O. P. Le-ma??trema??tre and O. M. Knio, Spectral Methods for Uncertainty Quantification: With Applications to Computational Fluid Dynamics, 2010.
DOI : 10.1007/978-90-481-3520-2

D. Xiu, Numerical Methods for Stochastic Computations: A Spectral Method Approach, 2010.

C. Soize, Stochastic Models of Uncertainties in Computational Mechanics, 2012.
DOI : 10.1061/9780784412237

URL : https://hal.archives-ouvertes.fr/hal-00749201

M. Grigoriu, Stochastic Systems: Uncertainty Quantification and Propagation, 2012.
DOI : 10.1007/978-1-4471-2327-9

H. Bijl, D. Lucor, S. Mishra, and C. Schwab, Uncertainty Quantification in Computational Fluid Dynamics, 2013.
DOI : 10.1007/978-3-319-00885-1

M. P. Pettersson, G. Iaccarino, and J. Nordström, Polynomial Chaos Methods for Hyperbolic Partial Differential Equations: Numerical Techniques for Fluid Dynamics Problems in the Presence of Uncertainties, 2015.
DOI : 10.1007/978-3-319-10714-1

R. Ohayon and C. Soize, Advanced Computational Vibroacoustics: Reduced-Order Models and Uncertainty Quantification, 2015.
DOI : 10.1017/CBO9781107785328

URL : https://hal.archives-ouvertes.fr/hal-01162161

T. J. Sullivan, Introduction to Uncertainty Quantification, 2015.
DOI : 10.1007/978-3-319-23395-6

S. Sarkar and J. A. Witteveen, Uncertainty Quantification in Computational Science, 2016.
DOI : 10.1142/9854

URL : http://www.worldscientific.com/doi/pdf/10.1142/9789814730587_fmatter

R. Ghanem, D. Higdon, and H. Owhadi, Handbook of Uncertainty Quantification, 2017.

C. Soize, Uncertainties and Stochastic Modeling. Short Course at PUC-Rio, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00826058

C. Soize, Stochastic Models in Computational Mechanics. Short Course at PUC-Rio, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00749201

C. Soize, Probabilité et Modélisation des Incertitudes: Eléments de base et concepts fondamentaux, Course Notes, 2013.

G. Iaccarino, Introduction to Uncertainty Quantification, Lecture at KAUST, 2012.

A. Doostan and P. Constantine, Numerical Methods for Uncertainty Propagation

C. Soize, A comprehensive overview of a non-parametric probabilistic approach of model uncertainties for predictive models in structural dynamics, Journal of Sound and Vibration, vol.288, issue.3, pp.623-652, 2005.
DOI : 10.1016/j.jsv.2005.07.009

URL : https://hal.archives-ouvertes.fr/hal-00686182

W. L. Oberkampf and T. G. Trucano, Verification and Validation in Computational Fluid Dynamics, 2002.

W. Oberkampf, T. Trucano, and C. Hirsch, Verification, validation, and predictive capability in computational engineering and physics, Applied Mechanics Reviews, vol.14, issue.5, pp.345-384, 2004.
DOI : 10.1063/1.4823173

W. L. Oberkampf and C. J. Roy, Verification and Validation in Scientific Computing, 2010.
DOI : 10.1017/CBO9780511760396

P. J. Roache, Code Verification by the Method of Manufactured Solutions, Journal of Fluids Engineering, vol.100, issue.1, pp.4-10, 2001.
DOI : 10.2514/6.2001-2606

C. J. Roy, Review of code and solution verification procedures for computational simulation, Journal of Computational Physics, vol.205, issue.1, pp.131-156, 2005.
DOI : 10.1016/j.jcp.2004.10.036

L. A. Petri, P. Sartori, J. K. Rogenski, and L. F. De-souza, Verification and validation of a Direct Numerical Simulation code, Computer Methods in Applied Mechanics and Engineering, vol.291, pp.291-266, 2015.
DOI : 10.1016/j.cma.2015.04.001

G. I. Schuëller, A state-of-the-art report on computational stochastic mechanics, Probabilistic Engineering Mechanics, vol.12, issue.4, pp.197-321, 1997.
DOI : 10.1016/S0266-8920(97)00003-9

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

C. Soize, Stochastic modeling of uncertainties in computational structural dynamics???Recent theoretical advances, Journal of Sound and Vibration, vol.332, issue.10, pp.2379-2395, 2013.
DOI : 10.1016/j.jsv.2011.10.010

URL : https://hal.archives-ouvertes.fr/hal-00743699

D. Moens and D. Vandepitte, A survey of non-probabilistic uncertainty treatment in finite element analysis, Computer Methods in Applied Mechanics and Engineering, vol.194, issue.12-16, pp.1527-1555, 2005.
DOI : 10.1016/j.cma.2004.03.019

D. Moens and M. Hanss, Non-probabilistic finite element analysis for parametric uncertainty treatment in applied mechanics: Recent advances. Finite Elements in Analysis and Design, pp.47-51, 2011.

