Polynomial chaos expansion for sensitivity analysis

Sobol, 1993, Sensitivity estimates for nonlinear mathematical models, Mathematical Modelling and Computational Experiments, 1, 407

Homma, 1996, Importance measures in global sensitivity analysis of nonlinear models, Reliability Engineering and System Safety, 52, 1, 10.1016/0951-8320(96)00002-6

Ghanem, 1991

Li, 2002, Practical approaches to construct RS-HDMR component functions, Journal of Physical Chemistry A, 106, 8721, 10.1021/jp014567t

Rabitz, 1999, Efficient input–output model representations, Computer Physics Communications, 117, 11, 10.1016/S0010-4655(98)00152-0

Li, 2006, Random sampling-high dimensional model representation (RS-HDMR) and orthogonality of its different order component functions, Journal of Physical Chemistry A, 110, 2474, 10.1021/jp054148m

Storlie, 2008, Multiple predictor smoothing methods for sensitivity analysis: description of techniques, Reliability Engineering and System Safety, 93, 28, 10.1016/j.ress.2006.10.012

Ratto, 2007, State dependent parameter metamodelling and sensitivity analysis, Computer Physics Communications, 177, 863, 10.1016/j.cpc.2007.07.011

Oakley, 2004, Probabilistic sensitivity analysis of complex models: a Bayesian approach, Journal of the Royal Statistical Society Series B, 66, 751, 10.1111/j.1467-9868.2004.05304.x

Wiener, 1938, The homogeneous chaos, American Journal of Mathematics, 60, 897, 10.2307/2371268

Cameron, 1947, The orthogonal development of non-linear functionals in series of Fourier–Hermite functionals, Annals of Mathematics, 48, 385, 10.2307/1969178

Xiu, 2002, The Wiener–Askey polynomial chaos for stochastic differential equations, Journal of Scientific Computing, 26

Le Maıˆtre, 2004, Uncertainty propagation using Wiener–Haar expansions, Journal of Computational Physics, 197, 28, 10.1016/j.jcp.2003.11.033

Le Maıˆtre, 2004, Multi-resolution analysis of Wiener-type uncertainty propagation schemes, Journal of Computational Physics, 197, 502, 10.1016/j.jcp.2003.12.020

Le Maıˆtre, 2007, Multi-resolution-analysis scheme for uncertainty quantification in chemical systems, Journal of Scientific Computing, 29, 864, 10.1137/050643118

Wan, 2006, Multi-element generalized polynomial chaos for arbitrary probability measures, Journal of Scientific Computing, 28, 901, 10.1137/050627630

Reagan, 2003, Uncertainty quantification in reacting-flow simulations through non-intrusive spectral projection, Combustion and Flames, 132, 545, 10.1016/S0010-2180(02)00503-5

Tebbens, 2007, Sample-based estimation of correlation ratio with polynomial approximation, ACM Transactions on Modeling and Computer Simulation, 18

Smolyak, 1963, Quadrature and interpolation formulas for tensor products of certain classes of functions, Doklady Akademii Nauk SSSR, 4, 240

Gerstner, 1998, Numerical integration using sparse grids, Numerical Algorithms, 18, 209, 10.1023/A:1019129717644

Helton, 2003, Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems, Reliability Engineering and System Safety, 81, 23, 10.1016/S0951-8320(03)00058-9

Sobol, 1967, On the distribution of points in a cube and the approximate evaluation of integrals, USSR Computational Mathematics and Mathematical Physics, 7, 86, 10.1016/0041-5553(67)90144-9

Waldvogel, 2003, Fast construction of the Fejér and Clenshaw–Curtis quadrature rules, BIT Numerical Mathematics, 43, 001, 10.1023/A:1023659813269

Chun, 2000, An uncertainty importance measure using a distance metric for the change in a cumulative distribution function, Reliability Engineering and System Safety, 70, 313, 10.1016/S0951-8320(00)00068-5

Saltelli, 1995, About the use of rank transformation in sensitivity analysis of model output, Reliability Engineering and System Safety, 50, 225, 10.1016/0951-8320(95)00099-2

Gerstner, 2003, Dimension—adaptive tensor-product quadrature, Computer, 71, 65, 10.1007/s00607-003-0015-5

Crestaux T, Le Maıˆtre O, Martinez JM, Adaptive cubature for non-intrusive spectral projection methods, in preparation.

Soize, 2004, Physical systems with random uncertainties: chaos representations with arbitrary probability measure, Journal of Scientific Computing, 26, 395, 10.1137/S1064827503424505