S. Abraham, M. Raisee, G. Ghorbaniasl, F. Contino, and C. Lacor, A robust and efficient stepwise regression method for building sparse polynomial chaos expansions, Journal of Computational Physics, vol.332, pp.461-474, 2017.

M. Arnst, R. Ghanem, and C. Soize, Identification of bayesian posteriors for coefficients of chaos expansions, Journal of Computational Physics, pp.3134-3154, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00684317

M. Berveiller, B. Sudret, and M. Lemaire, Stochastic finite element: a non intrusive approach by regression, European Journal of Computational Mechanics/Revue Européenne de Mécanique Numérique, vol.15, pp.81-92, 2006.
URL : https://hal.archives-ouvertes.fr/hal-01665506

G. Blatman and B. Sudret, Sparse polynomial chaos expansions and adaptive stochastic finite elements using a regression approach, Comptes Rendus Mécanique, vol.336, pp.518-523, 2008.

G. Blatman and B. Sudret, Adaptive sparse polynomial chaos expansion based on least angle regression, Journal of Computational Physics, vol.230, pp.2345-2367, 2011.

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

B. P. Carlin and T. A. Louis, Bayesian Methods for Data Analysis, 2008.

B. Chen-charpentier and D. Stanescu, Parameter estimation using polynomial chaos and maximum likelihood, International Journal of Computer Mathematics, vol.91, pp.336-346, 2014.

P. Congdon, Bayesian Statistical Modelling, vol.704, 2007.

S. Das, R. Ghanem, and S. Finette, Polynomial chaos representation of spatio-temporal random fields from experimental measurements, Journal of Computational Physics, vol.228, pp.8726-8751, 2009.

S. Das, R. Ghanem, and J. C. Spall, Asymptotic sampling distribution for polynomial chaos representation from data: a maximum entropy and fisher information approach, SIAM Journal on Scientific Computing, vol.30, pp.2207-2234, 2008.

B. J. Debusschere, H. N. Najm, P. P. Pébay, O. M. Knio, R. G. Ghanem et al., Numerical challenges in the use of polynomial chaos representations for stochastic processes, SIAM journal on scientific computing, vol.26, pp.698-719, 2004.

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.66, pp.978-1001, 2006.
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.39, pp.831-838, 2007.

A. Doostan, R. G. Ghanem, and J. Red-horse, Stochastic model reduction for chaos representations, Computer Methods in Applied Mechanics and Engineering, vol.196, pp.3951-3966, 2007.

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

R. Ghanem, D. Higdon, and H. Owhadi, Handbook of Uncertainty Quantification, vol.1, 2017.

R. G. 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, pp.63-81, 2006.

R. G. Ghanem, A. Doostan, and J. , Red-Horse, A probabilistic construction of model validation, Computer Methods in Applied Mechanics and Engineering, vol.197, pp.2585-2595, 2008.

R. G. Ghanem and P. D. Spanos, Stochastic Finite Elements: a Spectral Approach, 1991.

D. Ghosh and R. Ghanem, Stochastic convergence acceleration through basis enrichment of polynomial chaos expansions, International journal for numerical methods in engineering, vol.73, pp.162-184, 2008.

G. Givens and J. Hoeting, Computational Statistics, 2013.

J. Guilleminot, C. Soize, D. Kondo, and C. Binetruy, Theoretical framework and experimental procedure for modelling mesoscopic volume fraction stochastic fluctuations in fiber reinforced composites, International Journal of Solids and Structures, vol.45, pp.5567-5583, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00684818

J. Kaipio and E. Somersalo, Statistical and Computational Inverse Problems, vol.160, 2005.

O. , L. Maître, and O. M. Knio, Spectral Methods for Uncertainty Quantification: With Applications to Computational Fluid Dynamics, 2010.

O. Le-maître, O. M. Knio, H. N. Najm, and R. Ghanem, Uncertainty propagation using wiener-haar expansions, Journal of computational Physics, vol.197, pp.28-57, 2004.

D. Lucor, C. Su, and G. E. Karniadakis, Generalized polynomial chaos and random oscillators, International Journal for Numerical Methods in Engineering, vol.60, pp.571-596, 2004.

I. Macdonald, Symmetric functions and Hall polynomials 2nd Ed, 2015.

R. Madankan, P. Singla, T. Singh, and P. D. Scott, Polynomial-chaos-based bayesian approach for state and parameter estimations, Journal of Guidance, Control, and Dynamics, vol.36, pp.1058-1074, 2013.

C. V. Mai and B. Sudret, Surrogate models for oscillatory systems using sparse polynomial chaos expansions and stochastic time warping, SIAM/ASA Journal on Uncertainty Quantification, vol.5, pp.540-571, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01421106

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, pp.1862-1902, 2009.

