×

zbMATH — the first resource for mathematics

Global fitting of the response surface via estimating multiple contours of a simulator. (English) Zbl 1437.62316
Summary: Computer simulators are widely used to understand complex physical systems in many areas such as aerospace, renewable energy, climate modelling, and manufacturing. One fundamental aspect of the study of computer simulators is known as experimental design, that is, how to select the input settings where the computer simulator is run and the corresponding response is collected. Extra care should be taken in the selection process because computer simulators can be computationally expensive to run. The selection should acknowledge and achieve the goal of the analysis. This article focuses on the goal of producing more accurate prediction which is important for risk assessment and decision making. We propose two new methods of design approaches that sequentially select input settings to achieve this goal. The approaches make novel applications of simultaneous and sequential contour estimations. Numerical examples are employed to demonstrate the effectiveness of the proposed approaches.
MSC:
62K20 Response surface designs
60G15 Gaussian processes
05B15 Orthogonal arrays, Latin squares, Room squares
62L05 Sequential statistical design
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Ba S (2015) SLHD: maximin-distance (sliced) Latin hypercube designs. R package version 2.1-1
[2] Bayarri, Mj; Berger, Jo; Calder, Es; Dalbey, K.; Lunagomez, S.; Patra, Ak; Pitman, Eb; Spiller, Et; Wolpert, Rl, Using statistical and computer models to quantify volcanic hazards, Technometrics, 51, 402-413 (2009)
[3] Bower, Rg; Benson, Aj, The broken hierarchy of galaxy formation, Mon Not R Astron Soc, 370, 645-655 (2006)
[4] Chipman, H.; Ranjan, P.; Wang, W., Sequential design for computer experiments with a flexible Bayesian additive model, Can J Stat, 40, 4, 663-678 (2012) · Zbl 1349.62366
[5] Currin, C.; Mitchell, T.; Morris, M.; Ylvisaker, D., Bayesian prediction of deterministic functions, with applications to the design and analysis of computer experiments, J Am Stat Assoc, 86, 416, 953-963 (1991)
[6] Dancik G (2018) mlegp: maximum likelihood estimates of Gaussian processes. R package version 3.1.7
[7] Deng, X.; Lin, Cd; Liu, Kw; Rowe, Rk, Additive Gaussian process for computer models with qualitative and quantitative factors, Technometrics, 59, 283-292 (2017)
[8] Dette, H.; Pepelyshev, A., Generalized Latin hypercube design for computer experiments, Technometrics, 52, 421-429 (2010)
[9] Dixon, Lcw; Szego, Gp, The global optimization problem: an introduction, Towards Glob Optim, 2, 1-15 (1978)
[10] Fang, Kt; Li, R.; Sudjianto, A., Design and modeling for computer experiments (2005), New York: CRC Press, New York
[11] Gramacy, Rb; Lee, Hkh, Bayesian treed Gaussian process models with an application to computer modeling, J Am Stat Assoc, 103, 483, 1119-1130 (2008) · Zbl 1205.62218
[12] Gramacy, Rb; Lee, Hkh, Adaptive design and analysis of supercomputer experiments, Technometrics, 51, 2, 130-145 (2009)
[13] Gramacy, Rb; Lee, Hk, Cases for the nugget in modeling computer experiments, Stat Comput, 22, 3, 713-722 (2012) · Zbl 1252.62098
[14] Gramacy RB, Taddy MA (2016) tgp: Bayesian treed Gaussian process models. R package version 2-4-14
[15] Greenberg, D., A numerical model investigation of tidal phenomena in the Bay of Fundy and Gulf of Maine, Mar Geod, 2, 161-187 (1979)
[16] Gu M, Palomo J, Berger J (2018) RobustGaSP: robust Gaussian stochastic process emulation. R package version 0.5.6
