C. Chevalier and D. Ginsbourger, Corrected Kriging Update Formulae for Batch-Sequential Data Assimilation, 2012.
DOI : 10.1007/978-3-642-32408-6_29
URL : https://hal.archives-ouvertes.fr/hal-00683362

J. P. Chiì-es and P. Delfiner, Geostatistics: Modeling Spatial Uncertainty, 2012.

X. Emery, The kriging update equations and their application to the selection of neighboring data, Computational Geosciences, vol.87, issue.3???4, pp.211-219, 2009.
DOI : 10.1007/s10596-008-9116-8

M. D. Hoshiya, M. Schonlau, and J. William, Kriging and conditional simulation of gaussian field Efficient global optimization of expensive black-box functions, Journal of engineering mechanics Journal of Global Optimization, vol.121, issue.134, pp.181-186, 1995.

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

J. Mockus, Bayesian Approach to Global Optimization. Theory and Applications, 1989.

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. Mockus, V. Tiesis, and A. Zilinskas, The application of Bayesian methods for seeking the extremum, Towards Global Optimization, vol.2, pp.117-129, 1978.

M. Schonlau, Computer Experiments and global optimization, 1997.

D. Ginsbourger, Métamodèles multiples pour l'approximation et l'optimisation de fonctions numériques multivariables, 2009.

D. Ginsbourger, R. Le-riche, L. , and C. , Kriging Is Well-Suited to Parallelize Optimization, of Adaptation Learning and Optimization, pp.131-162, 2010.
DOI : 10.1007/978-3-642-10701-6_6
URL : https://hal.archives-ouvertes.fr/emse-00436126

J. Janusevskis, R. Le-riche, and D. Ginsbourger, Parallel expected improvements for global optimization: summary, bounds and speed-up, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00613971

J. Janusevskis, R. Le-riche, D. Ginsbourger, and R. Girdziusas, Expected Improvements for the Asynchronous Parallel Global Optimization of Expensive Functions: Potentials and Challenges, LION 6 Conference (Learning and Intelligent OptimizatioN ), 2012.
DOI : 10.1007/978-3-642-34413-8_37
URL : https://hal.archives-ouvertes.fr/emse-00686504

P. I. Frazier, Parallel global optimization using an improved multi-points expected improvement criterion, 2012.

J. P. Chiì-es and P. Delfiner, Geostatistics: Modeling Spatial Uncertainty, 1999.

G. Tallis, The moment generating function of the truncated multi-normal distribution, J. Roy. Statist. Soc. Ser. B, vol.23, issue.1, pp.223-229, 1961.

D. Veiga, S. Marrel, and A. , Gaussian process modeling with inequality constraints, Annales de la facult?? des sciences de Toulouse Math??matiques, vol.21, issue.3, pp.529-555, 2012.
DOI : 10.5802/afst.1344

A. Genz, Numerical Computation of Multivariate Normal Probabilities, Journal of Computational and Graphical Statistics, vol.1, issue.2, pp.141-149, 1992.
DOI : 10.1007/978-1-4613-9655-0

A. Genz and F. Bretz, Computation of Multivariate Normal and t Probabilities, 2009.
DOI : 10.1007/978-3-642-01689-9

A. Azzalini, mnormt: The multivariate normal and t distributions. (2012) R package version 1, pp.4-5

S. Finck, N. Hansen, R. Ros, and A. Auger, Real-parameter black-box optimization bencharking 2009: Presentation of the noiseless functions, 2009.

N. Hansen, S. Finck, R. Ros, and A. Auger, Real-parameter black-box optimization bencharking 2009: Noiseless functions definitions, p.2009, 2010.

W. Mebane and J. Sekhon, Genetic optimization using derivatives: The rgenoud package for r, Journal of Statistical Software, vol.42, issue.11, pp.1-26, 2011.