Y. M. Marzouk, H. N. Najm, and L. A. Rahn, Stochastic spectral methods for efficient bayesian solution of inverse problems, Journal of Computational Physics, vol.224, pp.560-586, 2007.

H. N. Najm, Uncertainty quantification and polynomial chaos techniques in computational fluid dynamics, Annual review of fluid mechanics, vol.41, pp.35-52, 2009.

A. Nouy and C. Soize, Random field representations for stochastic elliptic boundary value problems and statistical inverse problems, European Journal of Applied Mathematics, vol.25, pp.339-373, 2014.

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, pp.2917-2945, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00770006

G. Perrin, C. Soize, D. Duhamel, and C. Funfschilling, Karhunen-loève expansion revisited for vector-valued random fields: Scaling, errors and optimal basis, Journal of Computational Physics, pp.607-622, 2013.

B. Puig, F. Poirion, and C. Soize, Non-gaussian simulation using hermite polynomial expansion: convergences and algorithms, Probabilistic Engineering Mechanics, vol.17, pp.10-13, 2002.
URL : https://hal.archives-ouvertes.fr/hal-00686282

B. V. Rosi?, A. Litvinenko, O. Pajonk, and H. G. Matthies, Sampling-free linear bayesian update of polynomial chaos representations, Journal of Computational Physics, pp.5761-5787, 2012.

R. Y. Rubinstein and D. P. Kroese, Simulation and the Monte Carlo Method, 2008.

R. J. Serfling, Approximation theorems of mathematical statistics, vol.162, 1980.

Q. Shao, A. Younes, M. Fahs, and T. A. Mara, Bayesian sparse polynomial chaos expansion for global sensitivity analysis, Computer Methods in Applied Mechanics and Engineering, vol.318, pp.474-496, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01476649

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.2150-2164, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00684324

C. Soize, A computational inverse method for identification of non-gaussian random fields using the bayesian approach in very high dimension, Computer Methods in Applied Mechanics and Engineering, vol.200, pp.3083-3099, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00684294

C. Soize, Polynomial chaos expansion of a multimodal random vector, SIAM/ASA Journal on Uncertainty Quantification, vol.3, pp.34-60, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01105959

C. Soize, Uncertainty Quantification. An Accelerated Course with Advanced Applications in Computational Engineering, 2017.
URL : https://hal.archives-ouvertes.fr/hal-00826082

C. Soize and C. Desceliers, Computational aspects for constructing realizations of polynomial chaos in high dimension, SIAM Journal on Scientific Computing, vol.32, pp.2820-2831, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00684323

C. Soize and R. Ghanem, Physical systems with random uncertainties: chaos representations with arbitrary probability measure, SIAM Journal on Scientific Computing, vol.26, pp.395-410, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00686211

C. Soize and R. G. Ghanem, Reduced chaos decomposition with random coefficients of vectorvalued random variables and random fields, Computer Methods in Applied Mechanics and Engineering, vol.198, pp.1926-1934, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00684487

J. C. Spall, Introduction to Stochastic Searh and Optimization

I. Sraj, O. P. Le-maître, O. M. Knio, and I. Hoteit, Coordinate transformation and polynomial chaos for the bayesian inference of a gaussian process with parametrized prior covariance function, Computer Methods in Applied Mechanics and Engineering, vol.298, pp.205-228, 2016.

A. M. Stuart, Inverse problems: a bayesian perspective, Acta numerica, vol.19, pp.451-559, 2010.

A. Tarantola, Inverse Problem Theory And Methods For Model Parameter Estimation, vol.89, 2005.

G. Terrell and D. Scott, Variable kernel density estimation, The Annals of Statistics, vol.20, pp.1236-1265, 1992.

C. Thimmisetty, P. Tsilifis, and R. Ghanem, Homogeneous chaos basis adaptation for design optimization under uncertainty: Application to the oil well placement problem, Artificial Intelligence for Engineering Design, pp.265-276, 2017.

R. Tipireddy and R. Ghanem, Basis adaptation in homogeneous chaos spaces, Journal of Computational Physics, vol.259, pp.304-317, 2014.

P. Tsilifis and R. Ghanem, Bayesian adaptation of chaos representations using variational inference and sampling on geodesics, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.474, p.20180285, 2018.

P. Tsilifis and R. G. Ghanem, Reduced wiener chaos representation of random fields via basis adaptation and projection, Journal of Computational Physics, pp.102-120, 2017.

X. Wan and G. E. Karniadakis, Multi-element generalized polynomial chaos for arbitrary probability measures, SIAM Journal on Scientific Computing, vol.28, pp.901-928, 2006.

D. Xiu and G. E. Karniadakis, The wiener-askey polynomial chaos for stochastic differential equations, SIAM journal on scientific computing, vol.24, pp.619-644, 2002.