monte Carlo convergence using the Milstein scheme, in: A. Keller, S. Heinrich, H. Niederreiter (Eds.), Monte Carlo and Quasi-Monte Carlo Methods 2006, Springer
    • M.B. Giles, Improved multilevel Monte Carlo convergence using the Milstein scheme, in: A. Keller, S. Heinrich, H. Niederreiter (Eds.), Monte Carlo and Quasi-Monte Carlo Methods 2006, Springer, 2008, pp. 343-358.
    • (2008) , pp. 343-358
    • Giles, M.B.1
  • 5
    • 0037249229 scopus 로고    scopus 로고
    • The Wiener-Askey polynomial chaos for stochastic differential equations
    • Xiu D., Karniadakis G.E. The Wiener-Askey polynomial chaos for stochastic differential equations. Journal of Scientific Computing 2002, (24):619-644.
    • (2002) Journal of Scientific Computing , Issue.24 , pp. 619-644
    • Xiu, D.1    Karniadakis, G.E.2
  • 6
    • 21444449245 scopus 로고    scopus 로고
    • An adaptive multi-element generalized polynomial chaos method for stochastic differential equations
    • Wan X., Karniadakis G.E. An adaptive multi-element generalized polynomial chaos method for stochastic differential equations. Journal of Computaional Physics 2005, 209:617-642.
    • (2005) Journal of Computaional Physics , vol.209 , pp. 617-642
    • Wan, X.1    Karniadakis, G.E.2
  • 7
    • 33749326978 scopus 로고    scopus 로고
    • Multi-element generalized polynomial chaos for arbitrary probability measures
    • Wan X., Karniadakis G.E. Multi-element generalized polynomial chaos for arbitrary probability measures. SIAM Journall of Scientific Computing 2006, 28(3):901-928.
    • (2006) SIAM Journall of Scientific Computing , vol.28 , Issue.3 , pp. 901-928
    • Wan, X.1    Karniadakis, G.E.2
  • 8
    • 34548216854 scopus 로고    scopus 로고
    • A stochastic collocation method for elliptic partial differential equations with random input data
    • BabuŠka I., Nobile F., Tempone R. A stochastic collocation method for elliptic partial differential equations with random input data. SIAM Journal of Numerical Analysis 2007, 45(3):1005-1034.
    • (2007) SIAM Journal of Numerical Analysis , vol.45 , Issue.3 , pp. 1005-1034
    • Babuška, I.1    Nobile, F.2    Tempone, R.3
  • 9
    • 0001048297 scopus 로고
    • Quadrature and interpolation formulas for tensor products of certain classes of functions, in: Dokl. Akad. Nauk SSSR.
    • S.A. Smolyak, Quadrature and interpolation formulas for tensor products of certain classes of functions, in: Dokl. Akad. Nauk SSSR, vol. 4, 1963, p. 123.
    • (1963) , vol.4 , pp. 123
    • Smolyak, S.A.1
  • 10
    • 33646577797 scopus 로고    scopus 로고
    • High-order collocation methods for differential equations with random inputs
    • Xiu D., Hesthaven J.S. High-order collocation methods for differential equations with random inputs. SIAM Journal on Scientific Computing 2005, 27(3):1118-1139.
    • (2005) SIAM Journal on Scientific Computing , vol.27 , Issue.3 , pp. 1118-1139
    • Xiu, D.1    Hesthaven, J.S.2
  • 11
    • 34447270699 scopus 로고    scopus 로고
    • Efficient collocational approach for parametric uncertainty analysis
    • Xiu D. Efficient collocational approach for parametric uncertainty analysis. Communications in Computational Physics 2007, 2(2):293-309.
    • (2007) Communications in Computational Physics , vol.2 , Issue.2 , pp. 293-309
    • Xiu, D.1
  • 12
    • 52749093759 scopus 로고    scopus 로고
    • A sparse grid stochastic collocation method for partial differential equations with random input data
    • Nobile F., Tempone R., Webster C.G. A sparse grid stochastic collocation method for partial differential equations with random input data. SIAM Journal of Numerical Analysis 2008, 46(5):2309-2345.
    • (2008) SIAM Journal of Numerical Analysis , vol.46 , Issue.5 , pp. 2309-2345
    • Nobile, F.1    Tempone, R.2    Webster, C.G.3
  • 13
    • 61349191533 scopus 로고    scopus 로고
    • An adaptive hierarchical sparse Grid Collocation algorithm for the solution of stochastic differential equations
    • Ma X., Zabaras N. An adaptive hierarchical sparse Grid Collocation algorithm for the solution of stochastic differential equations. Journal of Computaional Physics 2009, 228(8):3084-3113.
