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

S. Das, R. Ghanem, and S. Finette, Polynomial chaos representation of spatio-temporal random fields from experimental measurements, Journal of Computational Physics, vol.228, issue.23, pp.8726-8751, 2009.
DOI : 10.1016/j.jcp.2009.08.025

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

C. Desceliers, C. Soize, and R. Ghanem, Identification of Chaos Representations of Elastic Properties of Random Media Using Experimental Vibration Tests, Computational Mechanics, vol.60, issue.5, pp.831-838, 2007.
DOI : 10.1007/s00466-006-0072-7

URL : https://hal.archives-ouvertes.fr/hal-00686150

R. Ghanem and A. 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, 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, rev, 2003.
DOI : 10.1007/978-1-4612-3094-6

P. Hansen, Numerical tools for analysis and solution of Fredholm integral equations of the first kind, Inverse Problems, vol.8, issue.6, pp.849-872, 1992.
DOI : 10.1088/0266-5611/8/6/005

E. T. Jaynes, Information Theory and Statistical Mechanics, Physical Review, vol.106, issue.4, pp.620-630, 1963.
DOI : 10.1103/PhysRev.106.620

L. Maître, O. , and O. Knio, Spectral Methods for Uncertainty Quantification, 2010.

Y. M. Marzouk, H. N. Najm, and L. A. Rahn, Stochastic spectral methods for efficient Bayesian solution of inverse problems, AIP Conference Proceedings, pp.560-586, 2007.
DOI : 10.1063/1.2149785

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

G. Perrin, C. Soize, D. Duhamel, and C. Funfschilling, Karhunen???Lo??ve expansion revisited for vector-valued random fields: Scaling, errors and optimal basis., Journal of Computational Physics, vol.242, 2013.
DOI : 10.1016/j.jcp.2013.02.036

G. Perrin, C. Soize, D. Duhamel, and C. Funfschilling, A Posteriori Error and Optimal Reduced Basis for Stochastic Processes Defined by a Finite Set of Realizations, SIAM/ASA Journal on Uncertainty Quantification, vol.2, issue.1
DOI : 10.1137/130905095

URL : https://hal.archives-ouvertes.fr/hal-01097139

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, Generalized probabilistic approach of uncertainties in computational dynamics using random matrices and polynomial chaos decompositions, International Journal for Numerical Methods in Engineering, vol.80, issue.21-26, pp.939-970, 2010.
DOI : 10.1002/nme.2712

URL : https://hal.archives-ouvertes.fr/hal-00684322

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, issue.33-36, pp.2150-2164, 2010.
DOI : 10.1016/j.cma.2010.03.013

URL : https://hal.archives-ouvertes.fr/hal-00684324

J. Weese, A reliable and fast method for the solution of Fredhol integral equations of the first kind based on Tikhonov regularization, Computer Physics Communications, vol.69, issue.1, pp.99-111, 1992.
DOI : 10.1016/0010-4655(92)90132-I