E. B. Anderes and M. L. Stein, Estimating deformations of isotropic gaussian random fields on the plane. The Annals of Statistics, pp.719-741, 2008.

J. Bect, D. Ginsbourger, L. Li, V. Picheny, and E. Vazquez, Sequential design of computer experiments for the estimation of a probability of failure, Statistics and Computing, vol.34, issue.4, pp.773-793, 2011.
DOI : 10.1007/s11222-011-9241-4

URL : https://hal.archives-ouvertes.fr/hal-00689580

D. Brillinger, The identification of a particular nonlinear time series system, Biometrika, vol.64, issue.3, pp.509-515, 1977.
DOI : 10.1093/biomet/64.3.509

C. Chevalier, J. Bect, D. Ginsbourger, E. Vazquez, V. Picheny et al., Fast Parallel Kriging-Based Stepwise Uncertainty Reduction With Application to the Identification of an Excursion Set, Technometrics, vol.13, issue.4, pp.455-465, 2014.
DOI : 10.1007/3-540-50871-6

URL : https://hal.archives-ouvertes.fr/hal-00641108

C. Chevalier, D. Ginsbourger, and X. Emery, Corrected kriging update formulae for batchsequential data assimilation, Mathematics of Planet Earth, pp.119-122, 2014.
DOI : 10.1007/978-3-642-32408-6_29

URL : https://hal.archives-ouvertes.fr/hal-00683362

T. Choi, J. Q. Shi, and B. Wang, A Gaussian process regression approach to a single-index model, Journal of Nonparametric Statistics, vol.19, issue.1, pp.21-36, 2011.
DOI : 10.1198/016214502388618861

J. Doob, Stochastic processes, 1953.

P. Duchesne and P. Micheaux, Computing the distribution of quadratic forms: Further comparisons between the Liu???Tang???Zhang approximation and exact methods, Computational Statistics & Data Analysis, vol.54, issue.4, pp.858-862, 2010.
DOI : 10.1016/j.csda.2009.11.025

D. Dupuy, C. Helbert, and J. Franco, DiceDesign and DiceEval: Two R packages for design and analysis of computer experiments, Journal of Statistical Software, issue.11, pp.651-689, 2015.

N. Durrande, D. Ginsbourger, and O. Roustant, Additive covariance kernels for highdimensional gaussian process modeling, Annales de la Faculté de Sciences de Toulouse, p.481, 2012.
DOI : 10.5802/afst.1342

URL : https://hal.archives-ouvertes.fr/hal-00644934

R. W. Farebrother, The distribution of a positive linear combination of ? 2 random variables, Journal of the Royal Statistical Society. Series C (Applied Statistics), vol.33, issue.3, pp.332-339, 1984.

M. Gibbs, Bayesian Gaussian processes for regression and classification, 1997.

D. Ginsbourger, O. Roustant, and N. Durrande, On degeneracy and invariances of random fields paths with applications in Gaussian process modelling, Journal of Statistical Planning and Inference, vol.170, pp.117-128, 2016.
DOI : 10.1016/j.jspi.2015.10.002

URL : https://hal.archives-ouvertes.fr/emse-01222506

D. Ginsbourger, O. Roustant, D. Schuhmacher, N. Durrande, and N. Lenz, On ANOVA Decompositions of Kernels and Gaussian Random Field Paths, Monte Carlo and Quasi- Monte Carlo Methods, pp.315-330, 2016.
DOI : 10.1007/978-3-319-33507-0_15

URL : https://hal.archives-ouvertes.fr/emse-01339368

R. B. Gramacy, Bayesian treed Gaussian process models, 2005.

R. B. Gramacy and H. K. Lee, Bayesian Treed Gaussian Process Models With an Application to Computer Modeling, Journal of the American Statistical Association, vol.103, issue.483, pp.1119-1130, 2008.
DOI : 10.1198/016214508000000689

URL : http://arxiv.org/abs/0710.4536

R. B. Gramacy and H. K. Lee, Adaptive Design and Analysis of Supercomputer Experiments, Technometrics, vol.51, issue.2, pp.130-145, 2009.
DOI : 10.1198/TECH.2009.0015

URL : http://arxiv.org/abs/0805.4359

R. B. Gramacy and H. Lian, Gaussian Process Single-Index Models as Emulators for Computer Experiments, Technometrics, vol.35, issue.6, pp.30-41, 2012.
DOI : 10.1016/j.csda.2008.12.010

URL : http://arxiv.org/abs/1009.4241

J. P. Imhof, Computing the distribution of quadratic forms in normal variables, Biometrika, pp.419-426, 1961.

D. R. Jones, M. Schonlau, and J. William, Efficient global optimization of expensive blackbox functions, Journal of Global Optimization, vol.13, issue.4, pp.455-492, 1998.
DOI : 10.1023/A:1008306431147

H. Liu, Y. Tang, and H. H. Zhang, A new chi-square approximation to the distribution of non-negative definite quadratic forms in non-central normal variables, Computational Statistics & Data Analysis, vol.53, issue.4, pp.853-856, 2009.
DOI : 10.1016/j.csda.2008.11.025

D. J. Mackay, Introduction to gaussian processes, NATO ASI Series F Computer and Systems Sciences, pp.133-166, 1998.

J. Mockus, Application of Bayesian approach to numerical methods of global and stochastic optimization, Journal of Global Optimization, vol.16, issue.4, pp.347-365, 1994.
DOI : 10.1007/BF01099263

C. Paciorek, Nonstationary Gaussian Processes for Regression and Spatial Modelling, 2003.

C. Paciorek and M. Schervish, Nonstationary covariance functions for gaussian process regression Advances in neural information processing systems, pp.273-280, 2004.

