References
François Bachoc. Parametric Estimation of Covariance Function in Gaussian-Process based Kriging Models. Application to Uncertainty Quantification for Computer Experiments. PhD thesis, Université Paris Diderot, 2012.
James O. Berger, Victor De Oliveira, and Bruno Sansó. Objective Bayesian Analysis of Spatially Correlated Data. Journal of the American Statistical Association, 96(456):1361–1374, 2001. doi:10.1198/016214501753382282.
Alain Berlinet and Christine Thomas-Agnan. Reproducing Kernel Hilbert Space in Probability and Statistics. Springer, 2004. doi:10.1007/978-1-4419-9096-9.
Mengyang Gu. Robust Uncertainty Quantification and Scalable Computation for Computer Models with Massive Output. PhD thesis, Duke University, 2016. URL: https://hdl.handle.net/10161/12882.
Mengyang Gu. Jointly Robust Prior for Gaussian Stochastic Process in Emulation, Calibration and Variable Selection. Bayesian Analysis, 14(3):857–885, 2019. doi:10.1214/18-BA1133.
Mengyang Gu, Xiaojing Wand, and James O. Berger. Robust Gaussian Stochastic Process Emulation. Annals of Statistics, 46(6A):3038–3066, 2018. doi:10.1214/17-AOS1648.
Kenneth Lange. Numerical Analysis for Statisticians. Statistics & Computing. Springer-Verlag, 2nd edition, 2010. doi:10.1007/978-1-4419-5945-4.
Kantilal V. Mardia, John T. Kent, Colin R. Goodall, and John A. Little. Kriging and Splines with Derivative Information. Biometrika, 83(1):207–221, 03 1996. doi:10.1093/biomet/83.1.207.
Antony O'Hagan. Curve fitting and optimal design for prediction. Journal of the Royal Statistical Society: Series B, pages 1–42, 1978. doi:10.1111/j.2517-6161.1978.tb01643.x.
Luc Pronzato. Sensitivity Analysis via Karhunen-Loève Expansion of a Random Field Model: Estimation of Sobol' Indices and Experimental Design. Reliability Engineering and System Safety, pages 93–109, 2019. doi:10.1016/j.ress.2018.01.010.
Carl E. Rasmussen and Christopher K.I. Williams. Gaussian Processes for Machine Learning. The MIT Press, 2006. doi:10.7551/mitpress/3206.001.0001.
Olivier Roustant, David Ginsbourger, and Yves Deville. DiceKriging, DiceOptim: Two R Packages for the Analysis of Computer Experiments by Kriging-Based Metamodeling and Optimization. Journal of Statistical Software, pages 1–55, 2012. doi:10.18637/jss.v051.i01.
Michael L. Stein. Interpolation of Spatial Data. Some Theory for Kriging. Springer Series in Statistics. Springer-Verlag, 2012. doi:10.1007/978-1-4612-1494-6.
Grace Wahba. Improper Priors, Spline Smoothing and the Problem of Guarding Against Model Errors in Regression. Journal of the Royal Statistical Society: Series B, 40(3):364–372, 1978. doi:10.1111/j.2517-6161.1978.tb01050.x.