R. J. Barnes and A. Watson, Efficient updating of kriging estimates and variances, Mathematical Geology, vol.24, issue.1, pp.129-133, 1992.
DOI : 10.1007/BF00890091

M. J. Bayarri, J. O. Berger, R. Paulo, J. Sacks, J. A. Cafeo et al., A Framework for Validation of Computer Models, Technometrics, vol.49, issue.2, pp.138-154, 2007.
DOI : 10.1198/004017007000000092

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.1-21, 2011.
DOI : 10.1007/s11222-011-9241-4
URL : https://hal.archives-ouvertes.fr/hal-00689580

B. J. Bichon, M. S. Eldred, L. P. Swiler, S. Mahadevan, and J. M. Mcfarland, Efficient Global Reliability Analysis for Nonlinear Implicit Performance Functions, AIAA Journal, vol.46, issue.10, pp.462459-2468, 2008.
DOI : 10.2514/1.34321

C. Chevalier and D. Ginsbourger, Corrected Kriging Update Formulae for Batch-Sequential Data Assimilation, 2012.
DOI : 10.1007/978-3-642-32408-6_29
URL : https://hal.archives-ouvertes.fr/hal-00683362

C. Chevalier, V. Picheny, and D. Ginsbourger, KrigInv: Kriging-based Inversion for Deterministic and Noisy Computer Experiments, 2012

V. Dubourg, Métamodèles adaptatifs pour l'analyse de fiabilité et l'optimisation sous contrainte fiabiliste, 2011.

B. Echard, N. Gayton, and M. Lemaire, Kriging-based Monte Carlo simulation to compute the probability of failure efficiently: AK-MCS method, 6` emes Journées Nationales de Fiabilité, pp.24-26, 2010.

X. Emery, The kriging update equations and their application to the selection of neighboring data, Computational Geosciences, vol.87, issue.3???4, pp.211-219, 2009.
DOI : 10.1007/s10596-008-9116-8

K. Fang, R. Li, and A. Sudjianto, Design and modeling for computer experiments, 2006.
DOI : 10.1201/9781420034899

A. I. Forrester, A. Sóbester, and A. J. Keane, Engineering design via surrogate modelling: a practical guide, 2008.
DOI : 10.1002/9780470770801

H. Gao, J. Wang, and P. Zhao, The updated kriging variance and optimal sample design, Mathematical Geology, vol.7, issue.no. 8, pp.295-313, 1996.
DOI : 10.1007/BF02083202

A. Genz, Numerical Computation of Multivariate Normal Probabilities, Journal of Computational and Graphical Statistics, vol.1, issue.2, pp.141-149, 1992.
DOI : 10.1007/978-1-4613-9655-0

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

L. Li, J. Bect, and E. Vazquez, Bayesian Subset Simulation : a kriging-based subset simulation algorithm for the estimation of small probabilities of failure
URL : https://hal.archives-ouvertes.fr/hal-00715316

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. P. Robert and G. Casella, Monte Carlo Statistical Methods, 2004.

R. Rubinstein and D. Kroese, Simulation and the Monte Carlo method, 2008.

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.409-435, 1989.
DOI : 10.1214/ss/1177012413

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

A. Torn and A. Zilinskas, Global Optimization, 1989.
DOI : 10.1007/3-540-50871-6

E. Vazquez and J. Bect, A sequential Bayesian algorithm to estimate a probability of failure References 1. Baddeley, A., Molchanov, I.: Averaging of random sets based on their distance functions, Proceedings of the 15th IFAC Symposium on System Identification, SYSID 2009 15th IFAC Symposium on System Identification, pp.79-92, 1998.

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, 2012.
DOI : 10.1007/s11222-011-9241-4
URL : https://hal.archives-ouvertes.fr/hal-00689580

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, 2012.
DOI : 10.1007/3-540-50871-6
URL : https://hal.archives-ouvertes.fr/hal-00641108

C. Chevalier, V. Picheny, and D. Ginsbourger, KrigInv: Kriging-based Inversion for Deterministic and Noisy Computer Experiments, 2012.

