Correlation model Enforced hyper-parameters MSE PVA exponential [1, 1, 1] 2.01 M L : 0, CHAPTER ,
A review of Gaussian random elds and correlation functions, 1997. ,
Estimating the Prediction Mean Squared Error in Gaussian Stochastic Processes with Exponential Correlation Structure, Scandinavian Journal of Statistics, vol.26, issue.4, p.563578, 1999. ,
DOI : 10.1111/1467-9469.00168
The eect of the nugget on Gaussian process emulators of computer models, Computational Statistics and Data Analysis, vol.56, p.42154228, 2012. ,
A Matrix-free Approach for Solving the Parametric Gaussian Process Maximum Likelihood Problem, SIAM Journal on Scientific Computing, vol.34, issue.1, pp.240-262, 2012. ,
DOI : 10.1137/110831143
The Geometry of Random Fields, 1981. ,
An introduction to continuity, extrema, and related topics for general Gaussian processes, 1990. ,
On the consistent separation of scale and variance for Gaussian random elds. The Annals of Statistics, p.870893, 2010. ,
Handbook of Mathematical Functions, American Journal of Physics, vol.34, issue.2, 1965. ,
DOI : 10.1119/1.1972842
Applied Functional Analysis Asymptotic analysis of the role of the spatial sampling for hyperparameter estimation of Gaussian processes, 2000. ,
Cross validation and maximum likelihood estimations of hyperparameters of Gaussian processes with model mispecication, Computational Statistics and Data Analysis, vol.66, p.5569, 2013. ,
Méthodes d'interpolation à noyaux pour l'approximation de fonctions type boîte noire coûteuses, 2010. ,
Calibration and improved prediction of computer models by universal Kriging. Nuclear Science and Engineering ,
A framework for validation of computer models, Technometrics, vol.49, issue.2, p.138154, 2007. ,
Robust Gaussian Process-Based Global Optimization Using a Fully Bayesian Expected Improvement Criterion, LION5, online proceedings, 2011. ,
DOI : 10.1002/qre.945
URL : https://hal.archives-ouvertes.fr/hal-00607816
Merging of Opinions with Increasing Information, The Annals of Mathematical Statistics, vol.33, issue.3, p.882886, 1962. ,
DOI : 10.1214/aoms/1177704456
Empirical Model Building and Response Surfaces, Series in Probability and Mathematical Statistics, 1987. ,
Inversion d'un système par Krigeage Application à la synthèse de catalyseurs à haut débits, 2009. ,
Sequential design of computer experiments for the estimation of a probability of failure, Statistics and Computing, vol.34, issue.4, p.773793, 2012. ,
DOI : 10.1007/s11222-011-9241-4
URL : https://hal.archives-ouvertes.fr/hal-00689580
Probability and measure ,
Diagnostics for Gaussian Process Emulators, Technometrics, vol.51, issue.4 ,
DOI : 10.1198/TECH.2009.08019
Sensitivity and uncertainty analysis, Theory. Chapman & Hall/CRC, 2003. ,
Geostatistics : Modeling Spatial Uncertainty, 1999. ,
DOI : 10.1002/9781118136188
Fast computation of the multipoint expected improvement with applications in batch selection, Proceedings of the LION7 conference, 2013. ,
Corrected kriging update formulae for batch-sequential data assimilation In To be presented at IAMG Madrid 2013, Session 4: Data assimilation in Geosciences, BIBLIOGRAPHY [CL67] H. Cramér and M.R. Leadbetter. Stationary and Related Stochastic Processes - Sample Function Properties and Their Applications, 1967. ,
The Asymptotic Distribution of REML Estimators, Journal of Multivariate Analysis, vol.45, issue.2, p.217233, 1993. ,
DOI : 10.1006/jmva.1993.1034
Statistics for Spatial Data, 1993. ,
Near-optimal signal recovery from random projections: Universal encoding strategies? Information Theory, IEEE Transactions on, vol.52, issue.12, pp.5406-5425, 2006. ,
DOI : 10.1109/tit.2006.885507
URL : http://arxiv.org/abs/math/0410542
