G. E. Archer, A. Saltelli, and I. M. Sobol, Sensitivity measures,anova-like Techniques and the use of bootstrap, Journal of Statistical Computation and Simulation, vol.2, issue.2, pp.99-120, 1997.
DOI : 10.1142/S0129183195000204

P. F. Barbante, Accurate and efficient modelling of high temperature non-equilibrium air flows, 2001.

P. S. Beran, C. L. Pettit, and D. R. Millman, Uncertainty quantification of limit-cycle oscillations, Journal of Computational Physics, vol.217, issue.1, pp.217-247, 2006.
DOI : 10.1016/j.jcp.2006.03.038

G. Blatman and B. Sudret, Efficient computation of global sensitivity indices using sparse polynomial chaos expansions, Reliability Engineering & System Safety, vol.95, issue.11, pp.1216-1229, 2010.
DOI : 10.1016/j.ress.2010.06.015

G. Blatman and B. Sudret, An adaptive algorithm to build up sparse polynomial chaos expansions for stochastic finite element analysis, Probabilistic Engineering Mechanics, vol.25, issue.2, pp.183-197, 2010.
DOI : 10.1016/j.probengmech.2009.10.003

G. Blatman and B. Sudret, Adaptive sparse polynomial chaos expansion based on least angle regression, Journal of Computational Physics, vol.230, issue.6, pp.2345-2367, 2011.
DOI : 10.1016/j.jcp.2010.12.021

E. Borgonovo, A new uncertainty importance measure, Reliability Engineering & System Safety, vol.92, issue.6, pp.771-784, 2007.
DOI : 10.1016/j.ress.2006.04.015

E. Borgonovo, G. Apostolakis, A. Tarantola, and . Saltelli, Comparison of global sensitivity analysis techniques and importance measures in PSA, Reliability Engineering & System Safety, vol.79, issue.2, pp.175-185, 2003.
DOI : 10.1016/S0951-8320(02)00228-4

E. Borgonovo and S. Tarantola, Advances in sensitivity analysis, Reliability Engineering & System Safety, vol.107, pp.1-2, 2012.
DOI : 10.1016/j.ress.2012.09.001

D. Bose, M. Wright, and T. Gokçen, Uncertainty and Sensitivity Analysis of Thermochemical Modeling for Titan Atmospheric Entry, 37th AIAA Thermophysics Conference, 2004.
DOI : 10.2514/6.2004-2455

J. Caniou and B. Sudret, Distribution-based global sensitivity analysis in case of correlated input parameters using polynomial chaos expansions, 2011.
DOI : 10.1201/b11332-105

S. Choi, R. V. Grandhi, R. A. Canfield, and C. L. Pettit, Polynomial Chaos Expansion with Latin Hypercube Sampling for Estimating Response Variability, AIAA Journal, vol.42, issue.6, pp.1191-1198, 2004.
DOI : 10.2514/1.2220

F. Coquel and M. S. Liou, Hybrid Upwind Splitting Scheme by a Field-by-Field Decomposition, 1995.

T. Crestaux, O. L. Maître, and J. Martinez, Polynomial chaos expansion for sensitivity analysis, Reliability Engineering & System Safety, vol.94, issue.7, pp.1161-1172, 2009.
DOI : 10.1016/j.ress.2008.10.008

J. Foo and G. E. Karniadakis, Multi-element probabilistic collocation method in high dimensions, Journal of Computational Physics, vol.229, issue.5, pp.1536-1557, 2010.
DOI : 10.1016/j.jcp.2009.10.043

Z. Gao and J. S. Hesthaven, On ANOVA expansions and strategies for choosing the anchor point, ISUMA'90, First International Symposium on Uncertainty Modeling and Analysis, pp.3274-3285, 1990.
DOI : 10.1016/j.amc.2010.08.061

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

O. , L. Maître, M. T. Reagan, H. N. Najm, R. G. Ghanem et al., A Stochastic Projection Method for Fluid Flow II. Random Process, Journal of Computational Physics, vol.181, issue.1, pp.9-44, 2002.

B. Van-leer, Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method, Journal of Computational Physics, vol.32, issue.1, pp.101-136, 1979.
DOI : 10.1016/0021-9991(79)90145-1

G. Li, H. Rabitz, P. E. Yelvington, O. O. Oluwole, F. Bacon et al., Global Sensitivity Analysis for Systems with Independent and/or Correlated Inputs, The Journal of Physical Chemistry A, vol.114, issue.19, pp.1146022-1146054, 2010.
DOI : 10.1021/jp9096919

G. Li, C. Rosenthal, and H. Rabitz, High Dimensional Model Representations . The journal of physical chemistry, A, vol.105, issue.33, 2001.
DOI : 10.1021/jp010450t

X. Ma and N. Zabaras, An adaptive high-dimensional stochastic model representation technique for the solution of stochastic partial differential equations, Journal of Computational Physics, vol.229, issue.10, pp.3884-3915, 2010.
DOI : 10.1016/j.jcp.2010.01.033

G. Hermann, A. Matthies, and . Keese, Galerkin methods for linear and nonlinear elliptic stochastic partial differential equations, Computer Methods in Applied Mechanics and Engineering, vol.194, pp.12-161295, 2005.