    • (2009) Journal of Computaional Physics , vol.228 , Issue.8 , pp. 3084-3113
    • Ma, X.1    Zabaras, N.2
  • 16
    • 0000695404 scopus 로고
    • Information-based objective functions for active data selection
    • MacKay D.J.C. Information-based objective functions for active data selection. Neural Computation 1992, 4(4):590-604.
    • (1992) Neural Computation , vol.4 , Issue.4 , pp. 590-604
    • MacKay, D.J.C.1
  • 17
    • 54949111733 scopus 로고    scopus 로고
    • Bayesian treed Gaussian Process models with an application to computer modeling
    • Gramacy R.B., Lee H.K.H. Bayesian treed Gaussian Process models with an application to computer modeling. Journal of the American Statistical Association 2008, 103(483):1119-1130.
    • (2008) Journal of the American Statistical Association , vol.103 , Issue.483 , pp. 1119-1130
    • Gramacy, R.B.1    Lee, H.K.H.2
  • 21
    • 85190788089 scopus 로고    scopus 로고
    • Gaussian processes, Tutorial at Neural Information Processing Systems 10.
    • D.J.C. MacKay, Gaussian processes, Tutorial at Neural Information Processing Systems 10.
    • MacKay, D.J.C.1
  • 24
    • 34247466026 scopus 로고    scopus 로고
    • Dependent Gaussian processes, in: Neural Information Processing Systems
    • P. Boyle, M. Frean, Dependent Gaussian processes, in: Neural Information Processing Systems 18, 2005, pp. 217-224.
    • (2005) , vol.18 , pp. 217-224
    • Boyle, P.1    Frean, M.2
  • 25
    • 84862602372 scopus 로고    scopus 로고
    • Semiparametric latent factor models, in: R.G. Cowell, Z. Ghahramani (Eds.), 10th International Workshop on Artificial Intelligence and Statistics, Society for Artificial Intelligence and Statistics
    • Y.W. Teh, M. Seeger, M.I. Jordan, Semiparametric latent factor models, in: R.G. Cowell, Z. Ghahramani (Eds.), 10th International Workshop on Artificial Intelligence and Statistics, Society for Artificial Intelligence and Statistics, 2005, pp. 333-340.
    • (2005) , pp. 333-340
    • Teh, Y.W.1    Seeger, M.2    Jordan, M.I.3
  • 26
    • 85190767766 scopus 로고    scopus 로고
    • Advance in Neural Information Processing 17, MIT Press, L.K. Saul, Y. Weiss, L. Bottou (Eds.)
    • Micchelli C.A., Pontil M. Kernels for multi-task learning 2005, 921-928. Advance in Neural Information Processing 17, MIT Press. L.K. Saul, Y. Weiss, L. Bottou (Eds.).
    • (2005) Kernels for multi-task learning , pp. 921-928
    • Micchelli, C.A.1    Pontil, M.2
  • 28
    • 70350733506 scopus 로고    scopus 로고
    • Bayesian emulation of complex multi-output and dynamic computer models
    • Conti S., OHagan A. Bayesian emulation of complex multi-output and dynamic computer models. Journal of Statistical Planning and Inference 2010, 140(3):640-651.
    • (2010) Journal of Statistical Planning and Inference , vol.140 , Issue.3 , pp. 640-651
    • Conti, S.1    OHagan, A.2
  • 29
    • 0001025418 scopus 로고
    • Bayesian interpolation
    • MacKay D.J.C. Bayesian interpolation. Neural Computation 1992, 4(3):415-447.
    • (1992) Neural Computation , vol.4 , Issue.3 , pp. 415-447
    • MacKay, D.J.C.1
  • 31
    • 52749087886 scopus 로고    scopus 로고
    • The Multi-Element probabilistic collocation method (ME-PCM): error analysis and applications
    • Foo J., Wan X., Karniadakis G.E. The Multi-Element probabilistic collocation method (ME-PCM): error analysis and applications. Journal of Computational Physics 2008, 227(22):9572-9595.