Fixed Domain Asymptotics and Consistent Estimation for Gaussian Random Field Models in Spatial Statistics and Computer Experiments, 2010. ,
Determination of the uncertainties of the constitutive relationships in the cathare 2 code, Proceedings of the 4th ASME/JSME International Conference on Nuclear Engineering, 1996. ,
Determination of the uncertainties of the constitutive relationships of the cathare 2 code, M&C 2001 Salt Lake City, 2001. ,
Fast and exact simulation of stationary Gaussian processes through circulant embedding of the covariance matrix, SIAM J. SCI. COMPUT, vol.18, pp.1088-1107, 1997. ,
Stochastic Processes, 1953. ,
Uncertainty in industrial practice, 2008. ,
DOI : 10.1002/9780470770733
Cross validation of Kriging in a unique neighborhood, Mathematical Geology, vol.15, p.687699, 1983. ,
Fixed-domain asymptotic properties of tapered maximum likelihood estimators, The Annals of Statistics, vol.37, issue.6A, p.33303361, 2009. ,
DOI : 10.1214/08-AOS676
Inversion probabiliste bayésienne en analyse d'incertitude, 2012. ,
Numerical integration using sparse grids. Numerical algorithms, p.209232, 1998. ,
Regularity dependence of the rate of convergence of the learning curve for gaussian process regression, 2012. ,
URL : https://hal.archives-ouvertes.fr/hal-00737342
Matrix computations, Johns Hopkins Studies in Mathematical Sciences, 1996. ,
Toeplitz and circulant matrices: A review, 2001. ,
The theory of stochastic processes, 1974. ,
DOI : 10.1007/978-3-642-61943-4
Bayesian inference for variant components using only error contrasts, Biometrika, vol.61, p.383385, 1974. ,
A supercomputing application for reactors core design and optimization, Joint International Conference on Supercomputing in Nuclear Applications and Monte Carlo 2010 (SNA + MC2010), 2010. ,
Combining eld data and computer simulations for calibration and prediction, SIAM Journal on Scientic Computing, vol.26, p.448466, 2004. ,
Tapenade 2.1 user's guide, 2004. ,
The elements of statistical learning, 2008. ,
Numerical studies of the metamodel tting and validation processes, International Journal of Advances in Systems and Measurements, vol.3, p.1121, 2010. ,
Gaussian Random Processes, 1978. ,
DOI : 10.1007/978-1-4612-6275-6
Geostatistical sampling optimization of contaminated premises. In DEM 2008 -Decommissionning Challenges: an industrial reality?, 2008. ,
Ecient global optimization of expensive black box functions, Journal of Global Optimization, vol.13, p.455492, 1998. ,
Evaluation and propagation of the 239 Pu ssion cross-section uncertainties using a ,
Bayesian calibration of computer models, Nuclear Science and Engineering Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.153, issue.63, p.17425464, 2001. ,
On the eciency of selection criteria in spline regression. Probability Theory and Related Fields, p.153176, 2003. ,
Gradient-Enhanced Universal Kriging for Uncertainty Propagation, Nuclear Science and Engineering, vol.170, issue.2, p.168195, 2012. ,
DOI : 10.13182/NSE10-86
Central limit theorems for weighted sums of a spatial process under a class of stochastic and xed designs, Sankhyã: The Indian Journal of Statistics, vol.65, p.356388, 2003. ,
Estimating structured correlation matrices in smooth Gaussian random eld models. The Annals of Statistics, p.880904, 2000. ,
Asymptotic distributions of M-estimators in a spatial regression model under some xed and stochastic spatial sampling designs, Annals of the Institute of Statistical Mathematics, vol.56, p.225250, 2004. ,
Fixed domain asymptotics for a subclass of Matérn type Gaussian random elds. The Annals of Statistics, p.23442394, 2005. ,
