Gaussian process models for computer experiments with qualitative and quantitative factors

Technometrics

Volumn 50, Issue 3, 2008, Pages 383-396

  Qian, Peter Z G ^a   Wu, Huaiqing ^b   Wu, C F Jeff ^c  

^a University of Wisconsin Madison   (United States)

^b Department of Statistics Center for Statistics and Applications in Forensic Evidence Iowa State University 2438 Osborn Dr Ames   (United States)

^c Georgia Institute of Technology   (United States)

Author keywords

Cokriging; Design of Experiments; Kriging; Multivariate Gaussian Process; Semidefinite Programming.

Indexed keywords

COMPUTER SYSTEMS; CORRELATION METHODS; DESIGN OF EXPERIMENTS; EXPERIMENTS; GAUSSIAN DISTRIBUTION; GAUSSIAN NOISE (ELECTRONIC); MAXIMUM LIKELIHOOD ESTIMATION; PROBABILITY DENSITY FUNCTION; PROCESS MONITORING; TRELLIS CODES;

COKRIGING; COMPUTER EXPERIMENTS; COMPUTER MODELING; CORRELATION FUNCTIONS; DATA CENTERS; GAUSSIAN PROCESS MODELS; ITERATIVE ESTIMATIONS; KRIGING; MULTIVARIATE GAUSSIAN PROCESS; NEW MODELS; OPTIMIZATION TECHNIQUES; QUANTITATIVE FACTORS; REAL EXAMPLES; SEMIDEFINITE PROGRAMMING.;

PROCESS ENGINEERING;

EID: 55149088117     PISSN: 00401706     EISSN: None     Source Type: Journal    
DOI: 10.1198/004017008000000262     Document Type: Article

References (41)