    • (2008) Journal of Computational Physics , vol.227 , Issue.22 , pp. 9572-9595
    • Foo, J.1    Wan, X.2    Karniadakis, G.E.3
  • 34
    • 0002295913 scopus 로고    scopus 로고
    • Gaussian processes for regression, in: D.S. Touretzky, M.C. Mozer, M.E. Hasselmo (Eds.), Advances in Neural Information Processing Systems. MIT Press
    • C.K.I. Williams, C.E. Rasmussen, Gaussian processes for regression, in: D.S. Touretzky, M.C. Mozer, M.E. Hasselmo (Eds.), Advances in Neural Information Processing Systems, vol. 8, MIT Press, 1996, pp. 514-520.
    • (1996) , vol.8 , pp. 514-520
    • Williams, C.K.I.1    Rasmussen, C.E.2
  • 35
    • 84972528615 scopus 로고
    • Bayesian experimental design: a review
    • Chaloner K., Verdinelli I. Bayesian experimental design: a review. Statistical Science 1995, 10(3):273-304.
    • (1995) Statistical Science , vol.10 , Issue.3 , pp. 273-304
    • Chaloner, K.1    Verdinelli, I.2
  • 36
    • 0030221433 scopus 로고    scopus 로고
    • Neural network exploration using optimal experiment design
    • D.A. Cohn, Neural network exploration using optimal experiment design, Neural Networks 9 (6).
    • Neural Networks , vol.9 , Issue.6
    • Cohn, D.A.1
  • 37
    • 0033726013 scopus 로고    scopus 로고
    • Gaussian process regression: active data selection and test point rejection
    • IEEE Press, Los Alamitos, CA
    • Seo S., Wallat M., Graepel T., Obermayer K. Gaussian process regression: active data selection and test point rejection. International Joint Conference on Neural Networks 2000, vol. 3:241-246. IEEE Press, Los Alamitos, CA.
    • (2000) International Joint Conference on Neural Networks , vol.3 , pp. 241-246
    • Seo, S.1    Wallat, M.2    Graepel, T.3    Obermayer, K.4
  • 38
    • 65349171456 scopus 로고    scopus 로고
    • Adaptive design and analysis of supercomputer experiments
    • Gramacy R.B., Lee H.K.H. Adaptive design and analysis of supercomputer experiments. Technometrics 2009, 51(2):130-145.
    • (2009) Technometrics , vol.51 , Issue.2 , pp. 130-145
    • Gramacy, R.B.1    Lee, H.K.H.2
  • 39
    • 30944443976 scopus 로고    scopus 로고
    • Trilinos Users Guide
    • Sandia National Laboratories
    • M.A. Heroux, J.M. Willenbring, Trilinos Users Guide, Tech. rep., Sandia National Laboratories, 2003.
    • (2003) Tech. rep.
    • Heroux, M.A.1    Willenbring, J.M.2
  • 41
    • 52749083629 scopus 로고    scopus 로고
    • A sparse grid collocation method for elliptic partial differential equations with random input data
    • Nobile F., Tempone R., Webster C. A sparse grid collocation method for elliptic partial differential equations with random input data. SIAM Journal of Numerical Analysis 2008, 45:2309-2345.
    • (2008) SIAM Journal of Numerical Analysis , vol.45 , pp. 2309-2345
    • Nobile, F.1    Tempone, R.2    Webster, C.3
  • 43
    • 85190817141 scopus 로고    scopus 로고
    • Nektar, Suite of simulation codes.
    • Nektar, Suite of simulation codes, . http://www.cfm.brown.edu/people/tcew/nektar.html.
  • 44
    • 0004220749 scopus 로고    scopus 로고
    • Monte Carlo implementation of Gaussian process models for bayesian regression and classification
    • Departement of Statistics, University of Toronto, Toronto
    • R.M. Neal, Monte Carlo implementation of Gaussian process models for bayesian regression and classification, Tech. Rep. 9702, Departement of Statistics, University of Toronto, Toronto, 1997.
    • (1997) Tech. Rep. 9702
    • Neal, R.M.1
  • 45
    • 84859218670 scopus 로고    scopus 로고
    • Cases for the nugget in modeling computer experiments
    • Gramacy R.B., Lee H.K.H. Cases for the nugget in modeling computer experiments. Statistics and Computing 2012, 22(3):713-722.
    • (2012) Statistics and Computing , vol.22 , Issue.3 , pp. 713-722
    • Gramacy, R.B.1    Lee, H.K.H.2
  • 46
    • 0003768769 scopus 로고
    • Practical Methods of Optimization
    • Wiley
    • Fletcher R. Practical Methods of Optimization. second ed. 1987, Wiley.
    • (1987) second ed.
    • Fletcher, R.1


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