E. Padonou and O. Roustant, Polar Gaussian Processes and Experimental Designs in Circular Domains, SIAM/ASA Journal on Uncertainty Quantification, vol.4, issue.1, pp.1014-1033, 2016.
DOI : 10.1137/15M1032740

URL : https://hal.archives-ouvertes.fr/hal-01119942

J. Park and J. Baek, Efficient computation of maximum likelihood estimators in a spatial linear model with power exponential covariogram, Computers & Geosciences, vol.27, issue.1, pp.1-7, 2001.
DOI : 10.1016/S0098-3004(00)00016-9

E. S. Pearson, Note on an Approximation to the Distribution of Non-Central ?? 2, Biometrika, vol.46, issue.3/4, 1959.
DOI : 10.2307/2333533

F. Perales, F. Dubois, Y. Monerie, B. Piar, and L. Stainier, A NonSmooth Contact Dynamics-based multi-domain solver Code coupling (Xper) and application to fracture, Revue europ??enne de m??canique num??rique, vol.19, issue.4, pp.389-417, 2010.
DOI : 10.3166/ejcm.19.389-417

URL : https://hal.archives-ouvertes.fr/hal-01004918

V. Picheny, D. Ginsbourger, O. Roustant, R. T. Haftka, and N. Kim, Adaptive Designs of Experiments for Accurate Approximation of a Target Region, Journal of Mechanical Design, vol.132, issue.7, p.132, 2010.
DOI : 10.1115/1.4001873

URL : https://hal.archives-ouvertes.fr/emse-00699752

L. Pronzato and W. G. Müller, Design of computer experiments: space filling and beyond, Statistics and Computing, vol.44, issue.1, pp.681-701, 2011.
DOI : 10.1007/s11222-011-9242-3

URL : https://hal.archives-ouvertes.fr/hal-00685876

P. Ranjan, D. Bingham, and G. Michailidis, Sequential Experiment Design for Contour Estimation From Complex Computer Codes, Technometrics, vol.50, issue.4, pp.527-541, 2008.
DOI : 10.1198/004017008000000541

C. R. Rasmussen and C. K. Williams, Gaussian Processes in Machine Learning, 2006.
DOI : 10.1162/089976602317250933

URL : http://hdl.handle.net/11858/00-001M-0000-0013-F365-A

J. Rougier, A representation theorem for stochastic processes with separable covariance functions, and its implications for emulation

O. Roustant, D. Ginsbourger, and Y. Deville, DiceKriging, DiceOptim: Two R packages for the analysis of computer experiments by Kriging-Based Metamodelling and Optimization, Journal of Statistical Software, vol.51, issue.1, pp.1-55, 2012.
URL : https://hal.archives-ouvertes.fr/emse-00741762

J. Sacks, W. J. Welch, T. J. Mitchell, and H. P. Wynn, Design and Analysis of Computer Experiments, Statistical Science, vol.4, issue.4, pp.409-423, 1989.
DOI : 10.1214/ss/1177012413

P. D. Sampson and P. Guttorp, Nonparametric Estimation of Nonstationary Spatial Covariance Structure, Journal of the American Statistical Association, vol.40, issue.417, pp.108-119, 1992.
DOI : 10.1080/01621459.1992.10475181

T. J. Santner, B. J. Williams, and W. Notz, The design and analysis of computer experiments, 2003.
DOI : 10.1007/978-1-4757-3799-8

M. Scheuerer, A comparison of models and methods for spatial interpolation in statistics and numerical analysis, 2009.

J. Snoek, K. Swersky, R. Zemel, and R. P. Adams, Input warping for bayesian optimization of non-stationary functions, ICML, pp.1674-1682, 2014.

N. Srinivas, A. Krause, S. M. Kakade, and M. W. Seeger, Information-Theoretic Regret Bounds for Gaussian Process Optimization in the Bandit Setting, IEEE Transactions on Information Theory, vol.58, issue.5, pp.3250-3265, 2012.
DOI : 10.1109/TIT.2011.2182033

M. L. Stein, Interpolation of Spatial Data: Some Theory for Kriging, 1999.
DOI : 10.1007/978-1-4612-1494-6

E. Vazquez and J. Bect, Sequential search based on kriging: convergence analysis of some algorithms, ISI -58th World Statistics Congress of the International Statistical Institute (ISI'11), 2011.
URL : https://hal.archives-ouvertes.fr/hal-00643159

B. J. Williams, T. J. Santner, and W. I. Notz, Sequential design of computer experiments to minimize integrated response functions, Statistica Sinica, vol.10, pp.1133-1152, 2000.

Y. Xia, A Multiple-Index Model and Dimension Reduction, Journal of the American Statistical Association, vol.103, issue.484, pp.1631-1640, 2008.
DOI : 10.1198/016214508000000805

Y. Xiong, W. Chen, D. Apley, and X. Ding, A non-stationary covariance-based Kriging method for metamodelling in engineering design, International Journal for Numerical Methods in Engineering, vol.128, issue.6, pp.733-756, 2007.
DOI : 10.1002/nme.1969