[17] Iman, Rl; Conover, Wj, A distribution-free approach to inducing rank correlation among input variables, Commun Stat Part B Simul Comput, 11, 311-334 (1982) · Zbl 0496.65071
[18] Johnson, M.; Moore, L.; Ylvisaker, D., Minimax and maximin distance design, J Stat Plan Inference, 26, 131-148 (1990)
[19] Joseph, Vr; Dasgupta, T.; Tuo, R.; Wu, Cj, Sequential exploration of complex surfaces using minimum energy designs, Technometrics, 57, 64-74 (2015)
[20] Joseph, Vr; Gul, E.; Ba, S., Maximum projection designs for computer experiments, Biometrika, 102, 371-380 (2015) · Zbl 1452.62593
[21] Joseph, Vr; Hung, Y., Orthogonal-maximin Latin hypercube designs, Stat Sin, 18, 171-186 (2008) · Zbl 1137.62050
[22] Lam, Cq; Notz, Wi, Sequential adaptive designs in computer experiments for response surface model fit, Stat Appl, 6, 207-233 (2008)
[23] Linkletter, C.; Bingham, D.; Hengartner, N.; Higdon, D.; Ye, Kq, Variable selection for Gaussian process models in computer experiments, Technometrics, 48, 4, 478-490 (2006)
[24] Loeppky, Jl; Moore, Lm; Williams, Bj, Batch sequential designs for computer experiments, J Stat Plan Inference, 140, 6, 1452-1464 (2010) · Zbl 1185.62142
[25] Loeppky, Jl; Sacks, J.; Welch, Wj, Choosing the sample size of a computer experiment: a practical guide, Technometrics, 51, 4, 366-376 (2009)
[26] MacDonald B, Ranjan P, Chipman H (2015) GPfit: an R package for Gaussian process model fitting using a new optimization algorithm. R package version 1.0-1
[27] Mckay, Md; Beckman, Rj; Conover, Wj, A comparison of three methods for selecting values of input variables in the analysis of output from a computer code, Technometrics, 21, 239-45 (1979) · Zbl 0415.62011
[28] Morris, Md; Mitchell, Tj, Exploratory designs for computer experiments, J Stat Plan Inference, 43, 381-402 (1995) · Zbl 0813.62065
[29] Owen, Ab, Orthogonal arrays for computer experiments, integration and visualization, Stat Sin, 2, 439-452 (1992) · Zbl 0822.62064
[30] Palomo, J.; Paulo, R.; Garcia-Donato, G., SAVE: an r package for the statistical analysis of computer models, J Stat Softw, 64, 13, 1-23 (2015)
[31] Park JS (1991) Tuning complex computer codes to data and optimal designs. Unpublished Ph.D. thesis, University of Illinois, Champaign-Urbana
[32] Roustant O, Ginsbourger D, Deville Y (2018) DiceKriging: kriging methods for computer experiments. R package version 1.5.6
[33] Ranjan, P.; Bingham, D.; Michailidis, G., Sequential experiment design for contour estimation from complex computer codes, Technometrics, 50, 4, 527-541 (2008)
[34] Rasmussen, Ce; Williams, Cki, Gaussian processes for machine learning (2006), Cambridge, MA: The MIT Press, Cambridge, MA
[35] Santner, Tj; Williams, Bj; Notz, Wi, The design and analysis of computer experiments (2003), New York: Springer, New York
[36] Sacks, J.; Schiller, Sb; Welch, Wj, Designs for computer experiments, Technometrics, 31, 41-47 (1989)
[37] Sacks, J.; Schiller, S.; Gupta; Berger, Spatial designs, Statistical decision theory and related topics IV, 385-399 (1988), New York: Springer, New York
[38] Sacks, J.; Welch, Wj; Mitchell, Tj; Wynn, Hp, Design and analysis of computer experiments, Stat Sci, 4, 409-423 (1989) · Zbl 0955.62619
[39] Tang, B., Orthogonal array-based Latin hypercubes, J Am Stat Assoc, 88, 1392-1397 (1993) · Zbl 0792.62066
[40] Zhang, R.; Lin, Cd; Ranjan, P., Local approximate Gaussian process model for large-scale dynamic computer experiments, J Comput Graph Stat, 27, 798-807 (2018)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.