C. Soize and R. Ghanem, Data-driven probability concentration and sampling on manifold, Journal of Computational Physics, vol.321, pp.242-258, 2016.
DOI : 10.1016/j.jcp.2016.05.044

URL : https://hal.archives-ouvertes.fr/hal-01283842

R. R. Coifman, S. Lafon, A. B. Lee, M. Maggioni, B. Nadler et al., Geometric diffusions as a tool for harmonic analysis and structure definition of data: Diffusion maps, Proceedings of the National Academy of Sciences, vol.102, issue.21, pp.7426-7431, 2005.
DOI : 10.1073/pnas.0500334102

A. W. Bowman and A. Azzalini, Applied Smoothing Techniques for Data Analysis, 1997.

D. W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization , Second Edition, 2015.

C. Soize, Construction of probability distributions in high dimension using the maximum entropy principle: Applications to stochastic processes, random fields and random matrices, International Journal for Numerical Methods in Engineering, vol.195, issue.4, pp.1583-1611, 2008.
DOI : 10.1002/nme.2385

URL : https://hal.archives-ouvertes.fr/hal-00684517

C. Soize, Polynomial chaos expansion of a multimodal random vector, SIAM, ASA Journal on Uncertainty Quantification, vol.3, issue.3460, 2015.

R. M. Neal, A. Brooks, G. Gelman, and X. Jones, MCMC Using Hamiltonian Dynamics, 2010.
DOI : 10.1201/b10905-6

URL : http://arxiv.org/abs/1206.1901

M. Girolami and B. Calderhead, Riemann manifold Langevin and Hamiltonian Monte Carlo methods, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.13, issue.10, pp.123-214, 2011.
DOI : 10.1111/j.1467-9868.2010.00765.x

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

J. C. Spall, Introduction to Stochastic Search and Optimization, 2003.
DOI : 10.1002/0471722138

R. R. Coifman and S. Lafon, Diffusion maps, Applied and Computational Harmonic Analysis, vol.21, issue.1, pp.5-30, 2006.
DOI : 10.1016/j.acha.2006.04.006

URL : http://doi.org/10.1016/j.acha.2006.04.006

R. Talmon and R. R. Coifman, Intrinsic modeling of stochastic dynamical systems using empirical geometry, Applied and Computational Harmonic Analysis, vol.39, issue.1, pp.138-160, 2015.
DOI : 10.1016/j.acha.2014.08.006

R. Ghanem and P. D. Spanos, Polynomial Chaos in Stochastic Finite Elements, Journal of Applied Mechanics, vol.57, issue.1, pp.197-202, 1990.
DOI : 10.1115/1.2888303

R. Ghanem and P. D. Spanos, Stochastic Finite Elements: A spectral Approach, 1991.
DOI : 10.1007/978-1-4612-3094-6

R. Ghanem and R. M. Kruger, Numerical solution of spectral stochastic finite element systems, Computer Methods in Applied Mechanics and Engineering, vol.129, issue.3, pp.289-303, 1996.
DOI : 10.1016/0045-7825(95)00909-4

D. B. Xiu and G. E. 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

P. Frauenfelder, C. Schwab, and R. A. Todor, Finite elements for elliptic problems with stochastic coefficients, Computer Methods in Applied Mechanics and Engineering, vol.194, issue.2-5, pp.205-228, 2005.
DOI : 10.1016/j.cma.2004.04.008

B. J. Debusschere, H. N. Najm, P. P. Pebay, O. M. Knio, R. Ghanem et al., Numerical Challenges in the Use of Polynomial Chaos Representations for Stochastic Processes, SIAM Journal on Scientific Computing, vol.26, issue.2, pp.698-719, 2004.
DOI : 10.1137/S1064827503427741

C. Desceliers, R. Ghanem, and C. Soize, Maximum likelihood estimation of stochastic chaos representations from experimental data, International Journal for Numerical Methods in Engineering, vol.11, issue.6, pp.978-1001, 2006.
DOI : 10.1002/nme.1576

URL : https://hal.archives-ouvertes.fr/hal-00686154

I. Babuska, F. Nobile, and R. Tempone, A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data, SIAM Journal on Numerical Analysis, vol.45, issue.3, pp.1005-1034, 2007.
DOI : 10.1137/050645142

A. Doostan, R. Ghanem, and J. , Red-Horse, Stochastic model reduction for chaos representations, Computer Methods in Applied Mechanics and Engineering, vol.196, pp.37-40, 2007.
DOI : 10.1016/j.cma.2006.10.047

B. Ganapathysubramanian and N. Zabaras, Sparse grid collocation schemes for stochastic natural convection problems, Journal of Computational Physics, vol.225, issue.1, pp.652-685, 2007.
DOI : 10.1016/j.jcp.2006.12.014

A. Nouy, A generalized spectral decomposition technique to solve a class of linear stochastic partial differential equations, Computer Methods in Applied Mechanics and Engineering, vol.196, issue.45-48, pp.45-48, 2007.
DOI : 10.1016/j.cma.2007.05.016

URL : https://hal.archives-ouvertes.fr/hal-00366619

S. Das, R. Ghanem, and J. Spall, Asymptotic Sampling Distribution for Polynomial Chaos Representation from Data: A Maximum Entropy and Fisher Information Approach, SIAM Journal on Scientific Computing, vol.30, issue.5, pp.2207-2234, 2008.
DOI : 10.1137/060652105

R. Ghanem, R. Doostan, and J. , Red-Horse, A probability construction of model validation, Computer Methods in Applied Mechanics and Engineering, vol.197, pp.29-32, 2008.