Analysis of Computer Experiments Using Penalized Likelihood in Gaussian Kriging Models, Technometrics, vol.47, issue.2, p.111120, 2005. ,
DOI : 10.1198/004017004000000671
La Théorie des Variables Régionalisées et ses Applications Fasicule 5 in Les Cahiers du, 1970. ,
An ecient methodology for modeling complex computer codes with Gaussian processes, Computational Statistics and Data Analysis, vol.52, p.47314744, 2008. ,
Machine Learning, 1997. ,
Maximum likelihood estimation of models for residual covariance in spatial regression, Biometrika, vol.71, issue.1, p.135146, 1984. ,
DOI : 10.1093/biomet/71.1.135
Krigeage par processus gaussiens Librairie gpLib, pp.12-026 ,
Design and Analysis of Experiments, 2005. ,
Factorial Sampling Plans for Preliminary Computational Experiments, Technometrics, vol.1, issue.2, p.161174, 1991. ,
DOI : 10.2307/1266468
Germinal -a computer code for predicting fuel pin behaviour, Journal of Nuclear Materials, vol.188, p.303307, 1992. ,
On the use of Kriging models to approximate deterministic computer models, DETC'04 ASME 2004 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference Salt Lake City, 2004. ,
Random Number Generation and Quasi-Monte Carlo Methods, Series SIAM CBMS-NSF, 1992. ,
DOI : 10.1137/1.9781611970081
Recent developments in spectral stochastic methods for the numerical solution of stochastic partial dierential equations, Archives of Computational Methods in Engineering, vol.16, p.251285, 2009. ,
High dimensional integration of smooth functions over cubes, Numerische Mathematik, vol.75, issue.1, p.7997, 1996. ,
DOI : 10.1007/s002110050231
Numerical Optimization, 2006. ,
DOI : 10.1007/b98874
Best-Estimate Model Calibration and Prediction Through Experimental Data Assimilation - II: Application to a Blowdown Benchmark Experiment, Nuclear Science and Engineering, vol.165, issue.1, p.45100, 2008. ,
DOI : 10.13182/NSE09-37C
Design of computer experiments: space filling and beyond, Statistics and Computing, vol.44, issue.1, p.681701, 2012. ,
DOI : 10.1007/s11222-011-9242-3
URL : https://hal.archives-ouvertes.fr/hal-00685876
Numerical recipes: The art of Scientic computing, 2007. ,
On the eect of covariance function estimation on the accuracy of kriging predictors, Bernoulli, vol.7, issue.3, p.421438, 2001. ,
Monte Carlo statistical methods, 1999. ,
Packages for the Analysis of Computer Experiments by Kriging-Based Metamodeling and Optimization, Journal of Statistical Software, vol.51, issue.1, p.155, 2012. ,
DOI : 10.18637/jss.v051.i01
URL : https://hal.archives-ouvertes.fr/hal-00495766
Spatial Statistics, 1981. ,
The Bayesian Choice: From Decision-Theoretic Foundations to Computational Implementation, 2001. ,
DOI : 10.1007/978-1-4757-4314-2
Gaussian Processes in Machine Learning, 2006. ,
DOI : 10.1162/089976602317250933
Difference Filter Preconditioning for Large Covariance Matrices, SIAM Journal on Matrix Analysis and Applications, vol.33, issue.1, pp.52-72, 2012. ,
DOI : 10.1137/110834469
Stochastic approximation of score functions for Gaussian processes, The Annals of Applied Statistics, vol.7, issue.2, p.11621191, 2013. ,
DOI : 10.1214/13-AOAS627
Predictive Approaches for Choosing Hyperparameters in Gaussian Processes, Neural Computation, vol.36, issue.1, p.11031118, 2001. ,
DOI : 10.2307/2286745
Quadrature and interpolation formulas for tensor products of certain classes of functions, Soviet Math. Dokl, vol.4, p.240243, 1963. ,
Learning with Kernels: Support Vector Machines, Regularization,Optimization, and Beyond, 2002. ,
Asymptotically ecient prediction of a random eld with a misspecied covariance function. The Annals of Statistics, p.5563, 1988. ,
Bounds on the eciency of linear predictions using an incorrect covariance function. The Annals of Statistics, p.11161138, 1990. ,
