K. Fang, R. Li, and A. Et-sudjianto, Design and Modeling for Computer Experiments . Computer Science and Data Analysis, 2006.

K. T. Fang, D. K. Lin, P. Winker, and Y. Et-zhang, Uniform Design: Theory and Application, Technometrics, vol.34, issue.3, pp.237-248, 2000.
DOI : 10.1016/0167-9473(94)00041-G

K. T. Fang and Y. Wang, Number-Theoretic Methods in Statistics, 1994.
DOI : 10.1007/978-1-4899-3095-8

R. Fisher, Design of Experiments, BMJ, vol.1, issue.3923, 1971.
DOI : 10.1136/bmj.1.3923.554-a

J. H. Friedman, Multivariate Adaptive Regression Splines, The Annals of Statistics, vol.19, issue.1, pp.1-141, 1991.
DOI : 10.1214/aos/1176347963
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.382.970

A. Haldar and S. Et-mahadevan, Reliability Assessment Using Stochastic Finite Element Analysis, 2000.

T. Hastie, R. Tibshirani, and J. Et-friedman, The Elements of Statistical Learning, 2001.

A. E. Hoerl and R. W. Et-kennard, Ridge Regression: Biased Estimation for Nonorthogonal Problems, Technometrics, vol.24, issue.1, pp.55-67, 1970.
DOI : 10.2307/1909769

R. Jin, W. Chen, and A. Et-sudjianto, An efficient algorithm for constructing optimal design of computer experiments, Journal of Statistical Planning and Inference, vol.134, issue.1, pp.268-287, 2005.
DOI : 10.1016/j.jspi.2004.02.014

M. E. Johnson, L. M. Moore, and D. Et-ylvisaker, Minimax and maximin distance designs, Journal of Statistical Planning and Inference, vol.26, issue.2, pp.131-148, 1990.
DOI : 10.1016/0378-3758(90)90122-B

D. R. Jones, M. Schonlau, and W. J. Welch, 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

V. R. Joseph and Y. Et-hung, Orthogonal-maximin latin hypercube designs, Statistica Sinica, vol.18, pp.171-186, 2008.

M. C. Kennedy and A. Et-o-'hagan, 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

G. Kimeldorf and G. Et-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

J. P. Kleijnen, Statistical Tools for Simulation Practitioners, 1987.

J. R. Koehler and A. B. Et-owen, Computer experiments. In Design and analysis of experiments, de Handbook of Statistics, pp.261-308, 1996.

D. Krige, A statistical approach to some mine valuations and allied problems at the witwatersrand, 1951.

R. Li and A. Et-sudjianto, Analysis of Computer Experiments Using Penalized Likelihood in Gaussian Kriging Models, Technometrics, vol.47, issue.2, pp.111-120, 2005.
DOI : 10.1198/004017004000000671

N. Lophaven, H. Nielsen, and J. Et-sondergaard, Aspects of the matlab toolbox dace. Rapport technique IMM-REP-2002-13, Informatics and Mathematical Modelling, DTU. Available as http, 2002.

. Dace, Rapport technique IMM-TR-2002-12, DTU. Available to

S. D. Marchi and R. Et-schaback, Stability of kernel-based interpolation, Advances in Computational Mathematics, 2008.
DOI : 10.1007/s10444-008-9093-4

A. Marrel, B. Iooss, B. Laurent, and O. Et-roustant, Calculations of sobol indices for the gaussian process metamodel. Reliability engineering & systems safety, pp.742-751, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00239494

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

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

M. D. Mckay, R. J. Beckman, and W. J. Et-conover, A comparison of three methods for selecting values of input variables in the analysis of output from a computer code, Technometrics, vol.21, issue.2, pp.239-245, 1979.

