Additive Gaussian Process for Computer Models With Qualitative and Quantitative Factors

References

• Ba, S., and Joseph, V. R. (2012), “Composite Gaussian Process Models for Emulating Expensive Functions,” The Annals of Applied Statistics, 6, 1838–1860.
   Web of Science ®Google Scholar
• Ba, S., Myers, W. R., and Brenneman, W. A. (2015), “Optimal Sliced Latin Hypercube Designs,” Technometrics, 57, 479–487.
   Web of Science ®Google Scholar
• Bhuiyan, H., Chen, J., Khan, M., and Marathe, M. V. (2014), “Fast Parallel Algorithms for Edge-Switching to Achieve a Target Visit Rate in Heterogeneous Graphs,” Parallel Processing (ICPP), 2014 43rd International Conference on IEEE,pp. 60–69.
   Google Scholar
• Deng, X., Hung, Y., and Lin, C. D. (2015), “Design for Computer Experiments With Qualitative and Quantitative Factors,” Statistica Sinica, 25, 1567–1581.
   Google Scholar
• Durrande, N., Ginsbourger, D., Roustant, O., and Carraro, L. (2011), “ Additive Covariance Kernels for High-Dimensional Gaussian Process Modeling,” arXiv preprint arXiv:1111.6233.
   Google Scholar
• Duvenaud, D. K., Nickisch, H., and Rasmussen, C. E. (2011), “Additive Gaussian Processes,” Advances in Neural Information Processing Systems, pp. 226–234.
   Google Scholar
• Fang, K. T., Li, R., and Sudjianto, A. (2005), Design and Modeling for Computer Experiments, New York: Chapman & Hall/CRC Press.
   Google Scholar
• Han, G., Santner, T. J., Notz, W. I., and Bartel, D. L. (2009), “Prediction for Computer Experiments Having Quantitative and Qualitative Input Variables,” Technometrics, 51, 278–288.
   Web of Science ®Google Scholar
• Hastie, T. J., and Tibshirani, R. J. (1990), Generalized Additive Models, New York: CRC Press.
   Google Scholar
• Horn, R. A., and Johnson, C. R. (2012), Matrix Analysis ( 2nd ed.), New York: Cambridge University Press.
   Google Scholar
• Joseph, V. R., and Delaney, J. D. (2007), “Functionally Induced Priors for the Analysis of Experiments,” Technometrics, 49, 1–11.
   Web of Science ®Google Scholar
• Kaufman, C. G., Bingham, D., Habib, S., Heitmann, K., and Frieman, J. A. (2011), “Efficient Emulators of Computer Experiments Using Compactly Supported Correlation Functions, With an Application to Cosmology,” The Annals of Applied Statistics, 5, 2470–2492.
   Web of Science ®Google Scholar
• Liu, K.-W., and Rowe, R. K. (2015), “Numerical Study of the Effects of Geosynthetic Reinforcement Viscosity on Behaviour of Embankments Supported by Deep-Mixing-Method (DMM) Columns,” Geotextiles and Geomembranes, 43, 567–578.
   Google Scholar
• Matern, B. (1986), Spatial Variation ( 2nd ed.), New York: Springer-Verlag.
   Google Scholar
• 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.
   Web of Science ®Google Scholar
• 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.
   PubMedGoogle Scholar
• Pinheiro, J. C., and Bates, D. M. (1996), “Unconstrained Parametrizations for Variance-Covariance Matrices,” Statistics and Computing, 6, 289–296.
   Web of Science ®Google Scholar
• Qian, P. Z. G., Wu, H., and Wu, C. F. J. (2008), “Gaussian Process Models for Computer Experiments With Qualitative and Quantitative Factors,” Technometrics, 50, 283–396.
   Web of Science ®Google Scholar
• Rebonato, R., and Jackel, P. (1999), “The Most General Methodology for Creating a Valid Correlation Matrix for Risk Management and Option Pricing Purposes,” The Journal of Risk, 2, 17–27.
   Google Scholar
• Reich, B. J., Storlie, C. B., and Bondell, H. D. (2009), “Variable Selection in Bayesian Smoothing Spline ANOVA Models: Application to Deterministic Computer Codes,” Technometrics, 51, 110–120.
   PubMed Web of Science ®Google Scholar
• Rowe, R. K., and Liu, K.-W. (2015), “3D Finite Element Modeling of a Full-Scale Geosynthetic-Reinforced, Pile-supported Embankment,” Canadian Geotechnical Journal, 52, 2041–2054.
   Google Scholar
• Sacks, J., Welch, W. J., Mitchell, T. J., and Wynn, H. P. (1989), “Design and Analysis of Computer Experiments,” Statistical Science, 4, 409–423.
   Google Scholar
• Santner, T. J., Williams, B. J., and Notz, W. I. (2003), The Design and Analysis of Computer Experiments, New York: Springer.
   Google Scholar
• Swiler, L. P., Hough, P. D., Qian, P., Xu, X., Storlie, C., and Lee, H. (2014), “Surrogate Models for Mixed Discrete-Continuous Variables,” in Constraint Programming and Decision Making, M. Ceberio and V. Kreinovich(eds.), New York: Springer, pp. 181–202.
   Google Scholar
• Wu, C. F. J., and Hamada, M. (2009), Experiments: Planning, Analysis, and Optimization, New York: Wiley.
   Google Scholar
• Zhang, Y., and Notz, W. I. (2015), “Computer Experiments With Qualitative and Quantitative Variables: A Review and Reexamination,” Quality Engineering, 27, 2–13.
   Web of Science ®Google Scholar
• Zhou, Q., Qian, P. Z. G., and Zhou, S. (2011), “A Simple Approach to Emulation for Computer Models With Qualitative and Quantitative Factors,” Technometrics, 53, 266–273.
   Web of Science ®Google Scholar