Chaospy: An open source tool for designing methods of uncertainty quantification

Rubinstein, 2007 Xiu, 2010 Eldred, 2007 Andrianov, 2007, Open TURNS, an open source initiative to Treat Uncertainties, Risks’ N Statistics in a structured industrial approach Debusschere, 2004, Numerical challenges in the use of polynomial chaos representations for stochastic processes, SIAM J. Sci. Comput., 26, 2, 10.1137/S1064827503427741 Conrad, 2013, Adaptive Smolyak pseudospectral approximations, SIAM J. Sci. Comput., 35, 6, 10.1137/120890715 Efron, 1979, Bootstrap methods: another look at the jackknife, Ann. Stat., 10.1214/aos/1176344552 Feinberg, 2014 McKinney, 2012 Laux, 2010, Impact of climate change on agricultural productivity under rainfed conditions in Cameroon – a method to improve attainable crop yields by planting date adaptations, Agric. For. Meteorol., 150, 10.1016/j.agrformet.2010.05.008 Boardman, 2011, A review of the application of copulas to improve modelling of non-bigaussian bivariate relationships (with an example using geological data) Dobric, 2007, A goodness of fit test for copulas based on Rosenblatt's transformation, Comput. Stat. Data Anal., 51, 10.1016/j.csda.2006.08.012 Achard, 2006, Complex parameter landscape for a complex neuron model, PLoS Comput. Biol., 2, 10.1371/journal.pcbi.0020094 J. Feinberg, H.P. Langtangen, Multivariate Polynomial Chaos with Dependent Variables Unpublished Journal Article. http://bit.ly/1Bkp72S. Rosenblatt, 1952, Remarks on a multivariate transformation, Ann. Math. Stat., 23, 10.1214/aoms/1177729394 Nelsen, 1999 Lee, 1993, Generating random binary deviates having fixed marginal distributions and specified degrees of association, Am. Stat., 47 Feinberg, 2013, RoseDist. Generalized tool for simulating with non-standard probability distributions, 367 Tezuka, 1995 Galanti, 1997, Low-discrepancy sequences: Monte Carlo simulation of option prices, J. Deriv., 5, 10.3905/jod.1997.407985 Halton, 1960, On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals, Numer. Math., 2, 10.1007/BF01386213 Hammersley, 1960, Monte Carlo methods for solving multivariable problems, Ann. N. Y. Acad. Sci., 86, 10.1111/j.1749-6632.1960.tb42846.x Haselgrove, 1961, A method for numerical integration, Math. Comput., 10.1090/S0025-5718-1961-0146960-1 Korobov, 1957, The approximate calculation of multiple integrals using number theoretic methods, Dokl. Acad. Nauk SSSR Niederreiter, 1987, Point sets and sequences with small discrepancy, Mon. Math., 104 Sobol, 1967, On the distribution of points in a cube and the approximate evaluation of integrals, USSR Comput. Math. Math. Phys., 7, 10.1016/0041-5553(67)90144-9 McKay, 1979, Comparison of three methods for selecting values of input variables in the analysis of output from a computer code, Technometrics, 21 Xiu, 2005, High-order collocation methods for differential equations with random inputs, SIAM J. Sci. Comput., 10.1137/040615201 Askey, 1985 Gautschi, 1968, Construction of Gauss-Christoffel quadrature formulas, Math. Comput., 22, 10.1090/S0025-5718-1968-0228171-0 Bertran, 1975, Note on orthogonal polynomials in v-variables, SIAM J. Math. Anal., 6, 10.1137/0506025 Gautschi, 2004 Stieltjes, 1884, Quelques recherches sur la théorie des quadratures dites mécaniques, Ann. Sci. École Norm. Sup., 3 Xiu, 2002, Stochastic modeling of flow-structure interactions using generalized polynomial chaos, J. Fluids Eng., 10.1115/1.1436089 Feinberg, 2013, Uncertainty quantification of diffusion in layered media by a new method based on polynomial chaos expansion Xiu, 2009, Fast numerical methods for stochastic computations: a review, Commun. Comput. Phys., 5 Sakamoto, 2002, Polynomial chaos decomposition for the simulation of non-Gaussian nonstationary stochastic processes, J. Eng. Mech., 128, 10.1061/(ASCE)0733-9399(2002)128:2(190) Ghanem, 2003 Back, 2011, Stochastic spectral Galerkin and collocation methods for PDEs with random coefficients: a numerical comparison, 43 Gottlieb, 1977 Hosder, 2007, Efficient sampling for non-intrusive polynomial chaos applications with multiple uncertain input variables Clenshaw, 1960, A method for numerical integration on an automatic computer, Numer. Math., 2, 10.1007/BF01386223 Stroud, 1971 Golub, 1967, Calculation of Gauss quadrature rules, Math. Comput. Patterson, 1968, The optimum addition of points to quadrature formulae, Math. Comput., 22, 10.1090/S0025-5718-68-99866-9 Genz, 1996, Fully symmetric interpolatory rules for multiple integrals over infinite regions, J. Comput. Appl. Math., 10.1016/0377-0427(95)00232-4 A. Naraya, J. Jakeman, Adaptive Leja Sparse Grid Construction for Stochastic Collocation and High-dimensional Approximation, 2014. arXiv e-print https://cfwebprod.sandia.gov/cfdocs/CompResearch/docs/1404.5663v1.pdf. Smolyak, 1963, Quadrature and interpolation formulas for tensor products of certain classes of functions, Dok. Akad. Nauk SSSR, 4, 123 Burkardt, 2009, The “combining coefficient” for anisotropic sparse grids, Tech. rep., Virginia Tech., 125 Rifkin, 2009, Notes on regularized least squares, J. Linear Algebra Efron, 2004, Least angle regression, Ann. Stat., 32, 10.1214/009053604000000067 Chen, 1998, Atomic decomposition by basis pursuit, SIAM J. Sci. Comput., 20, 10.1137/S1064827596304010 Wipf, 2007, A new view of automatic relevance determination, 1625 MacKay, 1992, Bayesian interpolation, Neural Comput., 4, 10.1162/neco.1992.4.3.415 Zou, 2005, Regularization and variable selection via the elastic net, J. R. Stat. Soc.: Ser. B (Stat. Methodol.), 67, 10.1111/j.1467-9868.2005.00503.x Hastie, 2007, Forward stagewise regression and the monotone lasso, Electr. J. Stat., 10.1214/07-EJS004 Zou, 2007, On the “degrees of freedom” of the lasso, Ann. Stat., 35, 10.1214/009053607000000127 Mallat, 1993, Matching pursuits with time-frequency dictionaries, IEEE Trans. Signal Process., 41, 10.1109/78.258082 Isukapalli, 1999 Jones, 2001 Pedregosa, 2011, Scikit-learn: machine learning in python, J. Mach. Learn. Res. Seabold, 2010, Statsmodels: econometric and statistical modeling with Python, 57, 10.25080/Majora-92bf1922-011