Comparing and generating Latin Hypercube designs in Kriging models

AStA Advances in Statistical Analysis

Volumn 94, Issue 4, 2010, Pages 353-366

  Pistone, Giovanni ^a   Vicario, Grazia ^b  

^a Laboratorio R Revelli Collegio Carlo Alberto   (Italy)

^b POLITECNICO DI TORINO   (Italy)

Author keywords

Computer experiments; Gaussian linear prediction; Latin hypercube; Mean square prediction error

Indexed keywords

EID: 78650730077     PISSN: 18638171     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10182-010-0142-1     Document Type: Article

References (27)

1. Bates, R. A., Buck, R. J., Riccomagno, E., Wynn, H. P.: Experimental designs and observations for large systems. J. R. Stat. Soc. B 58, 77-94 (1996).
2. Berg, C., Christensen, J. P. R., Ressel, P.: Harmonic Analysis on Semigroups. Theory of Positive Definite and Related Functions. Graduate Texts in Mathematics, vol. 100. Springer, New York (1984).
3. Butler, N. A.: Optimal and orthogonal Latin Hypercube designs for computer experiments. Biometrika 88(3), 847-857 (2001).
4. Catanese, F., Hoşten, S., Khetan, A., Sturmfels, B.: The maximum likelihood degree. Am. J. Math. 128(3), 671-697 (2006).
5. CoCoATeam (online) CoCoA: a system for doing computations in commutative algebra. Available at cocoa. dima. unige. it.
6. Cressie, N.: Kriging nonstationary data. J. Am. Stat. Assoc. 81(395), 625-634 (1986).
7. Fang, K. T., Lin, D. K. J., Winker, P., Zhang, Y.: Uniform design: theory and application. Technometrics 42(3), 237-248 (2000).
8. Fang, K. T., Li, R., Sudjianto, A.: Design and Modeling for Computer Experiments. Computer Science and Data Analysis Series. Chapman & Hall/CRC, Boca Raton, FL (2006).
9. Gibilisco, P., Riccomagno, E., Rogantin, M., Wynn, H. P. (eds.): Algebraic and Geometric Methods in Statistics. Cambridge University Press, Cambridge (2009).
10. Jourdan, A., Franco, J.: Optimal Latin hypercube designs for the Kullback-Leibler criterion. Adv. Stat. Anal. 94(4), 341-351 (2010).
11. Krige, D. G.: A statistical approach to some basic mine valuation problems on the witwatersrand. J. Chem. Metall. Min. Soc. S. Afr. 52(6), 119-139 (1951).
12. Lauritzen, S. L.: Graphical Models. Clarendon/Oxford University Press, New York (1996),.
13. Levy, S. Steinberg, D. M.: Computer experiments: a review. Adv. Stat. Anal. 94(4), 311-324 (2010).
14. McKay, M. D., Beckman, R. J., Conover, W. J.: A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 21, 239-245 (1979).
15. Morris, M. D., Mitchell, T. J.: Exploratory designs for computational experiments. J. Stat. Plan. Inference 43(3), 381-402 (1995).
16. Ortega, J. M.: Matrix Theory. The University Series in Mathematics. Plenum, New York (1987), a second course.
17. Park, J. S.: Optimal Latin-hypercube designs for computer experiments. J. Stat. Plan. Inference 39(1), 95-111 (1994).
18. Petelet, M., Iooss, B., Asserin, O., Loredo, A.: Latin hypercube sampling with inequality constraints. Adv. Stat. Anal. 94(4), 325-339 (2010).
19. Pistone, G., Vicario, G.: Random generation of designs in computer experiments. In: Statistics for Innovation. Statistical Design of "Continuous" Product Innovation. Springer, Berlin, pp. 91-102 (2009).
20. Sacks, J., Schiller, S. B., Welch, W. J.: Designs for computer experiments. Technometrics 31(1), 41-47 (1989a).
21. Sacks, J., Welch, W. J., Mitchell, T. J., Wynn, H. P.: Design and analysis of computer experiments (with discussion). Stat. Sci. 4, 409-435 (1989b).
22. Santner, T. J., Williams, B. J., Notz, W. I.: The Design and Analysis of Computer Experiments. Springer Series in Statistics. Springer, New York (2003).
23. Sasena, M. J.: Flexibility and efficiency enhancements for constrained global design optimization with Kriging approximations. PhD thesis. University of Michigan (2002).
24. Shewry, M. C., Wynn, H. P.: Maximum entropy sampling. J. Appl. Stat. 14, 165-170 (1987).
25. Tang, B.: Orthogonal array-based Latin hypercubes. J. Am. Stat. Assoc. 88(424), 1392-1397 (1993).
26. Welch, W. J., Buck, R. J., Sacks, J., Wynn, H. P., Mitchell, T. J., Morris, M. D. Screening, predicting, and computer experiment. Technometrics 34(1), 15-25 (1992).
27. Ye, K. Q., Li, W., Sudjianto, A.: Algorithmic construction of optimal symmetric Latin hypercube designs. J. Stat. Plan. Inference 90(1), 149-159 (2000).