M. Beer, S. Ferson, and V. Kreinovich, Imprecise probabilities in engineering analyses, Mechanical Systems and Signal Processing, vol.37, issue.1-2, pp.4-29, 2013.
DOI : 10.1016/j.ymssp.2013.01.024

URL : http://digitalcommons.utep.edu/cgi/viewcontent.cgi?article=1733&context=cs_techrep

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, 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 : 10.1007/978-94-011-2430-0_1

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

A. Batou, C. Soize, and M. Corus, Experimental identification of an uncertain computational dynamical model representing a family of structures, Computers & Structures, vol.89, issue.13-14, pp.1440-1448, 2011.
DOI : 10.1016/j.compstruc.2011.03.004

URL : https://hal.archives-ouvertes.fr/hal-00684292

G. Grimmett and D. Welsh, Probability: An Introduction, 2014.

A. Klenke, Probability Theory: A Comprehensive Course, 2014.

C. E. Shannon, A Mathematical Theory of Communication, Bell System Technical Journal, vol.27, issue.3, pp.379-423, 1948.
DOI : 10.1002/j.1538-7305.1948.tb01338.x

L. Wasserman, All of Nonparametric Statistics, 2007.

L. Wasserman, All of Statistics: A Concise Course in Statistical Inference, 2004.
DOI : 10.1007/978-0-387-21736-9

E. T. Jaynes, Information Theory and Statistical Mechanics, Physical Review, vol.101, issue.4, pp.620-630, 1957.
DOI : 10.1103/PhysRev.101.1227

E. T. Jaynes, Information Theory and Statistical Mechanics. II, Physical Review, vol.102, issue.2, pp.171-190, 1957.
DOI : 10.1103/PhysRev.102.151

J. N. Kapur and H. K. Kesavan, Entropy Optimization Principles and Their Applications, 1992.
DOI : 10.1007/978-94-011-2430-0_1

J. N. Kapur, Maximum-Entropy Models in Science and Engineering., Biometrics, vol.48, issue.1, 2009.
DOI : 10.2307/2532770

F. E. Udwadia, Response of uncertain dynamic systems. I, Applied Mathematics and Computation, vol.22, issue.2-3, pp.115-150, 1987.
DOI : 10.1016/0096-3003(87)90040-3

F. E. Udwadia, Response of uncertain dynamic systems. I, Applied Mathematics and Computation, vol.22, issue.2-3, pp.151-187, 1987.
DOI : 10.1016/0096-3003(87)90040-3

F. E. Udwadia, Some Results on Maximum Entropy Distributions for Parameters Known to Lie in Finite Intervals, SIAM Review, vol.31, issue.1, pp.31-103, 1989.
DOI : 10.1137/1031004

K. Sobezyk and J. Trçbicki, Maximum entropy principle in stochastic dynamics, Probabilistic Engineering Mechanics, vol.5, issue.3, pp.102-110, 1990.
DOI : 10.1016/0266-8920(90)90001-Z

K. Sobezyk and J. Tr¸ebickitr¸ebicki, Maximum entropy principle and nonlinear stochastic oscillators. Physica A: Statistical Mechanics and its Applications, pp.448-468, 1993.

J. Tr¸ebickitr¸ebicki and K. Sobezyk, Maximum entropy principle and non-stationary distributions of stochastic systems, Probabilistic Engineering Mechanics, vol.11, issue.3, pp.169-178, 1996.
DOI : 10.1016/0266-8920(96)00008-2

A. C. Jr, R. Nasser, R. Sampaio, H. Lopes, and K. Breitman, Uncertainty quantification through Monte Carlo method in a cloud computing setting, Computer Physics Communications, vol.185, pp.1355-1363, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01438643

N. Metropolis and S. Ulam, The Monte Carlo Method, Journal of the American Statistical Association, vol.44, issue.247, pp.335-341, 1949.
DOI : 10.1080/01621459.1949.10483310

J. S. Liu, Monte Carlo Strategies in Scientific Computing, 2001.
DOI : 10.1007/978-0-387-76371-2

G. Fishman, Monte Carlo: Concepts, Algorithms, and Applications, 2003.
DOI : 10.1007/978-1-4757-2553-7

R. Y. Rubinstein and D. P. Kroese, Simulation and the Monte Carlo Method, 2007.

S. Asmussen and P. W. Glynn, Stochastic Simulation: Algorithms and Analysis, 2007.

R. W. Shonkwiler and F. Mendivil, Explorations in Monte Carlo Methods, 2009.
DOI : 10.1007/978-0-387-87837-9

C. P. Robert and G. Casella, Monte Carlo Statistical Methods, 2010.

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

R. Ghanem and P. D. Spanos, Stochastic Finite Elements: A Spectral Approach, 2003.
DOI : 10.1007/978-1-4612-3094-6

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

P. Vos, Time-dependent polynomial chaos, 2006.

P. Constantine, A Primer on Stochastic Galerkin Methods, Lecture Notes, 2007.

A. O. Hagan, Polynomial Chaos: A tutorial and critique from a statistician's perspective, p.2013