M. Aarnst and R. Ghanem, Probabilistic equivalence and stochastic model reduction in multiscale analysis, Computer Methods in Applied Mechanics and Engineering, vol.197, issue.43-44, 2008.
DOI : 10.1016/j.cma.2008.03.016

B. Velamur-asokan, N. Narayanan, and . Zabaras, Variational multiscale stabilized FEM formulations for transport equations: stochastic advectiondiffusion and incompressible stochastic Navier-Stokes equations, J. Comput. Phys, vol.202, issue.1, pp.94-133, 2005.

I. Babuska, R. Tempone, and G. Zouraris, Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations, SIAM Journal on Numerical Analysis, vol.42, issue.2, pp.800-825, 2004.
DOI : 10.1137/S0036142902418680

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

S. Das and R. Ghanem, Hybrid representations for complex dynamical stochastic systems: coupled non-parametric and parametric models, Proceedings of the 6 th international Conference on Structural Dynamics, pp.53-60, 2005.

C. Descelliers, C. Soize, and R. Ghanem, 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

P. Frauenfelder, C. Schwab, and R. 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

R. Ghanem, Ingredients for a general purpose stochastic finite elements implementation, Computer Methods in Applied Mechanics and Engineering, vol.168, issue.1-4, pp.19-34, 1999.
DOI : 10.1016/S0045-7825(98)00106-6

R. Ghanem, A. Doostan, and J. Red-horse, A probabilistic construction of model validation, Computer Methods in Applied Mechanics and Engineering, vol.197, issue.29-32, 2008.
DOI : 10.1016/j.cma.2007.08.029

R. Ghanem and R. Doostan, On the construction and analysis of stochastic models: Characterization and propagation of the errors associated with limited data, Journal of Computational Physics, vol.217, issue.1, pp.63-81, 2006.
DOI : 10.1016/j.jcp.2006.01.037

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

M. Huebner and B. Rozovskii, On asymptotic properties of maximum likelihood estimators for parabolic stochastic pdes. Probability Theory and Related Fields, pp.143-163, 1995.

O. P. Le-maitre, H. Najm, R. Ghanem, and O. Knio, Multi-resolution analysis of Wiener-type uncertainty propagation schemes, Journal of Computational Physics, vol.197, issue.2, pp.502-531, 2004.
DOI : 10.1016/j.jcp.2003.12.020

O. P. Le-maitre, H. O. Knio, R. Najm, and . Ghanem, Uncertainty propagation using Wiener???Haar expansions, Journal of Computational Physics, vol.197, issue.1, pp.28-57, 2004.
DOI : 10.1016/j.jcp.2003.11.033

H. G. Matthies and A. Keese, Galerkin methods for linear and nonlinear elliptic stochastic partial differential equations, Computer Methods in Applied Mechanics and Engineering, vol.194, issue.12-16, pp.12-161295, 2005.
DOI : 10.1016/j.cma.2004.05.027
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.331.8047

N. Habib and . Najm, Uncertainty quantification and polynomial chaos techniques in computational fluid dynamics, Annual Review of Fluid Mechanics, vol.41, issue.1, 2009.

J. R. Red-horse and A. S. Benjamin, A probabilistic approach to uncertainty quantification with limited information, Reliability Engineering & System Safety, vol.85, issue.1-3, pp.183-190, 2004.
DOI : 10.1016/j.ress.2004.03.011

E. V. Slud, The Moment Problem for Polynomial Forms in Normal Random Variables, The Annals of Probability, vol.21, issue.4, pp.2200-2214, 1993.
DOI : 10.1214/aop/1176989017

C. Soize, Random matrix theory and non-parametric model of random uncertainties in vibration analysis, Journal of Sound and Vibration, vol.263, issue.4, pp.893-916, 2003.
DOI : 10.1016/S0022-460X(02)01170-7
URL : https://hal.archives-ouvertes.fr/hal-00686213

C. Soize, Random matrix theory for modeling uncertainties in computational mechanics, Computer Methods in Applied Mechanics and Engineering, vol.194, issue.12-16, pp.12-161333, 2005.
DOI : 10.1016/j.cma.2004.06.038
URL : https://hal.archives-ouvertes.fr/hal-00686187

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. 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

D. Xiu and G. Karniadakis, Modeling uncertainty in flow simulations via generalized polynomial chaos, Journal of Computational Physics, vol.187, issue.1, pp.137-167, 2003.
DOI : 10.1016/S0021-9991(03)00092-5