Bayesian design and analysis of computer experiments: Use of derivatives in surface prediction

Technometrics

Volumn 35, Issue 3, 1993, Pages 243-255

  Morris, Max D ^a   Mitchell, Toby J ^a   Ylvisaker, Donald ^b  

^a OAK RIDGE NATIONAL LABORATORY   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Bayesian prediction; Computer model; Interpolation; Latin hypercube design; Maximin distance design; Sensitivity analysis

Indexed keywords

EID: 0000923281     PISSN: 00401706     EISSN: 15372723     Source Type: Journal    
DOI: 10.1080/00401706.1993.10485320     Document Type: Article

References (29)

1. Aitken, A. C. (1956), Determinants and Matrices (9th ed.), Edinburgh and London: Oliver and Boyd.
2. Alsmiller, R. G., Barish, J., Drischler, J. D., Horwedel, J. E., Lucius, J. L., and McAdoo, J. W. (1983), “Sensitivity Theory and Its Application to a Large Energy-Economics Model,” Operations Research, 31, 915-937.
3. Bohachevsky, I. O., Johnson, M. E., and Stein, M. L. (1986), “Generalized Simulated Annealing for Function Optimization,” Technometrics, 28, 209-217.
4. Currin, C., Mitchell, T., Morris, M., and Ylvisaker, D. (1991), “Bayesian Prediction of Deterministic Functions, With Applications to the Design and Analysis of Computer Experiments,” Journal of the American StatisticalAssociation, 86, 953- 963.
5. Griewank, A. (1989), “On Automatic Differentiation,” in Mathematical Programming: Recent Developments and Applications, eds. M. Ira and K. Tanabe, Boston: Kluwer, pp. 83-108.
6. Griewank, A. (1991a), “The Chain Rule Revisited in Scientific Computing,” SIAM News, 24, 20-21.
7. Griewank, A. (1991b), “The Chain Rule Revisited in Scientific Computing, Part II,” SIAM News, 24, 8-9, 24.
8. Hall, M. C. G., Cacuci, D., and Schlesinger, M. E. (1982), “Sensitivity Analysis of a Radiative-Convective Model by the Adjoint Method,” Journal of the Atmospheric Sciences, 39, 2038- 2050.
9. Harper, W. V., and Gupta, S. K. (1983), “Sensitivity/Uncertainty Analysis of a Borehole Scenario Comparing Latin Hypercube Sampling and Deterministic Sensitivity Approaches,” BMI/ONWI-516, Office of Nuclear Waste Isolation, Battelle Memorial Institute, Columbus, OH.
10. Johnson, M., Moore, L., and Ylvisaker, D. (1990), “Minimax and Maximin Distance Designs,” Journal of Statistical Planning and Inference, 26, 131-148.
11. Kirkpatrick, S., Gelatt, C. D., Jr., and Vechhi, M. P. (1983), “Optimization by Simulated Annealing,” Science, 220, 671- 680.
12. Marable, J. H., Weisbin, C. R., and de Saussure, G. (1980), “Uncertainty in the Breeding Ratio of a Large Liquid-Metal Fast Breeder Reactor: Theory and Results,” Nuclear Science and Engineering, 75, 30-55.
13. McKay, M. D., Conover, W. J., and Beckman, R. J. (1979), “A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output From a Computer Code,” Technometrics, 21, 239-245.
14. Mitchell, T. J., Morris, M. D., and Ylvisaker, D. (1990), “Existence of Smoothed Stationary Processes on an Interval,” Srochastic Processes and their Application, 35, 109-119.
15. Oblow, E. M. (1985), “GRESS, Gradient-Enhanced Software System-Version D User’s Guide,” ORNLITM-9658, Oak Ridge National Laboratory, Oak Ridge, TN.
16. Oblow, E. M., Pin, F. G., and Wright, R. Q. (1986), “Sensitivity Analysis Using Computer Calculus: A Nuclear Waste Application,” Nuclear Science and Engineering, 94, 46.
17. Owen, A. (1990), “Controlling Correlations in Latin Hypercube Sampling,” technical report, available from author.
18. Park, J.-S. (1991), “Tuning Complex Computer Codes to Data and Optimal Designs,” unpublished Ph.D. thesis, University of Illinois, Dept. of Statistics.
19. Parzen, E. (1962) Stochastic Processes, San Francisco: Holden- Day.
20. Paterson, H. D. (1954), “The Errors of Lattice Sampling,” Journal of the Royal Statistical Society, Ser. B, 16, 140-149.
21. Sacks, J., Schiller, S. B., and Welch, W. J. (1989), “Designs for Computer Experiments,” Technometrics, 31, 41-47.
22. Sacks, J., Welch, W. J., Mitchell, T. J., and Wynn, H. P. (1989) “Design and Analysis of Computer Experiments,” Statisfical Science, 4, 409-423.
23. Shewry, M. C., and Wynn, H. P. (1987), “Maximum Entropy Sampling,” Journal of Applied Statistics, 14, 165- 170.
24. Stein, M. L. (1989), Discussion of “Design and Analysis of Computer Experiments,” by J. Sacks, W. J. Welch, T. J. Mitchell, and H. P. Wynn, Statistical Science, 4, 432-433.
25. Tang, B. (in press), “OA-Based Latin Hypercubes,” Journal of the American Statistical Association, 88.
26. Welch, W. J., Buck, R. J., Sacks, J., Wynn, H. P., Mitchell, T. J., and Morris, M. D. (1992), “Screening, Predicting, and Computer Experiments,” Technometrics, 34, 15-25.
27. Worley, B. A. (1987), “Deterministic Uncertainty Analysis,” ORNL-6428, available from National Technical Information Service, 5285 Port Royal Road, Springfield, VA 22161.
28. Worley, B. A., Wright, R. Q., Pin, F. G., and Harper, W. V. (1986), “Application of an Automated Procedure for Adding a Comprehensive Sensitivity Calculation Capability to the ORIGEN2 Point Depletion and Radioactivity Decay Code,” Nuclear Science and Engineering, 94, 180.
29. Ylvisaker, D. (1987), “Prediction and Design,” The Annals of Statistics, 15, l-19.