S. Abramowitz, M. Abramowitz, and I. A. Stegun, Handbook of Mathematical Functions, American Journal of Physics, vol.34, issue.2, 1965.
DOI : 10.1119/1.1972842

D. H. Ackley, A connectionist machine for genetic hillclimbing, 1987.
DOI : 10.1007/978-1-4613-1997-9

. Archer, Sensitivity measures,anova-like Techniques and the use of bootstrap, Journal of Statistical Computation and Simulation, vol.2, issue.2, pp.99-120, 1997.
DOI : 10.1142/S0129183195000204

N. Aronszajn, Theory of reproducing kernels, Transactions of the American Mathematical Society, vol.68, issue.3, pp.337-404, 1950.
DOI : 10.1090/S0002-9947-1950-0051437-7

. Auer, Finite-time analysis of the multiarmed bandit problem, Machine Learning, vol.47, issue.2/3, pp.235-256, 2002.
DOI : 10.1023/A:1013689704352

. Auer, The Nonstochastic Multiarmed Bandit Problem, SIAM Journal on Computing, vol.32, issue.1, pp.48-77, 2002.
DOI : 10.1137/S0097539701398375

F. Bachoc, Cross Validation and Maximum Likelihood estimations of hyper-parameters of Gaussian processes with model misspecification, Computational Statistics & Data Analysis, vol.66, 2013.
DOI : 10.1016/j.csda.2013.03.016

C. T. Baker, The Numerical Treatment of Integral Equations, Journal of Applied Mechanics, vol.46, issue.4, 1977.
DOI : 10.1115/1.3424708

. Bates, Experimental design and observation for large systems, Journal of the Royal Statistical Society, Series B, vol.58, issue.1, pp.77-94, 1996.

. Bect, 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

. Bibliography and . Berger, Objective bayesian analysis of spatially correlated data objective bayesian analysis of spatially correlated data, Journal of the American Statistical Association, vol.96, pp.1361-1374, 2001.

T. Berlinet, A. Berlinet, and C. Thomas-agnan, Reproducing kernel Hilbert spaces in probability and statistics, 2004.
DOI : 10.1007/978-1-4419-9096-9

. Bichon, Efficient Global Reliability Analysis for Nonlinear Implicit Performance Functions, AIAA Journal, vol.46, issue.10, pp.462459-2468, 2008.
DOI : 10.2514/1.34321

. Bishop, Pattern recognition and machine learning, 2006.

E. Borgonovo, A new uncertainty importance measure, Reliability Engineering & System Safety, vol.92, issue.6, pp.771-784, 2007.
DOI : 10.1016/j.ress.2006.04.015

A. Boukouvalas and D. Cornford, Learning heteroscedastic gaussian processes for complex datasets, 2009.

F. Boyle, P. Boyle, and M. Frean, Dependent gaussian processes, Advances in Neural Information Processing Systems, pp.217-224, 2005.

J. C. Bronski, Asymptotics of Karhunen-Loeve Eigenvalues and Tight Constants for Probability Distributions of Passive Scalar Transport, Communications in Mathematical Physics, vol.238, issue.3, pp.563-582, 2003.
DOI : 10.1007/s00220-003-0835-3

. Chambers, Graphical Methods for Data Analysis, 1983.

. Chastaing, Generalized Hoeffding-Sobol decomposition for dependent variables - application to sensitivity analysis, Electronic Journal of Statistics, vol.6, issue.0, pp.2420-2448, 2012.
DOI : 10.1214/12-EJS749
URL : https://hal.archives-ouvertes.fr/hal-00649404

D. Chilès, J. Chilès, and P. Delfiner, Geostatistics: modeling spatial uncertainty. Wiley series in probability and statistics (Applied probability and statistics section), 1999.
DOI : 10.1002/9781118136188

O. Conti, S. Conti, O. Hagan, and A. , 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

. Cook, . Nachtrheim, R. D. Cook, and C. J. Nachtrheim, A Comparison of Algorithms for Constructing Exact D-Optimal Designs, Technometrics, vol.34, issue.2, pp.315-324, 1980.
DOI : 10.1080/00401706.1977.10489496