J. Mercer, Functions of Positive and Negative Type, and their Connection with the Theory of Integral Equations, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.209, issue.441-458, pp.415-446, 1909.
DOI : 10.1098/rsta.1909.0016

T. Mitchell, M. Morris, and D. Et-ylvisaker, Existence of smoothed stationary processes on an interval, Stochastic Processes and Their Application, pp.109-119, 1990.
DOI : 10.1016/0304-4149(90)90126-D

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
URL : http://www.osti.gov/scitech/servlets/purl/10184343

M. D. Morris, T. J. Mitchell, and D. Et-ylvisaker, Bayesian Design and Analysis of Computer Experiments: Use of Derivatives in Surface Prediction, Technometrics, vol.15, issue.3, pp.243-255, 1993.
DOI : 10.1080/00401706.1992.10485229

H. Niederreiter, Random Number Generation and Quasi-Monte Carlo Methods, 1992.
DOI : 10.1137/1.9781611970081

A. B. Owen, Randomly orthogonal arrays for computer experiments, integration and visualization, Statistica Sinica, vol.2, pp.439-452, 1992.

H. D. Patterson and R. Et-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

N. S. Pillai, Q. Wu, F. Liang, S. Mukherjee, and R. L. Et-wolpert, Characterizing the function space for bayesian kernel models, Journal of Machine Learning Research, vol.8, pp.1769-1797, 2007.

M. J. Powell, Radial basis functions for multivariable interpolation : a review, editeurs : Algorithm for Approximation, pp.143-167, 1987.

N. G. Prasad and J. N. Et-rao, The Estimation of the Mean Squared Error of Small-Area Estimators, Journal of the American Statistical Association, vol.3, issue.409, pp.163-171, 1990.
DOI : 10.1002/9780470316436

E. Rafajlowicz and R. Et-schwabe, Halton and Hammersley sequences in multivariate nonparametric regression, Statistics & Probability Letters, vol.76, issue.8, pp.76803-812, 2006.
DOI : 10.1016/j.spl.2005.10.014

C. R. Rao, Linear Statistical Inference and its Applications, 1973.
DOI : 10.1002/9780470316436

J. Sacks, S. B. Schiller, T. J. Mitchell, and H. P. Et-wynn, Design and analysis of computer experiments (with discussion), Statistica Sinica, vol.4, pp.409-435, 1989.

J. Sacks, S. B. Schiller, and W. J. Welch, Designs for Computer Experiments, Technometrics, vol.15, issue.18, pp.3141-3188, 1989.
DOI : 10.1080/00401706.1989.10488474

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

R. Schaback, Comparison of Radial Basis Function Interpolants, Multivariate Approximation: From CAGD to Wavelets, pp.293-305, 1995.
DOI : 10.1142/9789814503754_0018

R. Schaback, Error estimates and condition numbers for radial basis function interpolation, Advances in Computational Mathematics, vol.4, issue.3, pp.251-264, 1995.
DOI : 10.1007/BF02432002

R. Schaback, Kernel-based meshless methods. Rapport technique, 2007.

B. Schölkopf and A. J. Et-smola, Learning with Kernels : Support Vector Machines, Regularization, Optimization, and Beyond, 2001.

T. W. Simpson, J. D. Peplinski, P. N. Koch, and J. K. Et-allen, Metamodels for Computer-based Engineering Design: Survey and recommendations, Engineering with Computers, vol.17, issue.2, pp.129-150, 2001.
DOI : 10.1007/PL00007198

I. M. Sobol, Sensitivity analysis for nonlinear mathematical models, Mathematical Modeling and Computational Experiment, vol.1, pp.407-414, 1993.

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 : Some Theory for Kriging, 1999.
DOI : 10.1007/978-1-4612-1494-6

C. J. Stone, M. H. Hansen, C. Kooperberg, and Y. K. Et-truong, Polynomial splines and their tensor products in extended linear modeling, Annals of Statistics, vol.25, pp.1371-1470, 1997.

Y. Tang, Orthogonal Array-Based Latin Hypercubes, Journal of the American Statistical Association, vol.2, issue.424, pp.1392-1397, 1993.
DOI : 10.1214/aos/1176347399

B. Bartoli, N. , D. Moral, and P. , Simulation & algorithmes stochastiques, 2001.

D. Bursztyn and D. M. Steinberg, Comparison of designs for computer experiments, Journal of Statistical Planning and Inference, vol.136, issue.3, 2006.
DOI : 10.1016/j.jspi.2004.08.007

S. Chib and E. Greenberg, Understanding the metropolis-hastings algorithm. The American Statistician, pp.327-335, 1995.

N. Cressie, Statistics for Spatial Data, 1993.

D. Den-hertog, J. P. Kleijnen, and A. Y. Siem, The correct Kriging variance estimated by bootstrapping, Journal of the Operational Research Society, vol.30, issue.4, pp.400-409, 2006.
DOI : 10.1111/1467-9469.00325

K. Fang, R. Li, and A. Sudjianto, Design and Modeling for Computer Experiments . Computer Science and Data Analysis, 2006.

