M. Abramowitz and I. Stegun, Handbook of Mathematical Functions, American Journal of Physics, vol.34, issue.2, 1970.
DOI : 10.1119/1.1972842

G. Andrianov, S. Burriel, S. Cambier, A. Dutfoy, I. Dutka-malen et al., Open TURNS, an open source initiative to Treat Uncertainties, Risks'N Statistics in a structured industrial approach, Proc. ESREL, 2007.

F. Bachoc, Cross Validation and Maximum Likelihood estimations of hyper-parameters of Gaussian processes with model misspecification, Computational Statistics & Data Analysis, vol.66, pp.55-69, 2013.
DOI : 10.1016/j.csda.2013.03.016

R. A. Bates, R. Buck, E. Riccomagno, and H. Wynn, Experimental design and observation for large systems, Journal of the Royal Statistical Society, Series B, vol.58, issue.1, pp.77-94, 1996.

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

M. Berveiller, B. Sudret, and M. Lemaire, Presentation of two methods for computing the response coefficients in stochastic finite element analysis, Proc. 9th ASCE Specialty Conference on Probabilistic Mechanics and Structural Reliability, 2004.

M. Berveiller, B. Sudret, and M. Lemaire, Stochastic finite element: a non intrusive approach by regression, Revue europ??enne de m??canique num??rique, vol.15, issue.1-2-3, pp.1-3, 2006.
DOI : 10.3166/remn.15.81-92

M. Bieri and C. Schwab, Sparse high order FEM for elliptic sPDEs, Computer Methods in Applied Mechanics and Engineering, vol.198, issue.13-14, pp.1149-1170, 2009.
DOI : 10.1016/j.cma.2008.08.019

G. Blatman, Adaptive sparse polynomial chaos expansions for uncertainty propagation and sensitivity analysis, 2009.
URL : https://hal.archives-ouvertes.fr/tel-00440197

G. Blatman and B. Sudret, Sparse polynomial chaos expansions and adaptive stochastic finite elements using a regression approach, Comptes Rendus M??canique, vol.336, issue.6, pp.518-523, 2008.
DOI : 10.1016/j.crme.2008.02.013

G. Blatman and B. Sudret, An adaptive algorithm to build up sparse polynomial chaos expansions for stochastic finite element analysis, Probabilistic Engineering Mechanics, vol.25, issue.2, pp.183-197, 2010.
DOI : 10.1016/j.probengmech.2009.10.003

G. Blatman and B. Sudret, Efficient computation of global sensitivity indices using sparse polynomial chaos expansions, Reliability Engineering & System Safety, vol.95, issue.11, pp.1216-1229, 2010.
DOI : 10.1016/j.ress.2010.06.015

G. Blatman and B. Sudret, Adaptive sparse polynomial chaos expansion based on least angle regression, Journal of Computational Physics, vol.230, issue.6, pp.2345-2367, 2011.
DOI : 10.1016/j.jcp.2010.12.021

S. Brown, J. Beck, H. Mahgerefteh, and E. Fraga, Global sensitivity analysis of the impact of impurities on CO2 pipeline failure, Reliability Engineering & System Safety, vol.115, pp.43-54, 2013.
DOI : 10.1016/j.ress.2013.02.006

G. Buzzard, Global sensitivity analysis using sparse grid interpolation and polynomial chaos, Reliability Engineering & System Safety, vol.107, 2012.
DOI : 10.1016/j.ress.2011.07.011

G. Buzzard and D. Xiu, Abstract, Communications in Computational Physics, vol.1, issue.03, pp.542-567, 2011.
DOI : 10.1137/060659831

G. Chastaing and L. L. Gratiet, ANOVA decomposition of conditional Gaussian processes for sensitivity analysis with dependent inputs, Journal of Statistical Computation and Simulation, vol.147, issue.2, pp.2164-2186, 2015.
DOI : 10.1007/978-1-4899-2937-2
URL : https://hal.archives-ouvertes.fr/hal-00872250

J. Chiì-es and P. Delfiner, Geostatistics: modeling spatial uncertainty. Wiley series in probability and statistics (Applied probability and statistics section), 1999.