H. Cramer, Mathematical Methods of Statistics (PMS-9), 1999.
DOI : 10.1515/9781400883868

L. Cramer, H. Cramer, and M. Leadbetter, Stationary And Related Stochastic Processes, 1967.

G. Cumming, J. A. Cumming, and M. Goldstein, Small Sample Bayesian Designs for Complex High-Dimensional Models Based on Information Gained Using Fast Approximations, Technometrics, vol.51, issue.4, pp.377-388, 2009.
DOI : 10.1198/TECH.2009.08015

. Currin, Bayesian Prediction of Deterministic Functions, with Applications to the Design and Analysis of Computer Experiments, Journal of the American Statistical Association, vol.15, issue.416, pp.86953-963, 1991.
DOI : 10.1093/biomet/64.2.309

[. Veiga, Local Polynomial Estimation for Sensitivity Analysis on Models With Correlated Inputs, Technometrics, vol.51, issue.4, pp.452-463, 2009.
DOI : 10.1198/TECH.2009.08124
URL : https://hal.archives-ouvertes.fr/hal-00266102

. Dewettinck, Modeling the steady-state thermodynamic operation point of top-spray fluidized bed processing, Journal of Food Engineering, vol.39, issue.2, pp.131-143, 1999.
DOI : 10.1016/S0260-8774(98)00144-7

R. Diggle, P. Jr-]-diggle, R. Jr, and P. , Bayesian Inference in Gaussian Model-based Geostatistics, Geographical and Environmental Modelling, vol.92, issue.2, pp.129-146, 2002.
DOI : 10.1029/98WR00003

. Dubourg, Reliability-based design optimization using kriging surrogates and subset simulation. Structural and Multidisciplinary Optimization, pp.44-5673, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00587311

O. Dubrule, Cross validation of kriging in a unique neighborhood, Journal of the International Association for Mathematical Geology, vol.15, issue.6, pp.687-699, 1983.
DOI : 10.1007/BF01033232

R. M. Dudley, The sizes of compact subsets of Hilbert space and continuity of Gaussian processes, Journal of Functional Analysis, vol.1, issue.3, pp.290-330, 1967.
DOI : 10.1016/0022-1236(67)90017-1

N. Durrande, Etude de classes de noyaux adaptées à la simplification et à l'interprétation des modèles d'approximation, 2011.

G. Elfving, Optimum Allocation in Linear Regression Theory, The Annals of Mathematical Statistics, vol.23, issue.2, pp.255-262, 1952.
DOI : 10.1214/aoms/1177729442

. Fang, Design and Modeling for Computer Experiments, 2006.
DOI : 10.1201/9781420034899

V. V. Fedorov, Theory of optimal experiments, 1972.

V. V. Fedorov and P. Hackl, Model-oriented design of experiments, 1997.
DOI : 10.1007/978-1-4612-0703-0

. Fernex, The Moret 4b monte carlo code new features to treat complex criticality systems, MandC International Conference on Mathematics and Computation Supercomputing, Reactor and Nuclear and Biological Application, 2005.

X. Fernique, Continuité des processus gaussiens, CR Acad. Sci. Paris, vol.258, pp.6058-6060, 1964.

J. Ferreira and V. Menegatto, Eigenvalues of integral operators defined by smooth positive definite kernels. Integral Equations and Operator Theory, pp.61-81, 2009.

R. Fisher, Statistical methods and scientific inference, 1956.

. Forrester, Multi-fidelity optimization via surrogate modelling, Proc. R. Soc. A, pp.3251-3269, 2007.
DOI : 10.1098/rspa.2007.1900
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.332.1319

A. Garsia, Continuity properties of gaussian processes with multidimensional time parameter, Proc. Sixth Berkeley Symp. Math. Statist. Probab, pp.369-374, 1972.

. Geisser, . Eddy, S. Geisser, and W. Eddy, A Predictive Approach to Model Selection, Journal of the American Statistical Association, vol.39, issue.365, pp.74153-160, 1979.
DOI : 10.1080/01621459.1979.10481632

. Geweke, Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments. Federal Reserve Bank of Minneapolis, 1991.