V. R. Joseph, Limit Kriging, Technometrics, vol.48, issue.4, pp.458-466, 2006.
DOI : 10.1198/004017006000000011

J. R. Koehler and A. B. Owen, Computer experiments. In Design and analysis of experiments, of Handbook of Statistics, pp.261-308, 1996.

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.391-409, 1994.
DOI : 10.1007/BF00893314

R. Li and A. Sudjianto, Analysis of Computer Experiments Using Penalized Likelihood in Gaussian Kriging Models, Technometrics, vol.47, issue.2, pp.111-120, 2005.
DOI : 10.1198/004017004000000671

W. R. Madych and S. A. Nelson, Bounds on multivariate polynomials and exponential error estimates for multiquadric interpolation, Journal of Approximation Theory, vol.70, issue.1, pp.94-114, 1992.
DOI : 10.1016/0021-9045(92)90058-V

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

M. D. Mckay, R. J. Beckman, and W. J. Conover, A comparison of three methods for selecting values of input variables in the analysis of output from a computer code, Technometrics, vol.21, issue.2, pp.239-245, 1979.

J. Sacks, S. B. Schiller, T. J. Mitchell, W. , and H. P. , Design and analysis of computer experiments (with discussion), Statistica Sinica, vol.4, pp.409-435, 1989.

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

R. Schaback, Error estimates and condition numbers for radial basis function interpolation, Advances in Computational Mathematics, vol.4, issue.3, pp.251-264, 1995.
DOI : 10.1007/BF02432002
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.45.8132

R. Schaback, Kernel-based meshless methods, 2007.

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

M. L. Stein, The screening effect in Kriging, The Annals of Statistics, vol.30, issue.1, pp.298-323, 2002.
DOI : 10.1214/aos/1015362194

E. Stinstra, D. Den-hertog, P. Stehouwer, and A. Vestjens, Constrained Maximin Designs for Computer Experiments, Technometrics, vol.45, issue.4, pp.340-346, 2003.
DOI : 10.1198/004017003000000168

E. R. Van-dam, B. Husslage, D. Den-hertog, and H. Melissen, Maximin Latin Hypercube Designs in Two Dimensions, Operations Research, vol.55, issue.1, pp.158-169, 2007.
DOI : 10.1287/opre.1060.0317

G. Celeux and J. Diebolt, The SEM algorithm: a probabilistic teacher algorithm derived from the em algorithm for the mixture problem, Computational Statistics Quaterly, vol.2, pp.73-82, 1985.

G. Celeux and J. Diebolt, A probabilistic teacher algorithm for iterative maximum likelihood estimation. In Classification and related methods of Data Analysis, pp.617-623, 1987.

G. Celeux, A. Grimaud, Y. Lefebvre, D. Rocquigny, and E. , Identifying intrinsic variability in multivariate systems through linearized inverse methods, Inverse Problems in Science and Engineering, vol.39, issue.3, pp.401-415, 2010.
DOI : 10.1093/biomet/80.2.267
URL : https://hal.archives-ouvertes.fr/hal-00943676

C. Currin, T. Mitchell, M. Morris, Y. , and D. , 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

D. Crecy and A. , 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.

B. Delyon, M. Lavielle, and E. Moulines, Convergence of a stochastic approximation version of the EM algorithm, Annals of Statistics, vol.27, pp.94-128, 1999.

E. J. Dempster, N. M. Laird, R. , and D. B. , Maximum likelihood from incomplete data via EM algorithm, Annals of the Royal Statistical Society, Series B, vol.39, pp.1-38, 1977.

K. Fang, R. Li, and A. Sudjianto, Design and Modeling for Computer Experiments . Computer Science and Data Analysis, 2006.

J. R. Koehler and A. B. Owen, Computer experiments. In Design and analysis of experiments, of Handbook of Statistics, pp.261-308, 1996.