J. P. Chiì-es and P. Delfiner, Geostatistics: Modeling Spatial Uncertainty, 1999.

V. Dubourg, Métamodèles adaptatifs pour l'analyse de fiabilité et l'optimisation sous contrainte fiabiliste, p.IFMA, 2011.

A. I. Forrester, A. Sóbester, and A. J. Keane, Engineering design via surrogate modelling: a practical guide, 2008.
DOI : 10.1002/9780470770801

I. Molchanov, Theory of Random Sets, 2005.

V. Picheny, D. Ginsbourger, O. Roustant, R. T. Haftka, and N. H. Kim, Adaptive Designs of Experiments for Accurate Approximation of a Target Region, Journal of Mechanical Design, vol.132, issue.7, 2010.
DOI : 10.1115/1.4001873
URL : https://hal.archives-ouvertes.fr/emse-00699752

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

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

E. Vazquez and M. Piera-martinez, Estimation of the volume of an excursion set of a Gaussian process using intrinsic, Kriging, 2006.

E. Vazquez and M. Piera-martinez, Estimation du volume des ensembles d'excursion d'un processus gaussien par krigeage intrinsèque, 39ème Journées de Statistiques, 2007.

E. Appendix, R. Kriginv, J. Package-bect, D. Ginsbourger, L. Li et al., Sequential design of computer experiments for the estimation of a probability of failure, Statistics and Computing, vol.22, issue.3, pp.773-793, 2012.

C. Chevalier and D. Ginsbourger, Corrected kriging update formulae for batch-sequential data assimilation. URL http, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00683362

J. Chiì-es and P. Delfiner, Geostatistics: Modeling Spatial Uncertainty, 1999.

S. Conti and A. O-'hagan, Bayesian emulation of complex multi-output and dynamic computer models, Journal of Statistical Planning and Inference, vol.140, issue.3, pp.640-651, 2010.
DOI : 10.1016/j.jspi.2009.08.006

N. Cressie, Statistics for spatial data, 1993.

L. Dixon and G. Szegö, Towards global optimisation 2, 1978.

X. Emery, The kriging update equations and their application to the selection of neighboring data, Computational Geosciences, vol.87, issue.3???4, pp.211-219, 2009.
DOI : 10.1007/s10596-008-9116-8

K. Fang, R. Li, and A. Sudjianto, Design and modeling for computer experiments, 2006.
DOI : 10.1201/9781420034899

A. I. Forrester, A. Sóbester, and A. J. Keane, Engineering design via surrogate modelling: a practical guide, 2008.
DOI : 10.1002/9780470770801

N. Gayton, J. M. Bourinet, and M. Lemaire, CQ2RS: a new statistical approach to the response surface method for reliability analysis, Structural Safety, vol.25, issue.1, pp.99-121, 2003.
DOI : 10.1016/S0167-4730(02)00045-0

A. Genz, Numerical Computation of Multivariate Normal Probabilities, Journal of Computational and Graphical Statistics, vol.1, issue.2, pp.141-149, 1992.
DOI : 10.1007/978-1-4613-9655-0

R. B. Gramacy and H. K. Lee, Gaussian processes and limiting linear models, Computational Statistics & Data Analysis, vol.53, issue.1, pp.123-136, 2008.
DOI : 10.1016/j.csda.2008.06.020
URL : http://arxiv.org/abs/0804.4685

Y. Hung, R. Joseph, V. Melkote, and S. , Analysis of Computer Experiments With Functional Response, Technometrics, vol.39, issue.1, 2012.
DOI : 10.1214/aos/1176346060

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

S. Kim and S. Na, Response surface method using vector projected sampling points, Structural Safety, vol.19, issue.1, pp.3-19, 1997.
DOI : 10.1016/S0167-4730(96)00037-9

A. Marrel, B. Iooss, F. Van-dorpe, and E. Volkova, An efficient methodology for modeling complex computer codes with Gaussian processes, Computational Statistics & Data Analysis, vol.52, issue.10, pp.4731-4744, 2008.
DOI : 10.1016/j.csda.2008.03.026
URL : https://hal.archives-ouvertes.fr/hal-00239492

W. Mebane and J. Sekhon, Genetic optimization using derivatives: The rgenoud package for r, Journal of Statistical Software, vol.42, issue.11, pp.1-26, 2011.