M. N. Gibbs, Bayesian Gaussian Processes for Regression and Classification, 1997.

. Gikhman, I. Skorokhod-]-gikhman, and A. Skorokhod, The theory of stochastic processes, 1974.
DOI : 10.1007/978-3-642-61921-2

. Ginsbourger, Kriging is well-suited to parallelize optimization Adaptation Learning and Optimization, Computational Intelligence in Expensive Optimization Problems, pp.131-162, 2010.

. Gneiting, Mat??rn Cross-Covariance Functions for Multivariate Random Fields, Journal of the American Statistical Association, vol.105, issue.491, pp.1167-1177, 2010.
DOI : 10.1198/jasa.2010.tm09420

W. Goldstein, M. Goldstein, and D. A. Wooff, Bayes Linear Statistics: Theory and Methods, 2007.
DOI : 10.1002/9780470065662

. Gradshteyn, Table of integrals, series, and products, 2007.

. Gramacy, . Lian, 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

. Grégoire, A second-order turbulence model for gaseous mixtures induced by Richtmyer???Meshkov instability, Journal of Turbulence, vol.325, pp.1-20, 2005.
DOI : 10.1103/PhysRevLett.74.534

W. Hartigan, J. A. Hartigan, and M. A. Wong, Algorithm AS 136: A K-Means Clustering Algorithm, Applied Statistics, vol.28, issue.1, pp.100-108, 1979.
DOI : 10.2307/2346830

D. Harville, Bayesian inference for variance components using only error contrasts, Biometrika, vol.61, issue.2, pp.61383-385, 1974.
DOI : 10.1093/biomet/61.2.383

D. Harville, Maximum likelihood approaches to variance component estimation and to related problems, Journal of the American Statistical Association, issue.358, pp.72320-338, 1977.

D. A. Harville, Matrix Algebra from Statistician's Perspective, 1997.

. Higdon, Combining Field Data and Computer Simulations for Calibration and Prediction, SIAM Journal on Scientific Computing, vol.26, issue.2, pp.448-466, 2004.
DOI : 10.1137/S1064827503426693

. Higdon, A Bayesian calibration approach to the thermal problem, Computer Methods in Applied Mechanics and Engineering, vol.197, issue.29-32, pp.1972431-2441, 2008.
DOI : 10.1016/j.cma.2007.05.031

W. Hoeffding, A Class of Statistics with Asymptotically Normal Distribution, The Annals of Mathematical Statistics, vol.19, issue.3, pp.293-325, 1948.
DOI : 10.1214/aoms/1177730196

. Bibliography and . Huang, Sequential kriging optimization using multiple-fidelity evaluations. Structural and Multidisciplinary Optimization, pp.369-382, 2006.

Y. Huang and K. Chan, A Modified Efficient Global Optimization Algorithm for Maximal Reliability in a Probabilistic Constrained Space, Journal of Mechanical Design, vol.132, issue.6, p.61002, 2010.
DOI : 10.1115/1.4001532

. Iooss, Response surfaces and sensitivity analyses for an environmental model of dose calculations, Reliability Engineering & System Safety, vol.91, issue.10-11, pp.911241-1251, 2006.
DOI : 10.1016/j.ress.2005.11.021

. Janon, UNCERTAINTIES ASSESSMENT IN GLOBAL SENSITIVITY INDICES ESTIMATION FROM METAMODELS, International Journal for Uncertainty Quantification, vol.4, issue.1, 2011.
DOI : 10.1615/Int.J.UncertaintyQuantification.2012004291
URL : https://hal.archives-ouvertes.fr/inria-00567977

L. Janusevskis, . Riche, J. Janusevskis, L. Riche, and R. , Simultaneous kriging-based estimation and optimization of mean response, Journal of Global Optimization, vol.10, issue.4, pp.313-336, 2013.
DOI : 10.1007/s10898-011-9836-5
URL : https://hal.archives-ouvertes.fr/emse-00674460

H. Jeffreys, An Invariant Form for the Prior Probability in Estimation Problems, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.186, issue.1007, pp.186453-461, 1007.
DOI : 10.1098/rspa.1946.0056

H. Jeffreys, Theory of Probability, 1961.

. Jones, Efficient global optimization of expensive black-box functions, Biometrika, vol.13, pp.455-492, 1998.