S. Osher and F. Solomon, Upwind difference schemes for hyperbolic systems of conservation laws, Mathematics of Computation, vol.38, issue.158, pp.339-374, 1982.
DOI : 10.1090/S0025-5718-1982-0645656-0

C. Park, R. L. Jaffe, and H. Partridge, Chemical-Kinetic Parameters of Hyperbolic Earth Entry, Journal of Thermophysics and Heat Transfer, vol.15, issue.1, pp.76-90, 2001.
DOI : 10.2514/2.6582

H. Rabitz and O. F. Alis, General foundations of high-dimensional model representations, Journal of Mathematical Chemistry, vol.25, issue.2/3, pp.197-233, 1999.
DOI : 10.1023/A:1019188517934

H. Rabitz, Ö. F. Alis, J. Shorter, and K. Shim, Efficient input???output model representations, Computer Physics Communications, vol.117, issue.1-2, pp.11-20, 1999.
DOI : 10.1016/S0010-4655(98)00152-0

S. Rahman, A polynomial dimensional decomposition for stochastic computing, International Journal for Numerical Methods in Engineering, vol.39, issue.4, pp.2091-2116, 2008.
DOI : 10.1002/nme.2394

S. Rahman, Global sensitivity analysis by polynomial dimensional decomposition, Reliability Engineering & System Safety, vol.96, issue.7, pp.825-837, 2011.
DOI : 10.1016/j.ress.2011.03.002

S. Rahman and X. Ren, Novel computational methods for high-dimensional stochastic sensitivity analysis, International Journal for Numerical Methods in Engineering, vol.66, issue.3, 2014.
DOI : 10.1002/nme.4659

S. Rahman and V. Yadav, ORTHOGONAL POLYNOMIAL EXPANSIONS FOR SOLVING RANDOM EIGENVALUE PROBLEMS, International Journal for Uncertainty Quantification, vol.1, issue.2, pp.163-187, 2011.
DOI : 10.1615/IntJUncertaintyQuantification.v1.i2.40

A. Saltelli, Variance based sensitivity analysis of model output. Design and estimator for the total sensitivity index, Computer Physics Communications, vol.181, issue.2, pp.259-270, 2010.
DOI : 10.1016/j.cpc.2009.09.018

I. M. Sobol, Uniformly distributed sequences with an additional uniform property, USSR Computational Mathematics and Mathematical Physics, vol.16, issue.5, pp.236-242, 1976.
DOI : 10.1016/0041-5553(76)90154-3

I. M. Sobol, On sensitivity estimation for nonlinear mathematical models, Matem. Mod, vol.2, issue.1, pp.112-118, 1990.

I. M. Sobol, Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates, Mathematics and Computers in Simulation, vol.55, issue.1-3, pp.271-280, 2001.
DOI : 10.1016/S0378-4754(00)00270-6

B. Sudret, Global sensitivity analysis using polynomial chaos expansions, Reliability Engineering & System Safety, vol.93, issue.7, pp.964-979, 2008.
DOI : 10.1016/j.ress.2007.04.002
URL : https://hal.archives-ouvertes.fr/hal-01432217

K. Tang, M. Pietro, R. Congedo, and . Abgrall, Sensitivity analysis using anchored ANOVA expansion and high-order moments computation, International Journal for Numerical Methods in Engineering, vol.92, issue.6, pp.1-31, 2015.
DOI : 10.1002/nme.4856
URL : https://hal.archives-ouvertes.fr/hal-01086259

J. Thoemel, J. Muylaert, F. Ratti, and J. Gavira, In-Flight Testing of Critical Technologies and Experimentation of Aerothermodynamic Phenomena, 16th AIAA/DLR/DGLR International Space Planes and Hypersonic Systems and Technologies Conference, 2009.
DOI : 10.2514/6.2009-7232

J. Tryoen, P. M. Congedo, R. Abgrall, N. Villedieu, and T. E. Magin, Bayesian-Based Method with Metamodels for Rebuilding Freestream Conditions in Atmospheric Entry Flows, AIAA Journal, vol.52, issue.10, pp.522190-2197, 2014.
DOI : 10.2514/1.J052831
URL : https://hal.archives-ouvertes.fr/hal-00936641

N. Villedieu, F. Panerai, O. Chazot, and T. E. Magin, Uncertainty quantification for gassurface interaction in plasmatron, Specialists Meeting on Catalytic Gas Surface Interactions (AVT-199), 2012.

X. Wang, On the approximation error in high dimensional model representation, 2008 Winter Simulation Conference, pp.453-462, 2008.
DOI : 10.1109/WSC.2008.4736100

M. J. Wright, D. Bose, G. E. Palmer, and E. Levin, Recommended Collision Integrals for Transport Property Computations Part 1: Air Species, AIAA Journal, vol.43, issue.12, pp.2558-2564, 2005.
DOI : 10.2514/1.16713

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

D. Xiu and G. E. 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

C. Xu and G. Gertner, Extending a global sensitivity analysis technique to models with correlated parameters, Computational Statistics & Data Analysis, vol.51, issue.12, pp.5579-5590, 2007.
DOI : 10.1016/j.csda.2007.04.003

C. Xu and G. Gertner, Uncertainty and sensitivity analysis for models with correlated parameters, Reliability Engineering & System Safety, vol.93, issue.10, pp.1563-1573, 2008.
DOI : 10.1016/j.ress.2007.06.003

V. Yadav and S. Rahman, Adaptive-sparse polynomial dimensional decomposition methods for high-dimensional stochastic computing, Computer Methods in Applied Mechanics and Engineering, vol.274, pp.56-83, 2014.
DOI : 10.1016/j.cma.2014.01.027