R. Paulo, G. García-donato, and J. Palomo, Calibration of computer models with multivariate output, Computational Statistics & Data Analysis, vol.56, issue.12, 2012.
DOI : 10.1016/j.csda.2012.05.023

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, 2010.
DOI : 10.1115/1.4001873
URL : https://hal.archives-ouvertes.fr/emse-00699752

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

Y. Richet, Y. Deville, and C. Chevalier, DiceView : Plot methods for computer experiments design and surrogate. URL http://cran.r-project, 2012.

J. Rougier, Efficient Emulators for Multivariate Deterministic Functions, Journal of Computational and Graphical Statistics, vol.17, issue.4, pp.827-843, 2008.
DOI : 10.1198/106186008X384032

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 URL, vol.51, 2012.
URL : https://hal.archives-ouvertes.fr/emse-00741762

R. Rubinstein and D. Kroese, The Cross-Entropy Method, 2004.

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.409-435, 1989.
DOI : 10.1214/ss/1177012413

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

Y. Zhao and T. Ono, A general procedure for first/second-order reliability method (form/sorm) Structural Safety 21, p.95, 1999.

R. J. References, J. E. Adler, and . Taylor, Random fields and geometry, p.80, 2007.

S. K. Au and J. Beck, Estimation of small failure probabilities in high dimensions by subset simulation, Probabilistic Engineering Mechanics, vol.16, issue.4, pp.263-277, 2001.
DOI : 10.1016/S0266-8920(01)00019-4

A. Azzalini, mnormt: The multivariate normal and t distributions, p.72, 2012.

. Baillargeon, Le krigeage, revue de la théorie et applicationàapplicationà l'interpolation spatiale de données de pr'ecipitations. Master's thesis, p.18, 2005.

J. Barnes and A. G. Watson, Efficient updating of kriging estimates and variances, Mathematical Geology, vol.24, issue.1, pp.129-133, 1992.
DOI : 10.1007/BF00890091

J. Lin and . Tu, A framework for validation of computer models, Technometrics, vol.49, issue.2, pp.138-154, 2007.

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, 2012.
DOI : 10.1007/s11222-011-9241-4
URL : https://hal.archives-ouvertes.fr/hal-00689580

J. Benassi, E. Bect, and . Vazquez, Robust Gaussian Process-Based Global Optimization Using a Fully Bayesian Expected Improvement Criterion, Lecture Notes in Computer Science, vol.24, issue.4, pp.176-190, 2011.
DOI : 10.1002/qre.945
URL : https://hal.archives-ouvertes.fr/hal-00607816

R. Bettinger, Inversion dun systeme par krigeage ApplicationàApplicationà la synthese de catalyseursàcatalyseursà haut débit, p.30, 2009.

J. Bichon, M. S. Eldred, L. P. Swiler, S. Mahadevan, and J. M. Mcfarland, Efficient Global Reliability Analysis for Nonlinear Implicit Performance Functions, AIAA Journal, vol.46, issue.10, pp.2459-2468, 2008.
DOI : 10.2514/1.34321

C. Chevalier and D. Ginsbourger, Fast Computation of the Multi-Points Expected Improvement with Applications in Batch Selection, Proceedings of the LION7 conference, p.26, 2013.
DOI : 10.1007/978-3-642-44973-4_7
URL : https://hal.archives-ouvertes.fr/hal-00732512

C. Chevalier, V. Picheny, and D. Ginsbourger, KrigInv: Kriging-based Inversion for Deterministic and Noisy Computer Experiments, 2012.