J. , J. Jordan, M. I. Jacobs, and R. A. , Hierarchical mixtures of experts and the em algorithm, Neural computation, vol.6, issue.2, pp.181-214, 1994.

L. P. Kaelbling, Learning in embedded systems, 1993.

T. Kailath, RKHS approach to detection and estimation problems--I: Deterministic signals in Gaussian noise, IEEE Transactions on Information Theory, vol.17, issue.5, pp.530-549, 1971.
DOI : 10.1109/TIT.1971.1054673

W. Karush, Minima of functions of several variables with inequalities as side constraints, 1939.

O. Kennedy, M. C. Kennedy, O. Hagan, and A. , Predicting the output from a complex computer code when fast approximations are available, Biometrika, vol.87, issue.1, pp.1-13, 2000.
DOI : 10.1093/biomet/87.1.1

O. Kennedy, M. C. Kennedy, O. Hagan, and A. , Bayesian calibration of computer models, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.63, issue.3, pp.425-464, 2001.
DOI : 10.1111/1467-9868.00294

J. Kiefer, Optimum designs in regression problems, ii. The Annals of Mathematical Statistics, pp.298-325, 1961.

. Kiefer, . Wolfowitz, J. Kiefer, and J. Wolfowitz, Optimum Designs in Regression Problems, The Annals of Mathematical Statistics, vol.30, issue.2, pp.271-294, 1959.
DOI : 10.1214/aoms/1177706252

. Kimeldorf, . Wahba, G. Kimeldorf, and G. Wahba, Some results on Tchebycheffian spline functions, Journal of Mathematical Analysis and Applications, vol.33, issue.1, pp.82-95, 1971.
DOI : 10.1016/0022-247X(71)90184-3

. Kleijnen, J. Van-beers-]-kleijnen, and W. Van-beers, Application-driven sequential designs for simulation experiments: Kriging metamodelling, Journal of the Operational Research Society, vol.17, issue.2, pp.876-883, 2004.
DOI : 10.1007/PL00007198

J. P. Kleijnen, Design and analysis of monte carlo experiments, Handbook of Computational Statistics, pp.529-547, 2012.

V. Kleijnen, J. P. Beers-]-kleijnen, and W. Van-beers, Robustness of Kriging when interpolating in random simulation with heterogeneous variances: Some experiments, European Journal of Operational Research, vol.165, issue.3, pp.826-834, 2005.
DOI : 10.1016/j.ejor.2003.09.037

O. Koehler, J. Koehler, and A. Owen, Computer experiments. Handbook of statistics, pp.261-308, 1996.

H. König, Eigenvalue distribution of compact operators, 1986.
DOI : 10.1007/978-3-0348-6278-3

D. G. Krige, A statistical approach to some basic mine valuation problems on the witwatersrand, Technometrics, vol.52, pp.119-139, 1951.

. Kucherenko, Estimation of global sensitivity indices for models with dependent variables, Computer Physics Communications, vol.183, issue.4, pp.937-946, 2012.
DOI : 10.1016/j.cpc.2011.12.020

T. Kuhn, H. W. Kuhn, and A. W. Tucker, Nonlinear programming, Second Berkeley symposium on mathematical statistics and probability, pp.481-492, 1951.

G. M. Laslett, Kriging and Splines: An Empirical Comparison of their Predictive Performance in Some Applications, Journal of the American Statistical Association, vol.44, issue.426, pp.391-400, 1994.
DOI : 10.1007/BF00893314

]. Gratiet and L. , Bayesian Analysis of Hierarchical Multifidelity Codes, SIAM/ASA Journal on Uncertainty Quantification, vol.1, issue.1, pp.244-269, 2013.
DOI : 10.1137/120884122
URL : https://hal.archives-ouvertes.fr/hal-00654716

C. Lehmann, E. L. Lehmann, and G. Casella, Theory of Point Estimation, 1998.

. Li, Global Sensitivity Analysis for Systems with Independent and/or Correlated Inputs, The Journal of Physical Chemistry A, vol.114, issue.19, pp.6022-6032, 2010.
DOI : 10.1021/jp9096919

. Li, Bayesian subset simulation: a krigingbased subset simulation algorithm for the estimation of small probabilities of failure. arXiv preprint arXiv, p.1207, 1963.
URL : https://hal.archives-ouvertes.fr/hal-00715316

J. S. Liu, Monte-Carlo Strategies in Scientific Computing, 2001.
DOI : 10.1007/978-0-387-76371-2

J. Macqueen, Some methods for classification and analysis of multivariate observations, Proc. 5th Berkeley Symp. on Math, 1967.

