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Follow-up experimental designs for computer models and physical processes. (English) Zbl 05902640
Summary: In many branches of physical science, when the complex physical phenomena are either too expensive or too time consuming to observe, deterministic computer codes are often used to simulate these processes. Nonetheless, true physical processes are also observed in some disciplines. It is preferred to integrate both the true physical process and the computer model data for better understanding of the underlying phenomena. In this paper, we develop a methodology for selecting optimal follow-up designs based on integrated mean squared error that help us capture and reduce prediction uncertainty as much as possible. We also compare the efficiency of the optimal designs with the intuitive choices for the follow-up computer and field trials.

MSC:
62 Statistics
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[1] Crary, SB, Design of computer experiments for metamodel generation, Analog Integrated Circuits and Signal Processing, 32, 7-16 (2002)
[2] Currin, C.; Mitchell, T.; Morris, M.; Ylvisaker, D., Bayesian prediction of deterministic functions with applications to the design and analysis of computer experiments, Journal of the American Statistical Association, 86, 953-963 (1991)
[3] Harris, CM; Hoffman, KL; Yarrow, L-A, Obtaining minimum-correlation Latin hypercube sampling plans using an IP-based heuristic, OR Spektrum, 17, 139-148 (1995) · Zbl 0840.62060
[4] Higdon, D., Kennedy, M., Cavendish, J.C., Cafeo, J.A. Ryne, R.D., 2004. Combining field data and computer simulation for calibration and prediction. SIAM Journal on Scientific Computing, 26, 448-466. · Zbl 1072.62018
[5] Johnson, ME; Moore, LM; Ylvisaker, D., Minimax and maximin distance designs, Journal of Statistical Planning and Inference, 26, 131-148 (1990)
[6] Jones, DR; Schonlau, M.; Welch, WJ, Efficient global optimization of expensive black-box functions, Journal of Global Optimization, 13, 455-492 (1998) · Zbl 0917.90270
[7] Kennedy, MC; O’Hagan, A., Bayesian calibration of computer models (with discussion), Journal of the Royal Statistical Society, Series B, 63, 424-462 (2001) · Zbl 1007.62021
[8] McKay, MD; Conover, WJ; Beckman, RJ, A comparison of three methods for selecting the input variables in the analysis of the output from a computer code, Technometrics, 21, 239-245 (1979) · Zbl 0415.62011
[9] Miller, AJ, A Fedorov exchange algorithm for D-optimal design, Journal of the Royal Statistical Society, Series B, 43, 669-677 (1994)
[10] Owen, AB, Latin supercube sampling for very high-dimensional simulations, ACM Trans. Model. Comput. Simul., 8, 71-102 (1998) · Zbl 0917.65022
[11] Sacks, J.; Schiller, SB; Welch, WJ, Design for computer experiments, Technometrics, 31, 41-47 (1992)
[12] Sacks, J.; Welch, WJ; Mitchell, T.; Wynn, HP, Designs and analysis of computer experiments (with discussion), Statistical Science, 4, 409-435 (1989) · Zbl 0955.62619
[13] Santner, T.J., Williams, B.J., Notz, W.I., 2003. The Design and Analysis of Computer Experiments. Springer, New York.
[14] Schonlau, M.; Welch, WJ; Jones, DR; Flournoy, N. (ed.); Rosenberg, WF (ed.); Wong, WK (ed.), Global versus local search in constrained optimization of computer models, 11-25 (1998)
[15] Schur, I., Potenzreihn im innern des einheitskreises, J. Reine. Angew. Math, 147, 202-232 (1917)
[16] Tang, B., Orthogonal array-based Latin hypercubes, Journal of the American Statistical Association, 88, 1392-1397 (1993) · Zbl 0792.62066
[17] Welch, W.; Buck, R.; Sacks, J.; Wynn, H.; Mitchell, T.; Morris, M., Screening, predicting, and computer experiments, Technometrics, 34, 15-25 (1992)
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