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. Accepted with minor revision to Technometrics, p.41, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00641108

C. Chevalier, D. Ginsbourger, J. Bect, and I. Molchanov, Estimating and quantifying uncertainties on level sets using the vorob'ev expectation and deviation with gaussian process models. mODa 10 Advances in Model-Oriented Design and Analysis, pp.2013-2050
URL : https://hal.archives-ouvertes.fr/hal-00731783

C. Chevalier, D. Ginsbourger, and X. Emery, Corrected Kriging Update Formulae for Batch-Sequential Data Assimilation, Proceedings of the IAMG2013 conference, p.79
DOI : 10.1007/978-3-642-32408-6_29
URL : https://hal.archives-ouvertes.fr/hal-00683362

C. Chevalier, V. Picheny, and D. Ginsbourger, KrigInv: An efficient and user-friendly implementation of batch-sequential inversion strategies based on kriging, Computational Statistics & Data Analysis, vol.71, p.51, 2013.
DOI : 10.1016/j.csda.2013.03.008
URL : https://hal.archives-ouvertes.fr/hal-00713537

J. Chiì-es and P. Delfiner, Geostatistics: Modeling Spatial Uncertainty, p.159, 2012.

W. J. Cody, Rational Chebyshev approximations for the error function, Mathematics of Computation, vol.23, issue.107, pp.631-637, 1969.
DOI : 10.1090/S0025-5718-1969-0247736-4

A. O. Conti and . Hagan, Bayesian emulation of complex multi-output and dynamic computer models, Journal of Statistical Planning and Inference, vol.140, issue.3, pp.640-651, 2010.
DOI : 10.1016/j.jspi.2009.08.006

N. Cressie, Statistics for spatial data, 1993.

A. S. Cressie, J. L. Davis, and . Folks, The moment-generating function and negative integer moments. The American Statistician, pp.148-150, 1981.

S. , D. Veiga, and A. Marrel, Gaussian process modeling with inequality constraints, Annales de la Faculté des Sciences de Toulouse, pp.529-555, 2012.

P. , D. Moral, A. Doucet, and A. Jasra, Sequential monte carlo samplers, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.68, issue.3, pp.411-436, 2006.

V. Dubourg, Métamodèles adaptatifs pour l'analyse de fiabilité et l'optimisation sous contrainte fiabiliste

B. Echard, N. Gayton, and M. Lemaire, AK-MCS: An active learning reliability method combining Kriging and Monte Carlo Simulation, Structural Safety, vol.33, issue.2, pp.145-154, 2011.
DOI : 10.1016/j.strusafe.2011.01.002

X. Emery, R. Fang, R. Li, and A. Sudjianto, The kriging update equations and their application to the selection of neighboring data Design and modeling for computer experiments, Computational Geosciences, vol.13, issue.1 23, pp.211-219, 2006.

F. Fernex, L. Heulers, O. Jacquet, J. Miss, and Y. Richet, The moret 4b monte carlo code -new features to treat complex criticality systems, M&C International Conference on Mathematics and Computation Supercomputing, Reactor Physics and Nuclear and Biological Application, p.59, 2005.

S. Finck, N. Hansen, R. Ros, and A. Auger, Real-parameter black-box optimization bencharking 2009: Presentation of the noiseless functions, 2009.

F. Fleuret and D. Geman, Graded learning for object detection, Proceedings of the workshop on Statistical and Computational Theories of Vision of the IEEE International Conference on Computer Vision and Pattern Recognition (CVPR/SCTV), 1999.

A. I. Forrester, A. Sóbester, and A. J. Keane, Engineering design via surrogate modelling: a practical guide, 2008.
DOI : 10.1002/9780470770801

P. I. Frazier, Parallel global optimization using an improved multi-points expected improvement criterion, INFORMS Optimization Society Conference, p.26

H. Gao, J. Wang, and P. Zhao, The updated kriging variance and optimal sample design, Mathematical Geology, vol.7, issue.no. 8, pp.295-313, 1996.
DOI : 10.1007/BF02083202

D. Geman and B. Jedynak, An active testing model for tracking roads in satellite images, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.18, issue.1, pp.1-14, 1996.
DOI : 10.1109/34.476006
URL : https://hal.archives-ouvertes.fr/inria-00073935

A. Genz, R. A. Genz, and F. Bretz, Numerical computation of multivariate normal probabilities Computation of multivariate normal and t probabilities, Journal of Computational and Graphical Statistics, vol.1, issue.195, pp.141-149, 1992.