T. Mannor, S. Mannor, and J. N. Tsitsiklis, The sample complexity of exploration in the multi-armed bandit problem, The Journal of Machine Learning Research, vol.5, pp.623-648, 2004.

M. , T. Mara, T. Tarantola, and S. , Variance-based sensitivity analysis of computer models with dependent inputs, Reliability Engineering & System Safety, vol.107, pp.115-121, 2012.

S. Marcus, M. Marcus, and L. Shepp, Continuity of Gaussian processes, Transactions of the American Mathematical Society, vol.151, issue.2, pp.377-391, 1970.
DOI : 10.1090/S0002-9947-1970-0264749-1

. Marrel, Global sensitivity analysis of stochastic computer models with joint metamodels, Statistics and Computing, vol.44, issue.1, pp.1-15, 2010.
DOI : 10.1007/s11222-011-9274-8
URL : https://hal.archives-ouvertes.fr/hal-00232805

. Marrel, Calculations of Sobol indices for the Gaussian process metamodel, Reliability Engineering & System Safety, vol.94, issue.3, pp.742-751, 2009.
DOI : 10.1016/j.ress.2008.07.008
URL : https://hal.archives-ouvertes.fr/hal-00239494

. Marseguerra, Variance decomposition-based sensitivity analysis via neural networks, Reliability Engineering & System Safety, vol.79, issue.2, pp.79229-238, 2003.
DOI : 10.1016/S0951-8320(02)00234-X

. Marzat, Worst-case global optimization of black-box functions through Kriging and relaxation, Journal of Global Optimization, vol.14, issue.6, pp.1-21, 2012.
DOI : 10.1007/s10898-012-9899-y
URL : https://hal.archives-ouvertes.fr/hal-00682475

B. Matérn, Spatial Variation, 1986.
DOI : 10.1007/978-1-4615-7892-5

G. Matheron, Principles of geostatistics, Economic Geology, vol.58, issue.8, pp.1246-1266, 1963.
DOI : 10.2113/gsecongeo.58.8.1246

. Mcfarland, Calibration and uncertainty analysis for computer simulations with multivariate output, AIAA journal, issue.5, pp.461253-1265, 2008.

J. Mercer, Functions of positive and negative type and their connection with the theory of integral equations, Philosophical Transactions of the Royal Society A, vol.209, pp.441-458, 1909.

. Meuleau, . Bourgine, N. Meuleau, and P. Bourgine, Exploration of multistate environments: Local measures and back-propagation of uncertainty, Machine Learning, pp.117-154, 1999.

Z. Michalewicz, Genetic Algorithms + Data Structures = Evolution Programs, 1992.

. Mitchell, Asymptotically optimum experimental designs for prediction of deterministic functions given derivative information, Journal of Statistical Planning and Inference, vol.41, issue.3, pp.41377-389, 1994.
DOI : 10.1016/0378-3758(94)90030-2

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

J. Mockus, Bayesian heuristic approach to global optimization and examples, Journal of Global Optimization, vol.22, pp.1-4191, 2002.

