Sequential experiment design for contour estimation from complex computer codes

Technometrics

Volumn 50, Issue 4, 2008, Pages 527-541

  Ranjan, Pritam ^a   Bingham, Derek ^a   Michailidis, George ^b  

^a SIMON FRASER UNIVERSITY   (Canada)

^b UNIVERSITY OF MICHIGAN   (United States)

Author keywords

Computer experiment; Gaussian process; Inverse problem

Indexed keywords

COMPUTER CODES; COMPUTER EXPERIMENT; CONTOUR ESTIMATIONS; DESIGN AND ANALYSIS OF COMPUTER EXPERIMENTS; ENGINEERING PROCESS; EXPERIMENT DESIGNS; GAIN INSIGHTS; GAUSSIAN PROCESS; KEY COMPONENTS; PRACTICAL IMPLEMENTATIONS; PROCESS OPTIMIZATIONS; QUEUING SYSTEMS; RESPONSE SURFACES; STOCHASTIC PROCESS MODELS; SURROGATE MODELS;

GAUSSIAN DISTRIBUTION; GAUSSIAN NOISE (ELECTRONIC); INVERSE PROBLEMS; STOCHASTIC MODELS; TRELLIS CODES; UNCERTAINTY ANALYSIS;

EXPERIMENTS;

EID: 54949098362     PISSN: 00401706     EISSN: None     Source Type: Journal    
DOI: 10.1198/004017008000000541     Document Type: Article

References (34)

1. Andre, J., Siarry, P., and Dognon, T. (2000), "An Improvement of the Standard Genetic Algorithm Fighting Premature Convergence," Advances in Engineering Software, 32, 49-60.
2. Balakrishnan, V., Boyd, S., and Balemi, S. (1991), "Branch and Bound Algorithm for Computing the Minimum Stability Degree of Parameter-Dependent Linear Systems," International Journal of Robust and Nonlinear Control, 1, 295-317.
3. Bambos, N., andMichailidis, G. (2004), "Queueing and Scheduling in Random Environments," Advances in Applied Probability, 36, 293-317.
4. Banerjee, S., and Gelfand, A. E. (2005), "BayesianWombling: Curvilinear Gradients Assessment Under Spatial Process Models," Journal of the American Statistical Association, 101, 1487-1501.
5. Barbujani, G., Oden, N. L., and Sokal, R. R. (1989), "Detecting Regions of Abrupt Change in Maps of Biological Variables," Systematic Zoology, 38, 376-389.
6. Brault, P., and Mounier, H. (2001), "Automated, Transformation- Invariant Shape Recognition Through Wavelet Multiresolution," in SPIE01, Proceedings of the International Society for Optical Engineering, San Diego, CA.
7. Dixon, L. C. W., and Szego, G. P. (1978), "The Global Optimization Problem: An Introduction," in Towards Global Optimization 2, eds. L. C. W. Dixon and G. P. Szego, Amsterdam: North-Holland, pp. 1-15.
8. Fang, K. T., Lin, D. K. J., Winker, P., and Zhang, Y. (2000), "Uniform Design: Theory and Applications," Technometrics, 42, 237-248.
9. Fletcher, R. (1987), Practical Methods of Optimization, New York: Wiley.
10. Henderson, C. R. (1975), "Best Linear Unbiased Estimation and Prediction Under a Selection Model," Biometrics, 31, 423-447.
11. Holland, J. H. (1975), Adaptation in Natural and Artificial Systems, Ann Arbor, MI: University of Michigan Press.
12. John, P. W. M., Johnson, M. E., Moore, L. M., and Ylvisaker, D. (1995), "Minimax Distance Designs in Two-Level Factorial Experiments," Jornal of Statistical Planning and Inference, 44, 249-263.
13. Johnson, M. E., Moore, L. M., and Ylvisaker, D. (1990), "Minimax and Maximin Distance Designs," Journal of Statistical Planning and Inference, 26, 131-148.
14. Jones, D. H., and Jin, Z. (1994), "Optimal Sequential Designs for On-Line Item Estimation," Psychometrika, 59, 57-75.
15. Jones, D., Schonlau, M., and Welch, W. (1998), "Efficient Global Optimization of Expensive Black-Box Functions," Journal of Global Optimization, 13, 455-492.
16. Levy, A. V., and Montalvo, A. (1985), "The Tunnelling Algorithm for the Global Minimization of Functions," SIAM Journal of Scientific and Statistical Computing, 6, 15-29.
17. Lu, H., and Carlin, B. P. (2005), "Bayesian Areal Wombling for Geographical Boundary Analysis," Geographical Analysis, 37, 265-285.
18. Mandal, A., Wu, C. F. J., and Johnson, K. (2006), "SELC: Sequential Elimination of Level Combinations by Means of Modified Genetic Algorithms," Technometrics, 48, 273-283.
19. McKay, M. D., Beckman, R. J., and Conover, W. 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.
20. Murty, K. G. (1995), Operations Research: Deterministic Optimization Models, Englewood Cliffs, NI: Prentice-Hall.
21. O'Connell, M., and Wolfinger, R. (1997), "Spatial Regression Models, Response Surfaces and Process Optimization," Journal of Computational and Graphical Statistics, 6, 224-241.
22. Owen, A. B. (1992), "Orthogonal Arrays for Computer Experiments, Integration and Visualization," Statistica Sinica, 2, 439-452.
23. Rao, C. R. (1972), "Estimation of Variance and Covariance Components in Linear Models," Journal of the American Statistical Association, 67, 112-115.
24. Rudin, W. (1987), Real and Complex Analysis (3rd ed.), New York: McGraw-Hill.
25. Sacks, J., Welch, W. J., Mitchell, T. J., and Wynn, H. P. (1989), "Design and Analysis of Computer Experiments," Statistical Science, 4, 409-423.
26. Santner, T. J., Williams, B. J., and Notz, W. I. (2003), The Design and Analysis of Computer Experiments, New York: Springer-Verlag.
27. Schittkowski, K. (1985), "NLQPL: A FORTRAN-Subroutine Solving Constrained Nonlinear Programming Problems," Annals of Operations Research, 5, 485-500.
28. Sethian, J. A. (1999), Level Set Methods and Fast Marching Methods, Cambridge, U.K.: Cambridge University Press.
29. Tang, B. (1993), "Orthogonal Array-Based Latin Hypercubes," Journal of the American Statistical Association, 88, 1392-1397.
30. Uhlir, K. (2003), "Modelling Methods With Implicitly Defined Objects," Technical Report DCSE/TR-2003-04, J. E. Purkinje University, Dept. of Urology.
31. Uhlir, K., and Skala, V. (2003), "Implicit Function Modelling System Comparison of C++ and C# Solutions," in Proceedings of C# and .NET Technologies 2003 Int. Workshop, Plozen, Czech Republic: UNION Agency-Science Press, pp. 87-92.
32. Veltkamp, R. C. (2001), "Shape Matching: Similarity Measures and Algorithms," in Proceedings of the Shape Modelling International Conference, Genova, Italy: IEEE, pp. 188-197.
33. Warland, J. (1988), Introduction to Queuing Networks, Englewood Cliffs, NI: Prentice-Hall.
34. Wolfinger, R. D., Tobias, R. D., and Sall, J. (1994), "Computing Gaussian Likelihoods and Their Derivatives for General Linear Mixed Models," SIAM Journal on Scientific Computing, 15, 1294-1310.