A. Genz, F. Bretz, T. Miwa, X. Mi, F. Leisch et al., mvtnorm: Multivariate Normal and t Distributions, 2012. URL http://cran.r-project

. Ginsbourger, Métamodèles multiples pour l'approximation et l'optimisation de fonctions numériques multivariables, p.14, 2009.

D. Ginsbourger and R. Le-riche, Towards Gaussian Process-based Optimization with Finite Time Horizon, mODa 9?Advances in Model-Oriented Design and Analysis, pp.89-96, 2010.
DOI : 10.1007/978-3-7908-2410-0_12
URL : https://hal.archives-ouvertes.fr/emse-00680794

D. Ginsbourger, R. Le-riche, and L. Carraro, Kriging Is Well-Suited to Parallelize Optimization, Computational Intelligence in Expensive Optimization Problems, pp.14-79, 2010.
DOI : 10.1007/978-3-642-10701-6_6
URL : https://hal.archives-ouvertes.fr/emse-00436126

R. Girdziusas, J. Janusevskis, and . Le-riche, On integration of multi-point improvements, Neural Information Processing Systems (NIPS) workshop, p.26, 2012.

R. Gramacy and H. Lee, Gaussian processes and limiting linear models, Computational Statistics & Data Analysis, vol.53, issue.1, pp.123-136, 2008.
DOI : 10.1016/j.csda.2008.06.020

R. Gramacy and N. Polson, Particle Learning of Gaussian Process Models for Sequential Design and Optimization, Journal of Computational and Graphical Statistics, vol.20, issue.1, pp.102-118, 2011.
DOI : 10.1198/jcgs.2010.09171

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

M. Hamada, C. Martz, A. Reese, and . Wilson, Finding near-optimal bayesian experimental designs via genetic algorithms. The American Statistician, pp.175-181, 2001.
DOI : 10.1198/000313001317098121

N. Hansen, S. Finck, R. Ros, and A. Auger, Real-parameter black-box optimization bencharking 2009: Noiseless functions definitions, 2009.

M. Hoshiya, Kriging and Conditional Simulation of Gaussian Field, Journal of Engineering Mechanics, vol.121, issue.2, pp.181-186, 1995.
DOI : 10.1061/(ASCE)0733-9399(1995)121:2(181)

Y. Hung, V. R. Joseph, and S. N. Melkote, Analysis of Computer Experiments With Functional Response, Technometrics, vol.39, issue.1, 2012.
DOI : 10.1214/aos/1176346060

. Irsn, Analysis guide -nuclear criticality risks and their prevention in plants and laboratories

J. Janusevskis, R. Le-riche, and D. Ginsbourger, Parallel expected improvements for global optimization: summary, bounds and speed-up, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00613971

J. Janusevskis, R. Le-riche, D. Ginsbourger, and R. Girdziusas, Expected Improvements for the Asynchronous Parallel Global Optimization of Expensive Functions: Potentials and Challenges, LION 6 Conference (Learning and Intelligent OptimizatioN), 2012.
DOI : 10.1007/978-3-642-34413-8_37
URL : https://hal.archives-ouvertes.fr/emse-00686504

Y. Jin, Surrogate-assisted evolutionary computation: Recent advances and future challenges, Swarm and Evolutionary Computation, vol.1, issue.2, pp.61-70, 2011.
DOI : 10.1016/j.swevo.2011.05.001

D. R. Jones, A taxonomy of global optimization methods based on response surfaces, Journal of Global Optimization, vol.21, issue.4, pp.345-383, 2001.
DOI : 10.1023/A:1012771025575

S. Kim and S. Na, Response surface method using vector projected sampling points, Structural Safety, vol.19, issue.1, pp.3-19, 1997.
DOI : 10.1016/S0167-4730(96)00037-9

G. Matheron, The intrinsic random functions and their applications, Advances in Applied Probability, vol.98, issue.03, pp.439-468, 1973.
DOI : 10.1017/S0001867800039379

W. Mebane and J. Sekhon, Genetic optimization using derivatives: The rgenoud package for r, Journal of Statistical Software Issue, vol.42, issue.11, pp.1-26, 2011.