1. Abrahamsen, P. (1997), "A Review of Gaussian Random Fields and Correlation Functions," Report 917, Norwegian Computer Center, available at http://publications.nr.no/917Rapport.pdf.
2. Banerjee, S., and Gelfand, A. E. (2002), "Prediction, Interpolation and Regression for Spatially Misaligned Data," Sankhya, 64, 227-245.
3. Bartholomew, D. J., and Knott, M. (1999), Latent Variable Models and Factor Analysis, London: Arnold.
4. Bertsekas, D. P. (1999), Nonlinear Programming, Nashua, NH: Athena Scientific.
5. Boscardin, W. J., and Zhang, X. (2004), "Modeling the Covariance and Correlation Matrix of Repeated Measures," in Applied Bayesian Modeling and Causal Inference From Incomplete-Data Perspectives, eds. A. Gelman and X.-L. Meng, New York: Wiley, pp. 215-226.
6. Box, G. E. P., and Jenkins, G. M. (1976), Time Series Analysis: Forecasting and Control, San Francisco: Holden-Day.
7. Brown, P. J., Le, N. D., and Zidek, J. V. (1994), "Multivariate Spatial Interpolation and Exposure to Air Pollutants," The Canadian Journal of Statistics, 22, 489-509.
8. Dattorro, J. (2005), Convex Optimization and Euclidean Distance Geometry, Palo Alto, CA: Meboo Publishing.
9. Dempster, A. P., Laird, N. M., and Rubin, D. B. (1977), "Maximum Likelihood From Incomplete Data via the EM Algorithm," Journal of the Royal Statistical Society, Ser. B, 39, 1-38.
10. Edwards, D. M. (2000), Introduction to Graphical Modeling, New York: Springer.
11. Fang, K. F., Li, R. Z., and Sudjianto, A. (2005), Design and Modeling for Computer Experiments, New York: Chapman & Hall/CRC Press.
12. Flometrics (2005), "Flotherm: Fluid Dynamics-Based Thermal Analysis Software," available at http://www.flomerics.com/.
13. Fluent, Inc. (1998), FLUENT, Release 5.5.14 (3d, segregated, laminar), Lebanon: Author.
14. Fridlyander, I. N. (2002), "Modern Aluminum and Magnesium Alloys and Composite Materials Based on Them," Metal Science and Heat Treatment, 44, 292-296.
15. Gelman, A., Carlin, J. B., Stern, H. S., and Rubin, D. B. (2004), Bayesian Data Analysis, Boca Raton, FL: Chapman & Hall/CRC Press.
16. Golub, G. H., and Van Loan, C. F. (1996), Matrix Computation, Baltimore: The Johns Hopkins University Press.
17. Graham, A. (1981), Kronecker Products and Matrix Calculus With Applications, Chichester, U.K.: Ellis Horwood Limited.
18. Grant, M., Boyd, S., and Ye, Y. (2006), CVX: Matlab Software for Disciplined Convex Programming, version 1.0 beta 3, Dept. of Managment Science and Engineering, Stanford University, available at http://www. stanford.edu/̃boyd/cvx/.
19. Han, G., Santner, T. J., Notz, W. I., and Bartel, D. L. (2007), "Prediction for Computer Experiments Having Quantitative and Qualitative Input Variables," Dept. of Statistics, Ohio State University, http://www.stat.osu.edu/̃hangang/hqqv_09_05.pdf.
20. Handcock, M. S., and Stein, M. L. (1993), "A Bayesian Analysis of Kriging," Technometrics, 35, 403-410.
21. Handcock, M. S., Meier, K., and Nychka, D. (1994), Comment on "Kriging and Splines: An Empirical Comparison of Their Predictive Performance in Some Applications," by G. M. Laslett, Journal of the American Statistical Association, 89, 401-403.
22. Joseph, V. R., and Delaney, J. D. (2007), "Functionally Induced Priors for the Analysis of Experiments," Technometrics, 49, 1-11.
23. Katz, M. H. (2006), Multivariable Analysis: A Practical Guide for Clinicians, Cambridge, U.K.: Cambridge University Press.
24. Lauritzen, S. L. (1996), Graphical Models, Oxford, U.K.: Clarendon Press.
25. Li, R., and Sudjianto, A. (2005), "Analysis of Computer Experiments Using Penalized Likelihood in Gaussian Kriging Models," Technometrics, 47, 111-120.
26. Liu, J. S. (2001), Monte Carlo Strategies in Scientific Computing, New York: Springer.
27. Mardia, K. V., and Goodall, C. R. (1993), "Spatial-Temporal Analysis of Multivariate Environmental Monitoring Data," in Multivariate Environmental Statistics, eds. G. P. Patil and C. R. Rao, Amsterdam: Elsevier, pp. 347-386.
28. McMillian, N. J., Sacks, J., Welch, W. J., and Gao, F. (1999), "Analysis of Protein Activity Data by Gaussian Stochastic Process Models," Journal of Biopharmaceutical Statistics, 9, 145-160.
29. Nesterov, Y., and Nemirovskii, A. (1994), "Intenor-Point Polynomial Algorithms in Convex Programming," in SIAM Studies in Applied Mathematics, 13, Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM).
30. Ruszczynski, A., and Shapiro, A. (eds.) (2003), Stochastic Programming, Amsterdam: Elsevier.
31. Sacks, J., Welch, W. J., Mitchell, T. J., and Wynn, H. P. (1989), "Design and Analysis of Computer Experiments," Statistical Science, 4, 409-435.
32. Santner, T. J., Williams, B. J., and Notz, W. I. (2003), The Design and Analysis of Computer Experiments, New York: Springer.
33. Schmidt, R. R. (2003), "Hot Spots in Data Centers," Online Forum of Electrical Cooling, available at http://www.electronics-cooling. com.
34. Schmidt, R. R., Cruz, E. E., and Iyengar, M. K. (2005), "Challenges of Data Center Thermal Management," IBM Journal of Research and Development, 49, 709-723.
35. Stein, M. L. (1999), Interpolation of Spatial Data, New York: Springer.
36. The MathWorks, Inc. (2006), Matlab: The Language of Technical Computing, version 6.5.1, Natick, MA: Author.
37. Vandenberghe, L., and Boyd, S. (1996), "Semidefinite Programming," SIAM Review, 38, 49-95.
38. 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.
39. Wolkowicz, H., Saigal, R., and Vandenberghe, L. (eds.) (2000), Handbook of Semidefinite Programming: Theory, Algorithms, and Applications, Boston: Kluwer Academic.
40. Wu, C. F. J., and Ding, Y. (1998), "Construction of Response Surface Designs for Qualitative and Quantitative Factors," Journal of Statistical Planning and Inference, 71, 331-348.
41. Wu, C. F. J., and Hamada, M. (2000), Experiments: Planning, Analysis, and Parameter Design Optimization, New York: Wiley.