References
- Ankenman, B., Nelson, B. L., and Staum, J. (2010), “Stochastic Kriging for Simulation Metamodeling,” Operations Research, 58, 371–382.
- Bayarri, M. J., Berger, J. O., Paulo, R., Sacks, J., Cafeo, J. A., Cavendish, J., Lin, C.-H., Tu, J. (2007), “A Framework for Validation of Computer Models,” Technometrics, 49, 138–154.
- Ben-Ari, E. N., and Steinberg, D. M. (2007), “Modeling Data from Computer Experiments: An Empirical Comparison of Kriging With MARS and Projection Pursuit Regression,” Quality Engineering, 19, 327–338.
- Christakos, G. (1984), “On the Problem of Permissible Covariance and Variogram Models,” Water Resources Research, 20, 251–265.
- Fasshauer, G. (2005), “Meshfree Methods,” in Handbook of Theoretical and Computational Nanotechnology, eds. M. Rieth and W. Schommers, Stevenson Ranch, CA: American Scientific Publishers, pp. 33–97.
- Gneiting, T. (2002), “Nonseparable, Stationary Covariance Functions for Space–Time Data,” Journal of the American Statistical Association, 97, 590–600.
- Gneiting, T., and Raftery, A. E. (2007), “Strictly Proper Scoring Rules, Prediction, and Estimation,” Journal of the American Statistical Association, 102, 359–378.
- Gneiting, T., and Schlather, M. (2004), “Stochastic Models that Separate Fractal Dimension and the Hurst Effect,” SIAM Review, 46, 269–282.
- Gough, W. A., and Welch, W. J. (1994), “Parameter Space Exploration of an Ocean General Circulation Model Using an Isopycnal Mixing Parameterization,” Journal of Marine Research, 52, 773–796.
- Haaland, B., and Qian, P. Z. G. (2011), “Accurate Emulators for Large-Scale Computer Experiments,” The Annals of Statistics, 39, 2974–3002.
- Hardy, R. L. (1971), “Multiquadric Equations of Topography and Other Irregular Surfaces,” Journal of Geophysical Research, 76, 1905–1915.
- Higdon, D., Kennedy, M., Cavendish, J. C., Cafeo, J. A., and Ryne, R. D. (2004), “Combining Field Data and Computer Simulations for Calibration and Prediction,” SIAM Journal on Scientific Computing, 26, 448–466.
- Hofmann, T., Schölkopf, B., and Smola, A. J. (2008), “Kernel Methods in Machine Learning,” The Annals of Statistics, 36, 1171–1220.
- Joseph, V. R. (2006), “Limit Kriging,” Technometrics, 48, 458–466.
- Kenett, R., and Zacks, S. (1998), Modern Industrial Statistics: Design and Control of Quality and Reliability, Pacific Grove, CA: Duxbury Press.
- Lee, M. R., and Owen, A. B. (2015), “Single Nugget Kriging.” arXiv preprint arXiv:1507.05128.
- Lindstrøm, T. (1993), “Fractional Brownian Fields as Integrals of White Noise,” Bulletin of the London Mathematical Society, 25, 83–88.
- Loeppky, J. L., Sacks, J., and Welch, W. J. (2009), “Choosing the Sample Size of a Computer Experiment: A Practical Guide,” Technometrics, 51, 366–376.
- MacDonald, B., Ranjan, P., and Chipman, H. (2015), “GPfit: An R Package for Fitting a Gaussian Process Model to Deterministic Simulator Outputs,” Journal of Statistical Software, 64, 1–23.
- Mandelbrot, B. B., Van Ness, J. W. (1968), “Fractional Brownian Motions, Fractional Noises and Applications,” SIAM Review, 10, 422–437.
- Matheron, G. (1963), “Principles of Geostatistics,” Economic Geology, 58, 1246–1266.
- Micchelli, C. A. (1986), “Interpolation of Scattered Data: Distance Matrices and Conditionally Positive Definite Functions,” Constructive Approximation, 2, 11–22.
- Moon, H., Dean, A. M., and Santner, T. J. (2012), “Two-Stage Sensitivity-Based Group Screening in Computer Experiments,” Technometrics, 54, 376–387.
- Morris, M. D., Mitchell, T. J., and Ylvisaker, D. (1993), “Bayesian Design and Analysis of Computer Experiments: Use of Derivatives in Surface Prediction,” Technometrics, 35, 243–255.
- Nilson, T., and Kuusk, A. (1989), “A Reflectance Model for the Homogeneous Plant Canopy and its Inversion,” Remote Sensing of Environment, 27, 157–167.
- Peng, C.-Y., and Wu, C. J. (2014), “On the Choice of Nugget in Kriging Modeling for Deterministic Computer Experiments,” Journal of Computational and Graphical Statistics, 23, 151–168.
- Qian, Z., Seepersad, C. C., Joseph, V. R., Allen, J. K., and Wu, C. F. J. (2006), “Building Surrogate Models Based on Detailed and Approximate Simulations,” Journal of Mechanical Design, 128, 668–677.
- Sacks, J., Welch, W. J., Mitchell, T. J., and Wynn, H. P. (1989), “Design and Analysis of Computer Experiments,” Statistical Science, 4, 409–423.
- Santner, T. J., Williams, B. J., and Notz, W. (2003), The Design and Analysis of Computer Experiments, New York: Springer Science & Business Media.
- Stein, M. L. (1999), Interpolation of Spatial Data: Some Theory for Kriging, New York: Springer Science & Business Media.
- Yi, T.-M., Fazel, M., Liu, X., Otitoju, T., Goncalves, J., Papachristodoulou, A., Prajna, S., and Doyle, J. (2005), “Application of Robust Model Validation Using SOSTOOLS to the Study of G-Protein Signaling in Yeast,” Proceedings of the First Conference on Foundations of Systems Biology in Engineering. Available: https://faculty.washington.edu/mfazel/FOSBE.html
- Zhang, N., and Apley, D. W. (2014), “Fractional Brownian Fields for Response Surface Metamodeling,” Journal of Quality Technology, 46, 285–301.
- ——— (2015), “Brownian Integrated Covariance Functions for Gaussian Process Modeling: Sigmoidal Versus Localized Basis Functions,” Journal of the American Statistical Association, DOI: 10.1080/01621459.2015.1077711.