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

H. N. Najm, Uncertainty Quantification and Polynomial Chaos Techniques in Computational Fluid Dynamics, Annual Review of Fluid Mechanics, vol.41, issue.1, pp.35-52, 2009.
DOI : 10.1146/annurev.fluid.010908.165248

M. Arnst, R. Ghanem, and C. Soize, Identification of Bayesian posteriors for coefficients of chaos expansions, Journal of Computational Physics, vol.229, issue.9, pp.3134-3154, 2010.
DOI : 10.1016/j.jcp.2009.12.033

URL : https://hal.archives-ouvertes.fr/hal-00684317

O. P. Le-maitre and O. M. Knio, Spectral Methods for Uncertainty Quantification with Applications to Computational Fluid Dynamics, 2010.

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

C. Soize, Identification of high-dimension polynomial chaos expansions with random coefficients for non-Gaussian tensor-valued random fields using partial and limited experimental data, Computer Methods in Applied Mechanics and Engineering, vol.199, pp.33-36, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00684324

A. Nouy and C. Soize, Random field representations for stochastic elliptic boundary value problems and statistical inverse problems, European Journal of Applied Mathematics, vol.19, issue.03, pp.339-373, 2014.
DOI : 10.1023/B:ACAP.0000013855.14971.91

D. Lucor, C. H. Su, and G. E. Karniadakis, Generalized polynomial chaos and random oscillators, International Journal for Numerical Methods in Engineering, vol.60, issue.3, pp.571-596, 2004.
DOI : 10.1002/nme.976

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

X. L. Wan and G. E. Karniadakis, Multi-Element Generalized Polynomial Chaos for Arbitrary Probability Measures, SIAM Journal on Scientific Computing, vol.28, issue.3, pp.901-928, 2006.
DOI : 10.1137/050627630

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

C. Soize and R. Ghanem, Reduced Chaos decomposition with random coefficients of vector-valued random variables and random fields, Computer Methods in Applied Mechanics and Engineering, vol.198, issue.21-26, pp.21-26, 2009.
DOI : 10.1016/j.cma.2008.12.035

URL : https://hal.archives-ouvertes.fr/hal-00684487

O. G. Ernst, A. Mugler, H. J. Starkloff, and E. Ullmann, On the convergence of generalized polynomial chaos expansions, ESAIM: Mathematical Modelling and Numerical Analysis, vol.46, issue.2, pp.317-339, 2012.
DOI : 10.1051/m2an/2011045

G. Perrin, C. Soize, D. Duhamel, and C. Funfschilling, Identification of Polynomial Chaos Representations in High Dimension from a Set of Realizations, SIAM Journal on Scientific Computing, vol.34, issue.6, pp.2917-2945, 2012.
DOI : 10.1137/11084950X

URL : https://hal.archives-ouvertes.fr/hal-00770006

R. Tipireddy and R. Ghanem, Basis adaptation in homogeneous chaos spaces, Journal of Computational Physics, vol.259, pp.304-317, 2014.
DOI : 10.1016/j.jcp.2013.12.009

D. Ghosh and R. Ghanem, Stochastic convergence acceleration through basis enrichment of polynomial chaos expansions, International Journal for Numerical Methods in Engineering, vol.28, issue.2, pp.162-184, 2008.
DOI : 10.1002/nme.2066

V. Keshavarzzadeh, R. Ghanem, S. F. Masri, and O. J. Aldraihem, Convergence acceleration of polynomial chaos solutions via sequence transformation, Computer Methods in Applied Mechanics and Engineering, vol.271, pp.167-184, 2014.
DOI : 10.1016/j.cma.2013.12.003

Y. M. Marzouk and H. N. Najm, Dimensionality reduction and polynomial chaos acceleration of Bayesian inference in inverse problems, Journal of Computational Physics, vol.228, issue.6, pp.1862-1902, 2009.
DOI : 10.1016/j.jcp.2008.11.024

C. Soize and C. Desceliers, Computational Aspects for Constructing Realizations of Polynomial Chaos in High Dimension, SIAM Journal on Scientific Computing, vol.32, issue.5, pp.2820-2831, 2010.
DOI : 10.1137/100787830

URL : https://hal.archives-ouvertes.fr/hal-00684323

M. Arnst, C. Soize, and R. Ghanem, Hybrid Sampling/Spectral Method for Solving Stochastic Coupled Problems, SIAM/ASA Journal on Uncertainty Quantification, vol.1, issue.1, p.218243, 2013.
DOI : 10.1137/120894403

URL : https://hal.archives-ouvertes.fr/hal-00829060

D. Center and B. , Bureau of Ocean Energy Management

C. Thimmisetty, A. Khodabakhshnejad, N. Jabbari, F. Aminzadeh, R. Ghanem et al., Multiscale Stochastic Representation in High-Dimensional Data Using Gaussian Processes with Implicit Diffusion Metrics, Proceedings of the Dynamic Data-driven Environmental Systems Science Conference, 2014.
DOI : 10.1007/978-3-319-25138-7_15