T. Crestaux, O. L. Ma?tre, and J. Martinez, Polynomial chaos expansion for sensitivity analysis, Reliability Engineering & System Safety, vol.94, issue.7, pp.1161-1172, 2009.
DOI : 10.1016/j.ress.2008.10.008

O. Ditlevsen and H. Madsen, Structural reliability methods, J. Wiley and Sons, 1996.

A. Doostan and H. Owhadi, A non-adapted sparse approximation of PDEs with stochastic inputs, Journal of Computational Physics, vol.230, issue.8, pp.3015-3034, 2011.
DOI : 10.1016/j.jcp.2011.01.002

S. Dubreuil, M. Berveiller, F. Petitjean, and M. Salaün, Construction of bootstrap confidence intervals on sensitivity indices computed by polynomial chaos expansion, Reliability Engineering & System Safety, vol.121, pp.263-275, 2014.
DOI : 10.1016/j.ress.2013.09.011
URL : https://hal.archives-ouvertes.fr/hal-00933583

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

B. Efron, T. Hastie, I. Johnstone, and R. Tibshirani, Least angle regression, Annals of Statistics, vol.32, pp.407-499, 2004.

N. Fajraoui, F. Ramasomanana, A. Younes, T. Mara, P. Ackerer et al., Use of global sensitivity analysis and polynomial chaos expansion for interpretation of nonreactive transport experiments in laboratory-scale porous media, Water Resources Research, vol.24, issue.2, 2011.
DOI : 10.1029/2010WR009639
URL : https://hal.archives-ouvertes.fr/insu-00576944

R. Ghanem and P. Spanos, Stochastic finite elements ? A spectral approach, 1991.
DOI : 10.1007/978-1-4612-3094-6

R. Gramacy and M. Taddy, Categorical inputs, sensitivity analysis, optimization and importance tempering with tgp version 2, an r package for treed gaussian process models, Journal of Statistical Software, vol.33, pp.1-48, 2012.

D. Harville, Maximum Likelihood Approaches to Variance Component Estimation and to Related Problems, Journal of the American Statistical Association, vol.27, issue.358, pp.320-338, 1977.
DOI : 10.1080/01621459.1973.10482448

B. Iooss and P. Lema??trelema??tre, Uncertainty management in simulation-optimization of complex systems: algorithms and applications, Chapter A review on global sensitivity analysis methods, 2015.

J. Jakeman, M. Eldred, and K. Sargsyan, Enhancing <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd" xmlns:sa="http://www.elsevier.com/xml/common/struct-aff/dtd"><mml:msub><mml:mrow><mml:mi>???</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math>-minimization estimates of polynomial chaos expansions using basis selection, Journal of Computational Physics, vol.289, pp.18-34, 2015.
DOI : 10.1016/j.jcp.2015.02.025

A. Janon, T. Klein, A. Lagnoux, M. Nodet, and C. Prieur, Asymptotic normality and efficiency of two Sobol index estimators, ESAIM: Probability and Statistics, pp.342-364, 2014.
DOI : 10.1051/ps/2013040
URL : https://hal.archives-ouvertes.fr/hal-00665048

C. Lantuéjoul and N. Desassis, Simulation of a Gaussian random vector: A propagative version of the Gibbs sampler, The 9th International Geostatistics Congress, p.1747181, 2012.

L. Gratiet, L. , and C. Cannamela, Cokriging-Based Sequential Design Strategies Using Fast Cross-Validation Techniques for Multi-Fidelity Computer Codes, Technometrics, vol.28, issue.3, 2015.
DOI : 10.1080/00401706.2012.723572

L. Gratiet, L. , C. Cannamela, and B. Iooss, A Bayesian Approach for Global Sensitivity Analysis of (Multifidelity) Computer Codes, SIAM/ASA Journal on Uncertainty Quantification, vol.2, issue.1, pp.336-363, 2014.
DOI : 10.1137/130926869
URL : https://hal.archives-ouvertes.fr/hal-00842432

R. Lebrun and A. Dutfoy, An innovating analysis of the Nataf transformation from the copula viewpoint, Probabilistic Engineering Mechanics, vol.24, issue.3, pp.312-320, 2009.
DOI : 10.1016/j.probengmech.2008.08.001

S. Marelli and B. Sudret, UQLab: A Framework for Uncertainty Quantification in Matlab, Vulnerability, Uncertainty, and Risk, pp.2554-2563, 2014.
DOI : 10.1061/9780784413609.257

A. Marrel, B. Iooss, B. Laurent, and O. Roustant, 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

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

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.2, pp.239-245, 1979.