J. Mockus, Bayesian Approach to Global Optimization. Theory and Applications, 1989.

J. Mockus, V. Tiesis, and A. Zilinskas, The application of Bayesian methods for seeking the extremum, Towards Global Optimization, pp.117-129, 1978.

I. Molchanov, Theory of Random Sets, p.47, 2005.

M. D. Morris and T. J. Mitchell, Exploratory designs for computational experiments, Journal of Statistical Planning and Inference, vol.43, issue.3, pp.381-402, 1995.
DOI : 10.1016/0378-3758(94)00035-T

A. O. Hagan, Curve fitting and optimal design for prediction, Journal of the Royal Statistical Society. Series B (Methodological), vol.40, issue.1, pp.1-42, 1978.

M. B. Palacios and M. F. Steel, Non-Gaussian Bayesian Geostatistical Modeling, Journal of the American Statistical Association, vol.101, issue.474, pp.604-618, 2006.
DOI : 10.1198/016214505000001195

R. Paulo, G. García-donato, and J. Palomo, Calibration of computer models with multivariate output, Computational Statistics & Data Analysis, vol.56, issue.12, 2012.
DOI : 10.1016/j.csda.2012.05.023

V. Picheny, Improving accuracy and compensating for uncertainty in surrogate modeling, p.52, 2009.
URL : https://hal.archives-ouvertes.fr/tel-00770844

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.52, 2010.
DOI : 10.1115/1.4001873
URL : https://hal.archives-ouvertes.fr/emse-00699752

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

Y. Richet, Y. Deville, and C. Chevalier, DiceView : Plot methods for computer experiments design and surrogate, 2012. URL http://cran.r-project

Y. Richet, G. Caplin, J. Crevel, D. Ginsbouger, and V. Picheny, Using the Efficient Global Optimization Algorithm to Assist Nuclear Criticality Safety Assessment, Nuclear Science and Engineering, vol.175, issue.1, p.60, 2013.
DOI : 10.13182/NSE11-116

D. Brian and . Ripley, Stochastic simulation, p.159, 2009.

C. P. Robert and G. Casella, Monte Carlo Statistical Methods, p.53, 2004.

J. Rougier, Efficient Emulators for Multivariate Deterministic Functions, Journal of Computational and Graphical Statistics, vol.17, issue.4, pp.827-843, 2008.
DOI : 10.1198/106186008X384032

O. Roustant, D. Ginsbourger, and Y. Deville, Dicekriging, Diceoptim: Two R packages for the analysis of computer experiments by kriging-based metamodelling and optimization The Cross-Entropy Method, Journal of Statistical Software, vol.51, 2004.

R. Y. Rubinstein and D. P. Kroese, Simulation and the Monte Carlo method, 2008.

J. Sacks, S. Schiller, and S. , Spatial designs. Statistical decision theory and related topics IV, pp.385-399, 1988.

J. Sacks, S. B. Schiller, and W. J. Welch, Designs for Computer Experiments, Technometrics, vol.15, issue.18, pp.41-47, 1989.
DOI : 10.1080/00401706.1989.10488474

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.409-435, 1989.
DOI : 10.1214/ss/1177012413

J. Santner, B. J. Williams, and W. Notz, The Design and Analysis of Computer Experiments, p.7, 2003.
DOI : 10.1007/978-1-4757-3799-8

M. Schonlau, Computer Experiments and global optimization, p.79, 1997.

M. L. Stein, Interpolation of Spatial Data: Some Theory for Kriging, p.22, 1999.
DOI : 10.1007/978-1-4612-1494-6

G. M. Tallis, The moment generating function of the truncated multi-normal distribution, J. Roy. Statist. Soc. Ser. B, vol.23, issue.13, pp.223-229, 1961.

