R. A. Ibrahim, Structural Dynamics with Parameter Uncertainties, Applied Mechanics Reviews, vol.40, issue.3, pp.309-328, 1987.
DOI : 10.1115/1.3149532

C. S. Manohar and R. A. Ibrahim, Progress in Structural Dynamics With Stochastic Parameter Variations: 1987-1998, Applied Mechanics Reviews, vol.52, issue.5, pp.177-197, 1999.
DOI : 10.1115/1.3098933

M. Ghanem, M. Grigoriu, E. A. Hoshiya, N. A. Johnson, H. J. Naess et al., A state-of-the-art report on computational stochastic mechanics, Probabilistic Engineering Mechanics, vol.12, pp.197-321, 1997.

G. I. Schueller, Computational stochastic mechanics ??? recent advances, Computers & Structures, vol.79, issue.22-25, pp.2225-2234, 2001.
DOI : 10.1016/S0045-7949(01)00078-5

R. Ghanem and P. Spanos, Stochastic Finite Elements:A Spectral Approach, 1991.

C. Soize, A nonparametric model of random uncertainties for reduced matrix models in structural dynamics, Probabilistic Engineering Mechanics, vol.15, issue.3, pp.277-294, 2000.
DOI : 10.1016/S0266-8920(99)00028-4

URL : https://hal.archives-ouvertes.fr/hal-00686293

C. Soize, Maximum entropy approach for modeling random uncertainties in transient elastodynamics, The Journal of the Acoustical Society of America, vol.109, issue.5, pp.1979-1996, 2001.
DOI : 10.1121/1.1360716

URL : https://hal.archives-ouvertes.fr/hal-00686287

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

C. Soize and R. Ghanem, Reduced chaos decomposition with random coeffi, p.32
DOI : 10.1016/j.cma.2008.12.035

URL : https://hal-upec-upem.archives-ouvertes.fr/hal-00684487/file/publi-2009-CMAME-198_21-26_1926-1934-soize-ghanem-preprint.pdf

N. Wiener, The Homogeneous Chaos, American Journal of Mathematics, vol.60, issue.4, pp.897-936, 1938.
DOI : 10.2307/2371268

D. 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

S. Kullback, Information Theory and Statistics, 1968.

H. Cramér, Mathematical Methods of Statistics, 1946.

M. Arnst and R. Ghanem, Probabilistic equivalence and stochastic model reduction in multiscale analysis, Computer Methods in Applied Mechanics and Engineering, vol.197, issue.43-44, pp.3584-3592, 2008.
DOI : 10.1016/j.cma.2008.03.016

C. Soize, E. Capiez-lernout, J. Durand, C. Fernandez, and L. Gagliardini, Probabilistic model identification of uncertainties in computational models for dynamical systems and experimental validation, Computer Methods in Applied Mechanics and Engineering, vol.198, issue.1, pp.150-163, 2008.
DOI : 10.1016/j.cma.2008.04.007

URL : https://hal.archives-ouvertes.fr/hal-00686138

M. Arnst, D. Clouteau, and M. Bonnet, Inversion of probabilistic structural models using measured transfer functions, Computer Methods in Applied Mechanics and Engineering, vol.197, issue.6-8, pp.589-608, 2008.
DOI : 10.1016/j.cma.2007.08.011

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

R. Ghanem, A. Doostan, and J. R. Horse, A probabilistic construction of model validation, Computer Methods in Applied Mechanics and Engineering, vol.197, issue.29-32, pp.2585-2595, 2008.
DOI : 10.1016/j.cma.2007.08.029

M. Hübner and B. L. Rozovskii, On asymptotic properties of maximum likeli, p.33

. Hood-estimators-for-parabolic-stochastic-pdes, Probability and Related Fields, pp.143-163, 1995.

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

Y. Marzouk and D. Xiu, A Stochastic Collocation Approach to Bayesian Inference in Inverse Problems, Communications in Computational Physics, vol.6, issue.4, pp.826-847, 2009.
DOI : 10.4208/cicp.2009.v6.p826

Y. Marzouk and H. 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

S. Das, R. Ghanem, and J. Spall, Asymptotic sampling distribution for polynomial chaos representation of data: A maximum entropy and fisher information approach, SIAM Journal on Scientific Computing, vol.28, pp.2207-2234, 2008.

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. H. Cameron and W. T. Martin, The Orthogonal Development of Non-Linear Functionals in Series of Fourier-Hermite Functionals, The Annals of Mathematics, vol.48, issue.2, pp.385-392, 1947.
DOI : 10.2307/1969178

A. Tarantola, Inverse Problem Theory and Methods for Model Parameter Estimation, 2005.
DOI : 10.1137/1.9780898717921

A. Gelman, J. Carlin, H. Stern, and D. Rubin, Bayesian Data Analysis, 2003.

J. Bernardo and A. Smith, Bayesian theory, 2000.
DOI : 10.1002/9780470316870

E. Jaynes, Probability Theory: The Logic of Science, 2003.
DOI : 10.1017/CBO9780511790423

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, p.15831611, 2008.
DOI : 10.1002/nme.2385

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

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

C. P. Robert and G. Casella, Monte Carlo Statistical Methods, 2005.

E. Parzen, On Estimation of a Probability Density Function and Mode, The Annals of Mathematical Statistics, vol.33, issue.3, pp.1065-1076, 1962.
DOI : 10.1214/aoms/1177704472

M. Rosenblatt, Remarks on Some Nonparametric Estimates of a Density Function, The Annals of Mathematical Statistics, vol.27, issue.3, pp.832-837, 1956.
DOI : 10.1214/aoms/1177728190

D. W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization, 1992.
DOI : 10.1002/9781118575574

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, Optimization by Simulated Annealing, Science, vol.220, issue.4598, pp.671-680, 1983.
DOI : 10.1126/science.220.4598.671

N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, Equation of State Calculations by Fast Computing Machines, The Journal of Chemical Physics, vol.21, issue.6, pp.1087-1092, 1953.
DOI : 10.1063/1.1699114

D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning, 1989.

E. H. Dowell, Aeroelasticity of Plates and Shells, Journal of Applied Mechanics, vol.43, issue.2, 1974.
DOI : 10.1115/1.3423871

N. J. Lindsley, C. L. Pettit, and P. S. Beran, Nonlinear plate aeroelastic response with uncertain stiffness and boundary conditions, Structure and Infrastructure Engineering, vol.26, issue.3-4, pp.201-220, 2006.
DOI : 10.2514/3.6041

. Fig, Bayesian stochastic inversion: first-order marginal posterior PDF over p 0 1 for the data set of length 25 estimated from 10, pp.1000-5000