Z. Molchanov, I. Molchanov, and S. Zuyev, Steepest descent algorithms in a space of measures, Statistics and Computing, vol.12, issue.2, pp.115-123, 2002.
DOI : 10.1023/A:1014878317736

. Morris, Bayesian Design and Analysis of Computer Experiments: Use of Derivatives in Surface Prediction, Technometrics, vol.15, issue.3, pp.35243-255, 1993.
DOI : 10.1080/00401706.1992.10485229

[. Zuniga, Adaptive directional stratification for controlled estimation of the probability of a rare event, Reliability Engineering & System Safety, vol.96, issue.12, pp.1691-1712, 2011.
DOI : 10.1016/j.ress.2011.06.016

S. Nash, J. Nash, and J. Sutcliffe, River flow forecasting through conceptual models part I ??? A discussion of principles, Journal of Hydrology, vol.10, issue.3, pp.282-290, 1970.
DOI : 10.1016/0022-1694(70)90255-6

A. I. Nazarov and Y. Y. Nikitin, Exact l 2 -small ball behaviour of integrated Gaussian processes and spectral asymptotics of boundary value problems, pp.469-494, 2004.

J. Oakley, Estimating percentiles of uncertain computer code outputs, Journal of the Royal Statistical Society: Series C (Applied Statistics), vol.14, issue.1, pp.83-93, 2004.
DOI : 10.1111/1467-9884.00300

O. Oakley, J. E. Oakley, O. Hagan, and A. , Probabilistic sensitivity analysis of complex models: a Bayesian approach, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.34, issue.3, pp.751-769, 2004.
DOI : 10.1214/ss/1009213004

A. O-'hagan-]-o-'hagan, A Markov property for covariance structures, 1998.

A. O-'hagan-]-o-'hagan, Bayesian analysis of computer code outputs: A tutorial, Reliability Engineering & System Safety, issue.10, pp.911290-1300, 2006.

B. Oksendal, Stochastic differential equations, 1998.
URL : https://hal.archives-ouvertes.fr/inria-00560229

V. Opper, M. Opper, and F. Vivarelli, General bounds on Bayes errors for regression with Gaussian processes, Advances in Neural Information Processing Systems 11, pp.302-308, 1999.

T. Patterson, H. Patterson, and . Thompson, Recovery of inter-block information when block sizes are unequal, Biometrika, vol.58, issue.3, pp.545-554, 1971.
DOI : 10.1093/biomet/58.3.545

W. Picard, R. Picard, and B. Williams, Rare event estimation for computer models. The American Statistician, pp.22-32, 2013.

V. Picheny, Improving Accuracy and Compensating for Uncertainty in Surrogate Modeling, 2009.
URL : https://hal.archives-ouvertes.fr/tel-00770844

. Picheny, Adaptive Designs of Experiments for Accurate Approximation of a Target Region, Journal of Mechanical Design, vol.132, issue.7, pp.71008-71009, 2010.
DOI : 10.1115/1.4001873
URL : https://hal.archives-ouvertes.fr/emse-00699752

R. S. Pusev, Small Deviations Asymptotics for Mat??rn Processes and Fields under Weighted Quadratic Norm, Theory of Probability & Its Applications, vol.55, issue.1, pp.164-172, 2011.
DOI : 10.1137/S0040585X97984723

. Qian, Construction of nested space-filling designs. The Annals of Statistics, pp.3616-3643, 2009.

W. Qian, P. Z. Qian, and C. F. Wu, Bayesian Hierarchical Modeling for Integrating Low-Accuracy and High-Accuracy Experiments, Technometrics, vol.50, issue.2, pp.192-204, 2008.
DOI : 10.1198/004017008000000082

R. C. Rao, Information and the Accuracy Attainable in the Estimation of Statistical Parameters, Bulletin of the Calcutta Mathematical Society, vol.37, issue.3, pp.81-91, 1945.
DOI : 10.1007/978-1-4612-0919-5_16

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

K. Ritter, Almost Optimal Differentiation Using Noisy Data, Journal of Approximation Theory, vol.86, issue.3, pp.293-309, 2000.
DOI : 10.1006/jath.1996.0071

K. Ritter, Average-Case Analysis of Numerical Problems, 2000.
DOI : 10.1007/BFb0103934

H. Robbins, Some aspects of the sequential design of experiments, Bulletin of the American Mathematical Society, vol.58, issue.5, pp.527-535, 1952.
DOI : 10.1090/S0002-9904-1952-09620-8

C. Robert, The Bayesian choice: from decision-theoretic foundations to computational implementation, 2007.
DOI : 10.1007/978-1-4757-4314-2