J. E. Taylor, K. J. Worsley, and F. Gosselin, Maxima of discretely sampled random fields, with an application to 'bubbles', Biometrika, vol.94, issue.1, pp.1-18, 2007.
DOI : 10.1093/biomet/asm004

A. Torn and A. Zilinskas, Global Optimization, 1989.
DOI : 10.1007/3-540-50871-6

E. Vazquez, Modélisation comportementale de systèmes non-linéaires multivariables par méthodesméthodesà noyaux et applications, p.159, 2005.

E. Vazquez and J. Bect, A sequential Bayesian algorithm to estimate a probability of failure, Proceedings of the 15th IFAC Symposium on System Identification , SYSID 2009 15th IFAC Symposium on System Identification, 2009.
DOI : 10.3182/20090706-3-FR-2004.00090
URL : https://hal.archives-ouvertes.fr/hal-00368158

E. Vazquez and M. Piera-martinez, Estimation of the volume of an excursion set of a Gaussian process using intrinsic Kriging, 2006.

E. Vazquez and M. Piera-martinez, Estimation du volume des ensembles d'excursion d'un processus gaussien par krigeage intrinsèque, 39ème Journées de Statistiques Conférence Journée de Statistiques, 2007.

J. Villemonteix, Optimisation de fonctions coûteuses, p.30, 2008.

O. Y. Vorobyev, Mean measure modeling, Nauka, p.46, 1984.

O. Y. Vorobyev and N. A. Lukyanova, A mean probability event for a set of events, Journal of Siberian Federal University. Mathematics and Physics, vol.6, issue.1, pp.128-136, 2013.

G. G. Wang and S. Shan, Review of Metamodeling Techniques in Support of Engineering Design Optimization, Journal of Mechanical Design, vol.129, issue.4, pp.370-380, 2006.
DOI : 10.1115/1.2429697

J. Welch, R. J. Buck, J. Sacks, H. P. Wynn, T. J. Mitchell et al., Screening, Predicting, and Computer Experiments, Technometrics, vol.34, issue.1, pp.15-25, 1992.
DOI : 10.2307/1269548

A. M. Yaglom, Correlation Theory of Stationary and Related Random Functions I: Basic Results. Springer Series in Statistics, p.20, 1986.

Y. Zhao and T. Ono, A general procedure for first/second-order reliability method (form/sorm) Structural Safety, p.95, 1999.

S. Nov, D. student -Lecturer Ph.D. in applied mathematics / statistics. Particular focus on Bayesian sequential evaluation strategies of multivariate functions, relying on Gaussian process models. Coordination of the ReDice consortium, http://www.redice-project.org/ gathering partners from industry and academia around innovative mathematical methods for the design and analysis of computer experiments, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00591048

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. Status: Accepted with minor revision to Technometrics, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00641108

D. Chevalier, J. Ginsbouger, I. Bect, and . Molchanov, Estimating and quantifying uncertainties on level sets using mODa 10 Advances in Model-Oriented Design and Analysis, 2013.

C. Chevalier and D. Ginsbouger, Fast Computation of the Multi-Points Expected Improvement with Applications in Batch Selection, Proceedings of the LION7 conference, 2013.
DOI : 10.1007/978-3-642-44973-4_7
URL : https://hal.archives-ouvertes.fr/hal-00732512

C. Chevalier, V. Picheny, and D. Ginsbourger, KrigInv: An efficient and user-friendly implementation of batch-sequential inversion strategies based on kriging, Computational Statistics & Data Analysis, vol.71, 2013.
DOI : 10.1016/j.csda.2013.03.008
URL : https://hal.archives-ouvertes.fr/hal-00713537

O. Mahlstein, C. Martius, D. Chevalier, and . Ginsbourger, Changes in the odds of extreme events in the Atlantic basin depending on the position of the extratropical jet CONFERENCES AND OTHER PRESENTATIONS, Geophysical research letters, vol.39, pp.10-1029, 2012.