E. Kuhn and M. Lavielle, Coupling a stochastic approximation version of EM with an MCMC procedure, ESAIM: Probability and Statistics, vol.8, pp.115-131, 2004.
DOI : 10.1051/ps:2004007

C. Liu and D. B. Rubin, The ECME algorithm: A simple extension of EM and ECM with faster monotone convergence, Biometrika, vol.81, issue.4, pp.633-648, 1994.
DOI : 10.1093/biomet/81.4.633

S. F. Nielsen, The Stochastic EM Algorithm: Estimation and Asymptotic Results, Bernoulli, vol.6, issue.3, pp.457-489, 2000.
DOI : 10.2307/3318671

A. Pasanisi, E. Bousquet, N. Parent, and E. , Rocquigny (de) Some useful features of the bayesian setting while dealing with uncertainties in industrial practice, Proceedings of the ESREL 2009 Conference, pp.1795-1802, 2009.

E. De-), Structural reliability under monotony: Properties of form, simulation or response surface methods and a new class of monotonous reliability methods (mrm) Structural Safety, Rocquigny, issue.5, pp.31363-374, 2009.

E. De-), N. Devictor, and S. Tarantola, Uncertainty in industrial practice, a guide to quantitative uncertainty management, Rocquigny, 2008.

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

R. Schaback, Kernel-based meshless methods, 2007.

D. Bingham, N. Hengartner, D. Higdon, K. , and Q. Y. , Variable Selection for Gaussian Process Models in Computer Experiments, Technometrics, vol.48, issue.4, pp.478-490, 2006.

C. Cannamela, J. Garnier, and B. Iooss, Controlled stratification for quantile estimation, The annals of applied statistics, pp.1554-1580, 2008.
DOI : 10.1214/08-AOAS186
URL : https://hal.archives-ouvertes.fr/hal-00355016

F. Cérou and A. Guyader, Adaptive Multilevel Splitting for Rare Event Analysis, Stochastic Analysis and Applications, vol.23, issue.2, pp.417-443, 2007.
DOI : 10.1214/aop/1176990746

F. Cérou and A. Guyader, Adaptive particle techniques and rare event estimation, Conference Oxford sur les méthodes de Monte Carlo séquentielles, pp.65-72, 2007.
DOI : 10.1051/proc:071909

D. Moral, P. Garnier, and J. , Genealogical particle analysis of rare events, The Annals of Applied Probability, vol.15, issue.4, pp.2496-2534, 2005.
DOI : 10.1214/105051605000000566
URL : https://hal.archives-ouvertes.fr/hal-00113982

H. Dette and A. Pepelyshev, Generalized Latin Hypercube Design for Computer Experiments, Technometrics, vol.52, issue.4, pp.421-429, 2010.
DOI : 10.1198/TECH.2010.09157
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.535.619

K. Fang, R. Li, and A. Sudjianto, Design and Modeling for Computer Experiments . Computer Science and Data Analysis, 2006.

P. Heidelberg, Fast simulation of rare events in queueing and reliability models, ACM Transactions on Modeling and Computer Simulation, vol.5, issue.1, pp.43-85, 1995.
DOI : 10.1145/203091.203094

D. R. Jones, M. Schonlau, W. , and W. J. , 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

V. R. Joseph, Limit Kriging, Technometrics, vol.48, issue.4, pp.458-466, 2006.
DOI : 10.1198/004017006000000011

J. R. Koehler and A. B. Owen, Computer experiments. In Design and analysis of experiments, of Handbook of Statistics, pp.261-308, 1996.

L. 'ecuyer, P. Demers, V. Tuffin, and B. , Rare events, splitting, and quasi-Monte Carlo, ACM Transactions on Modeling and Computer Simulation, vol.17, issue.2, p.9, 2007.
DOI : 10.1145/1225275.1225280

R. Li and A. Sudjianto, Analysis of Computer Experiments Using Penalized Likelihood in Gaussian Kriging Models, Technometrics, vol.47, issue.2, pp.111-120, 2005.
DOI : 10.1198/004017004000000671

D. Mease and D. Bingham, Latin Hyperrectangle Sampling for Computer Experiments, Technometrics, vol.48, issue.4, pp.467-477, 2006.
DOI : 10.1198/004017006000000101

M. Zuniga, M. Garnier, J. Remy, E. De-rocquigny, and E. , Adaptative directional stratification for controlled estimation of the probability of a rare event, 2010.