. Roustant, Packages for the Analysis of Computer Experiments by Kriging-Based Metamodeling and Optimization, Journal of Statistical Software, vol.51, issue.1, pp.1-55, 2012.
DOI : 10.18637/jss.v051.i01
URL : https://hal.archives-ouvertes.fr/hal-00495766

. Sacks, Designs for Computer Experiments, Technometrics, vol.15, issue.18, pp.3141-3188, 1989.
DOI : 10.1080/00401706.1989.10488474

. Sacks, Design and Analysis of Computer Experiments, Statistical Science, vol.4, issue.4, pp.409-423, 1989.
DOI : 10.1214/ss/1177012413

J. Sacks and D. Ylvisaker, Variance estimation for approximately linear models, Series Statistics, vol.6, issue.2, pp.147-162, 1981.
DOI : 10.1080/02331888108801577

. Saltelli, Sensitivity Analysis, Series in Probability and Statistics, 2000.
URL : https://hal.archives-ouvertes.fr/inria-00386559

. Santner, The Design and Analysis of Computer Experiments, 2003.
DOI : 10.1007/978-1-4757-3799-8

I. J. Schoeneberg, metric space and positive definite function. Trans, pp.522-536, 1938.

D. F. Shanno, Conditioning of quasi-Newton methods for function minimization, Mathematics of Computation, vol.24, issue.111, pp.647-656, 1970.
DOI : 10.1090/S0025-5718-1970-0274029-X

. Shewry, . Wynn, M. C. Shewry, and H. P. Wynn, Maximum entropy sampling, Journal of Applied Statistics, vol.14, issue.2, pp.165-170, 1987.
DOI : 10.2307/2987990

. Sobol, Estimating the approximation error when fixing unessential factors in global sensitivity analysis, Reliability Engineering & System Safety, vol.92, issue.7, pp.92957-960, 2007.
DOI : 10.1016/j.ress.2006.07.001

I. M. Sobol, Sensitivity estimates for non linear mathematical models, Mathematical Modelling and Computational Experiments, vol.1, pp.407-414, 1993.

H. Sollich, P. Sollich, and A. Halees, Learning Curves for Gaussian Process Regression: Approximations and Bounds, Neural Computation, vol.47, issue.1, pp.1393-1428, 2002.
DOI : 10.1023/A:1007601601278

M. L. Stein, Large Sample Properties of Simulations Using Latin Hypercube Sampling, Technometrics, vol.17, issue.2, pp.143-151, 1987.
DOI : 10.1080/00401706.1987.10488205

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

R. Stocki, A method to improve design reliability using optimal latin hypercube sampling, Computer Assisted Mechanics and Engineering Sciences, vol.12, pp.87-105, 2005.

R. A. Todor, Robust Eigenvalue Computation for Smoothing Operators, SIAM Journal on Numerical Analysis, vol.44, issue.2, pp.865-878, 2006.
DOI : 10.1137/040616449

G. Ueda, N. Ueda, and Z. Ghahramani, Bayesian model search for mixture models based on optimizing variational bounds, Neural Networks, vol.15, issue.10, pp.1223-1242, 2002.
DOI : 10.1016/S0893-6080(02)00040-0

G. E. Uhlenbeck and L. S. Ornstein, On the Theory of the Brownian Motion, Physical Review, vol.36, issue.5, p.823, 1930.
DOI : 10.1103/PhysRev.36.823

M. A. Schuëller and G. I. , A survey on approaches for reliability-based optimization. Structural and Multidisciplinary Optimization, pp.645-663, 2010.

W. Beers and J. Kleijnen, Customized sequential designs for random simulation experiments: Kriging metamodeling and bootstrapping, European Journal of Operational Research, vol.186, issue.3, pp.1099-1113, 2008.
DOI : 10.1016/j.ejor.2007.02.035

A. W. Van-der-vaart, Asymptotic Statistics, 1998.
DOI : 10.1017/CBO9780511802256

. Van-oijen, Bayesian calibration of process-based forest models: bridging the gap between models and data, Tree Physiology, vol.25, issue.7, pp.25915-927, 2005.
DOI : 10.1093/treephys/25.7.915

E. Vazquez, Modélisation comportementale de systèmes non-linéaires multivariables par méthodes à noyaux et applications, 2005.