A comparison of generalized cross validation and modied maximum likelihood for estimating the parameters of a stochastic process, The Annals of Statistics, vol.18, p.11391157, 1990. ,
Uniform asymptotic optimality of linear predictions of a random eld using an incorrect second-order structure. The Annals of Statistics, p.850872, 1990. ,
Spline Smoothing with an Estimated Order Parameter, The Annals of Statistics, vol.21, issue.3, p.15221544, 1993. ,
DOI : 10.1214/aos/1176349270
Interpolation of Spatial Data: Some Theory for Kriging, 1999. ,
DOI : 10.1007/978-1-4612-1494-6
Uniform asymptotic normality of the maximum likelihood estimator. The Annals of Statistics, p.13751381, 1980. ,
Design and Analysis of Computer Experiments, Statistical Science, vol.4, issue.4, p.409423, 1989. ,
DOI : 10.1214/ss/1177012413
The Design and Analysis of Computer Experiments, 2003. ,
DOI : 10.1007/978-1-4757-3799-8
An Introduction to Sobolev Spaces and Interpolation Spaces, Lecture Notes of the Unione Matematica Italiana, 2007. ,
Flica-4: a threedimensional two-phase ow computer code with advanced numerical methods for nuclear applications, Nuclear Engineering and Design, vol.200, p.139155, 2000. ,
A unifying approach to some old and new theorems on distribution and clustering, Linear Algebra and its Applications, vol.232, p.143, 1996. ,
Asymptotic Statistics, Cambridge Series in Statistical and Probabilistic Mathematics, 1998. ,
Modélisation comportementale de systèmes non-linéaires multivariables par méthodes à noyaux et applications, 2005. ,
Pointwise consistency of the Kriging predictor with known mean and covariance functions In mODa 9 -Advances in Model-Oriented Design and Analysis. 14th, 2010. ,
Estimation and model identication for continuous spatial processes, Journal of the Royal Statistical Society , Ser. B, vol.50, p.297312, 1988. ,
Gaussian process modeling with inequality constraints, Annales de la faculté des sciences de Toulouse, p.529555, 2012. ,
DOI : 10.5802/afst.1344
An algorithm for fast optimal Latin hypercube design of experiments, International Journal for Numerical Methods in Engineering, vol.49, issue.1, p.135156, 2010. ,
DOI : 10.1007/s00158-008-0338-0
Spline Models for Observational Data, SIAM, 1990. ,
DOI : 10.1137/1.9781611970128
Bayesian Validation of Computer Models, Technometrics, vol.51, issue.4, p.439451, 2009. ,
DOI : 10.1198/TECH.2009.07011
Maximum likelihood estimation of misspecied models, Econometrica, vol.50, issue.1, p.125, 1982. ,
Tail estimation of the spectral density for a stationary gaussian random eld, Journal of Multivariate Analysis, vol.116, p.7491, 2013. ,
Asymptotic properties of a maximum likelihood estimator with data from a Gaussian process, Journal of Multivariate Analysis, vol.36, p.280296, 1991. ,
A comparison of Kriging with nonparametric regression methods Mean squared prediction error in the spatial linear model with estimated covariance parameters, Journal of Multivariate Analysis Ann. Inst. Statist. Math, vol.16, issue.44, p.21532743, 1985. ,
Distribution Theory and Transform Analysis, 1965. ,
Inconsistent Estimation and Asymptotically Equal Interpolations in Model-Based Geostatistics, Journal of the American Statistical Association, vol.99, issue.465, pp.250-261, 2004. ,
DOI : 10.1198/016214504000000241
Kriging and cross-validation for massive spatial data, Environmetrics, vol.23, issue.1, p.290304, 2010. ,
DOI : 10.1002/env.1023
Towards reconciling two asymptotic frameworks in spatial statistics, Biometrika, vol.92, issue.4, p.921936, 2005. ,
DOI : 10.1093/biomet/92.4.921
Spatial sampling design under the inll asymptotic framework, Environmetrics, vol.17, p.323337, 2006. ,