×

On the interface between nested designs and the multi-step interpolator. (English) Zbl 1477.62216

Summary: Gaussian process or RKHS interpolator is often used to emulate computer experiments. For large-scale computer experiments, the multi-step interpolator is introduced by B. Haaland and P. Z. G. Qian [Ann. Stat. 39, No. 6, 2974–3002 (2011; Zbl 1246.65172)] to mitigate the nominal and numeric errors and improve the accuracy of emulation. In this paper, we investigate the impact of experimental design and parameter setting on the accuracy of the RKHS interpolator. In conjunction with a nested version of the MaxPro design [V. R. Joseph et al., Biometrika 102, No. 2, 371–380 (2015; Zbl 1452.62593)], we find that the prediction accuracy of the multi-step interpolator can be further improved. Numerical experiments are provided to validate our findings.

MSC:

62K99 Design of statistical experiments
62F15 Bayesian inference
62K05 Optimal statistical designs
62D05 Sampling theory, sample surveys
62K10 Statistical block designs
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Ba S (2015) SLHD: maximin-distance (sliced) Latin hypercube designs. r package version 2.1-1
[2] Ba S, Joseph VR (2018) MaxPro: maximum projection designs. R package version 4.1-2. https://cran.r-project.org/web/packages/MaxPro/. Accessed 11 June 2021
[3] 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, 953-963 (1991) · doi:10.1080/01621459.1991.10475138
[4] Floater, MS; Iske, A., Multistep scattered data interpolation using compactly supported radial basis functions, J Comput Appl Math, 73, 65-78 (1996) · Zbl 0859.65006 · doi:10.1016/0377-0427(96)00035-0
[5] Franco J, Dupuy D, Roustant O, Damblin G, Iooss B, Helbert MC (2015) Package ‘DiceDesign’
[6] Genz A (1984) Testing multidimensional integration routines. In: Proceedings of international conference on tools, methods and languages for scientific and engineering computation, pp 81-94
[7] Gramacy, RB, laGP: large-scale spatial modeling via local approximate Gaussian processes in R, J Stat Softw, 72, 1-46 (2016) · doi:10.18637/jss.v072.i01
[8] Haaland, B.; Qian, PZ, Accurate emulators for large-scale computer experiments, Ann Stat, 39, 2974-3002 (2011) · Zbl 1246.65172 · doi:10.1214/11-AOS929
[9] Haaland, B.; Wang, W.; Maheshwari, V., A framework for controlling sources of inaccuracy in Gaussian process emulation of deterministic computer experiments, SIAM/ASA J Uncertain Quantif, 6, 497-521 (2018) · Zbl 1403.62143 · doi:10.1137/17M1131210
[10] Joseph, VR; Gul, E.; Ba, S., Maximum projection designs for computer experiments, Biometrika, 102, 371-380 (2015) · Zbl 1452.62593 · doi:10.1093/biomet/asv002
[11] Laguna, M.; Marti, R., Experimental testing of advanced scatter search designs for global optimization of multimodal functions, J Glob Optim, 33, 235-255 (2005) · Zbl 1093.90092 · doi:10.1007/s10898-004-1936-z
[12] Mitchell, TJ; Morris, MD, Bayesian design and analysis of computer experiments: two examples, Stat Sin, 2, 359-379 (1992) · Zbl 0827.62029
[13] Morris, MD; Mitchell, TJ, Exploratory designs for computational experiments, J Stat Plan Inference, 43, 381-402 (1995) · Zbl 0813.62065 · doi:10.1016/0378-3758(94)00035-T
[14] Qian, PZ, Nested Latin hypercube designs, Biometrika, 96, 957-970 (2009) · Zbl 1179.62103 · doi:10.1093/biomet/asp045
[15] Sacks, J.; Welch, WJ; Mitchell, TJ; Wynn, HP, Design and analysis of computer experiments, Stat Sci, 4, 409-423 (1989) · Zbl 0955.62619
[16] Stein, M., Large sample properties of simulations using Latin hypercube sampling, Technometrics, 29, 143-151 (1987) · Zbl 0627.62010 · doi:10.1080/00401706.1987.10488205
[17] Zammit-Mangion, A.; Cressie, N., FRK: an R package for spatial and spatio-temporal prediction with large datasets, J Stat Softw, 98, 4, 1-48 (2021) · doi:10.18637/jss.v098.i04
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.