M. Zuniga, M. , S. Kucherenko, and N. Shah, Metamodelling with independent and dependent inputs, Computer Physics Communications, vol.184, issue.6, pp.1570-1580, 2013.
DOI : 10.1016/j.cpc.2013.02.005

H. Niederreiter, Random number generation and quasi-Monte Carlo methods, Society for Industrial and Applied Mathematics, 1992.
DOI : 10.1137/1.9781611970081

J. Oakley and A. O. Hagan, 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

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

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

E. H. Sandoval, F. Anstett-collin, and M. Basset, Sensitivity study of dynamic systems using polynomial chaos, Reliability Engineering & System Safety, vol.104, pp.15-26, 2012.
DOI : 10.1016/j.ress.2012.04.001
URL : https://hal.archives-ouvertes.fr/hal-00696271

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

K. Sargsyan, C. Safta, H. Najm, B. Debusschere, D. Ricciuto et al., DIMENSIONALITY REDUCTION FOR COMPLEX MODELS VIA BAYESIAN COMPRESSIVE SENSING, International Journal for Uncertainty Quantification, vol.4, issue.1, pp.63-93, 2014.
DOI : 10.1615/Int.J.UncertaintyQuantification.2013006821

R. Schöbi, B. Sudret, and J. Wiart, POLYNOMIAL-CHAOS-BASED KRIGING, International Journal for Uncertainty Quantification, vol.5, issue.2, pp.171-193, 2015.
DOI : 10.1615/Int.J.UncertaintyQuantification.2015012467

R. Schoebi, B. Sudret, and J. Wiart, POLYNOMIAL-CHAOS-BASED KRIGING, International Journal for Uncertainty Quantification, vol.5, issue.2, 2015.
DOI : 10.1615/Int.J.UncertaintyQuantification.2015012467

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

I. Sobol-' and S. Kucherenko, Derivative based global sensitivity measures and their link with global sensitivity indices, Mathematics and Computers in Simulation, vol.79, issue.10, pp.3009-3017, 2009.
DOI : 10.1016/j.matcom.2009.01.023

I. Sobol, S. Tarantola, D. Gatelli, S. Kucherenko, and W. Mauntz, Estimating the approximation error when fixing unessential factors in global sensitivity analysis, Reliability Engineering & System Safety, vol.92, issue.7, pp.957-960, 2007.
DOI : 10.1016/j.ress.2006.07.001

C. Soize and R. Ghanem, Physical Systems with Random Uncertainties: Chaos Representations with Arbitrary Probability Measure, SIAM Journal on Scientific Computing, vol.26, issue.2, pp.395-410, 2004.
DOI : 10.1137/S1064827503424505
URL : https://hal.archives-ouvertes.fr/hal-00686211

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

C. Storlie, L. Swiler, J. Helton, and C. Sallaberry, Implementation and evaluation of nonparametric regression procedures for sensitivity analysis of computationally demanding models, Reliability Engineering & System Safety, vol.94, issue.11, pp.1735-1763, 2009.
DOI : 10.1016/j.ress.2009.05.007

B. Sudret, Global sensitivity analysis using polynomial chaos expansions, Proc. 5th Int. Conf. on Comp. Stoch. Mech (CSM5), 2006.
DOI : 10.1016/j.ress.2007.04.002
URL : https://hal.archives-ouvertes.fr/hal-01432217

B. Sudret, Uncertainty propagation and sensitivity analysis in mechanical models ? contributions to structural reliability and stochastic spectral methods, 2007.

B. Sudret, Global sensitivity analysis using polynomial chaos expansions, Reliability Engineering & System Safety, vol.93, issue.7, pp.964-979, 2008.
DOI : 10.1016/j.ress.2007.04.002
URL : https://hal.archives-ouvertes.fr/hal-01432217

B. Sudret, Polynomial chaos expansions and stochastic finite element methods, Chapter 6. Risk and Reliability in Geotechnical Engineering, 2015.

B. Sudret and Y. Caniou, Analysis of covariance (ANCOVA) using polynomial chaos expansions, 2013.
DOI : 10.1201/b16387-473
URL : http://e-collection.ethbib.ethz.ch/show?type=inkonf&nr=900

B. Sudret and C. Mai, Computing derivative-based global sensitivity measures using polynomial chaos expansions, Reliability Engineering & System Safety, vol.134, pp.241-250, 2015.
DOI : 10.1016/j.ress.2014.07.009
URL : https://hal.archives-ouvertes.fr/hal-01154395

W. Van-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

W. 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

D. Xiu and G. Karniadakis, The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations, SIAM Journal on Scientific Computing, vol.24, issue.2, pp.619-644, 2002.
DOI : 10.1137/S1064827501387826

A. Younes, T. Mara, N. Fajraoui, F. Lehmann, B. Belfort et al., Use of Global Sensitivity Analysis to Help Assess Unsaturated Soil Hydraulic Parameters, Vadose Zone Journal, vol.12, issue.1, 2013.
DOI : 10.2136/vzj2011.0150
URL : https://hal.archives-ouvertes.fr/hal-01096940