E. Vazquez and J. Bect, Convergence properties of the expected improvement algorithm with fixed mean and covariance functions, Journal of Statistical Planning and Inference, vol.140, issue.11, pp.1403088-3095, 2010.
DOI : 10.1016/j.jspi.2010.04.018
URL : https://hal.archives-ouvertes.fr/hal-00217562

M. Vermorel, J. Vermorel, and M. Mohri, Multi-armed Bandit Algorithms and Empirical Evaluation, Machine Learning: ECML 2005, pp.437-448, 2005.
DOI : 10.1007/11564096_42

. Villemonteix, An informational approach to the global optimization of expensive-to-evaluate functions, Journal of Global Optimization, vol.10, issue.5, pp.509-534, 2009.
DOI : 10.1007/s10898-008-9354-2
URL : https://hal.archives-ouvertes.fr/hal-00354262

G. Wahba, Spline models for observational data, 1990.
DOI : 10.1137/1.9781611970128

. Waterhouse, Bayesian methods for mixtures of experts Advances in neural information processing systems, pp.351-357, 1996.

C. J. Watkins, Learning from delayed rewards, 1989.

R. D. Wilkinson, Bayesian calibration of expensive multivariate computer experiments. Large-Scale Inverse Problems and Quantification of Uncertainty, Comput. Stat, pp.195-216, 2010.

. Williams, Sequential design of computer experiments to minimize integrated response functions, Statistica Sinica, vol.10, issue.4, pp.1133-1152, 2000.

V. Williams, C. K. Williams, and F. Vivarelli, Upper and lower bounds on the learning curve for Gaussian processes, Machine Learning, pp.77-102, 2000.

C. Wu, Some algorithmic aspects of the theory of optimal designs. The Annals of Statistics, pp.1286-1301, 1978.

J. Wyatt, Exploration and inference in learning from reinforcement, 1998.

L. Xian, Finding global minima with a computable filled function, Journal of Global Optimization, vol.19, pp.191-204, 2001.

Q. Xiong, S. Xiong, . Qian, Z. G. Peter, J. Wu et al., Sequential Design and Analysis of High-Accuracy and Low-Accuracy Computer Codes, Technometrics, vol.34, issue.1, 2012.
DOI : 10.1080/00401706.2012.723572

. Yin, Kriging metamodel with modified nuggeteffect: The heteroscedastic variance case, Computers & Industrial Engineering, issue.3, pp.61760-777, 2011.

H. Zhang and Y. Wang, Kriging and cross-validation for massive spatial data, Environmetrics, vol.23, issue.1, pp.290-304, 2009.
DOI : 10.1002/env.1023

. Zhu, Gaussian regression and optimal finite dimensional linear models, 1998.

L. Gratiet, L. Siam, and A. J. , Bayesian Analysis of Hierarchical Multifidelity Codes, SIAM/ASA Journal on Uncertainty Quantification, vol.1, issue.1, pp.244-269, 2013.
DOI : 10.1137/120884122
URL : https://hal.archives-ouvertes.fr/hal-00654716

L. Gratiet, L. Garnier, and J. , Regularity dependence of the rate of convergence of the learning curve for Gaussian process regression, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00737342

L. Gratiet and L. , Asymptotic normality of a Sobol index estimator in Gaussian process regression framework, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00828596

L. Package-le-gratiet, MuFiCokriging : Multi-Fidelity Cokriging models, CRAN - Package MuFiCokriging, 2012.

L. Ensuite and . Thèsé-etudie-une-conjecture-sur-la-dépendance-de-la-courbe, apprentissage (c'estàestà dire le taux de décroissance de l'erreur quadratique moyenne) par rapportàrapportà la régularité de la fonctionàfonctionà approcher Une preuve dans un cadre général (qui comprend les modèles classiques de régression par processus gaussiens avec noyaux stationnaires) a ´ eté obtenue , tandis que les preuves précédentes ne sont valides que pour des noyaux dégénérés (c'està està dire quand le processus est de dimension finie) Ce résultat permet d'aborder des questions pratiques telles que l