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

V. Picheny, D. Ginsbourger, O. Roustant, and R. Haftka, 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/hal-00319385

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

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

P. Shahabuddin, Rare event simulation in stochastic models, WSC '95: Proceedings of the 27th conference on Winter simulation, pp.178-185, 1995.

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

O. Koehler and . Santner, Ces deux visions sont liées et suivant les cas, l'une ou l'autre est privilégiée. En théorie de l, Wendland, 2005) et aussi demanì ere statistique, 1992.

. Schaback, 3.3, nous avons vu que ces bornes avaient aussi un sens pour l'interprétation statistique . Il est alors intéressant de pouvoir construire de tels plans, ce que nous proposons de faire grâcè a un algorithme de recuit simulé dans le chapitre 4. Les applications auprobì eme statistique inverse dans le chapitre 5 etàetà l'estimation de la probabilité d'´ evénements rares dans le chapitre 6 que nous avons traitées, 1995.

. Dans-le-chapitre, 6) revientàrevientà considérer cette modélisation duprobì eme Y i = ? H(X i , d i ) + U i , 1 ? i ? n , au lieu de celle définie par l'´ equation (5.1) Unemanì ere de prendre en compte l'incertitude liéè a l'approximation de H par?Hpar? par?H est d'´ ecrire

. .. Nous-notons-respectivement-h-j-et?het?-et?h-j-la-1,, Nous rappelons que p est la dimension des vecteurs de sorties Y i, ), . . . , H j (X n , d n ) ? ? H j (X n , d n )) = (E j1 , . . . , E jn )

M. Morris, typiquement supérieurè a 50, le nombre de points du plan d'expérience doitêtredoitêtre conséquent pour permettre une approximation de bonne qualité Il est alors coûteux de choisir un plan d'expérience par le biais d'algorithmes de recuit simulé, Si la dimension des entrées est grande chapitre 4) ainsi il faut envisager d'autres stratégies. De plus, le métamodèle d'interpolateuràinterpolateurà noyaux est lourdàlourdà calculer. Construire un interpolateurà interpolateurà noyaux demanì ere locale est une solutionàsolutionà explorer dans ce cas, 1995.

B. Koehler, J. R. Et-owen, and A. B. , Computer experiments. In Design and analysis of experiments, de Handbook of Statistics, pp.261-308, 1996.

W. R. Madych and S. A. Et-nelson, Bounds on multivariate polynomials and exponential error estimates for multiquadric interpolation, Journal of Approximation Theory, vol.70, issue.1, pp.94-114, 1992.
DOI : 10.1016/0021-9045(92)90058-V

N. S. Pillai, Q. Wu, F. Liang, S. Mukherjee, and R. L. Et-wolpert, Characterizing the function space for bayesian kernel models, Journal of Machine Learning Research, vol.8, pp.1769-1797, 2007.

B. Rutherford, A response-modeling alternative to surrogate models for support in computational analyses, Reliability Engineering & System Safety, vol.91, issue.10-11, pp.10-111322, 2006.
DOI : 10.1016/j.ress.2005.11.050

T. J. Santner, B. , W. Et, W. , and N. , The Design and Analysis of Computer Experiments, 2003.
DOI : 10.1007/978-1-4757-3799-8

R. Schaback, Error estimates and condition numbers for radial basis function interpolation, Advances in Computational Mathematics, vol.4, issue.3, pp.251-264, 1995.
DOI : 10.1007/BF02432002

H. Wendland, Scattered data approximation, de Cambridge Monographs on Applied and Computational Mathematics, 2005.
DOI : 10.1017/CBO9780511617539

. Enfin, dans ladernì ere contribution, l'utilisation d'un tel métamodèle pour développer deux stratégies d'estimation et de majoration de probabilités d'´ evénements rares dépendant d'une fonction type bo??tebo??te-noire coûteuse

. Mots-clés, Expériences simulées, métamodèles, interpolationàinterpolationà noyaux, krigeage, plans d'expériences numériques,probì eme statistique inverse, ´ evénements rares