Bibliography¶
Aas K., Modelling the dependence structure of financial assets: a survey of four copulas, Norwegian Computing Center report nr. SAMBA/22/04, December 2004. pdf
Abate, J. and Whitt, W. (1992). The Fourier-series method for inverting transforms of probability distributions. Queueing Systems 10, 5–88., 1992, formula 5.5. pdf
Hervé Abdi, Paul Molin. Neil Salkind (Ed.) Lilliefors/Van Soest’s test of normality.. Encyclopedia of Measurement and Statistics, 2007.
Hervé Abdi, Paul Molin. New table and numerical approximations for approximations for Kolmogorov-Smirnov / Lillifors / Van Soest normality test., 1998.
Pierre-Olivier Amblard, Jean-François Coeurjolly, Frédéric Lavancier, Anne Philippe, Basic properties of the Multivariate Fractional Brownian Motion, pdf
Au, S. K. Estimation of small failure probabilities in high dimensions by subset simulation. Prob. Eng. Mech., 2001, 16(4), 263-277. pdf
Baudin M., Dutfoy A., Iooss B., Popelin A.-L. (2015) OpenTURNS: An Industrial Software for Uncertainty Quantification in Simulation. In: Ghanem R., Higdon D., Owhadi H. (eds) Handbook of Uncertainty Quantification. Springer pdf
Beirlant J., Goegebeur Y., Teugels J., Segers J., Statistics of extremes: theory and applications, Wiley, 2004
Bhattacharyya G.K., and R.A. Johnson, Statistical Concepts and Methods, John Wiley and Sons, New York, 1997.
Blatman, G. Adaptive sparse polynomial chaos expansions for uncertainty propagation and sensitivity analysis., PhD thesis. Blaise Pascal University-Clermont II, France, 2009. pdf
Blatman, G., and Sudret, B.. Adaptive sparse polynomial chaos expansion based on least angle regression. Journal of Computational Physics 230 (2011) 2345–2367.
Burnham, K.P., and Anderson, D.R. Model Selection and Multimodel Inference: A Practical Information Theoretic Approach, Springer, 2002.
Mathieu Cambou, Marius Hofert, Christiane Lemieux, Quasi-Random numbers for copula models, Stat. Comp., 2017, 27(5), 1307-1329. pdf
Caniou, Y. Global sensitivity analysis for nested and multiscale modelling. PhD thesis. Blaise Pascal University-Clermont II, France, 2012. pdf
Sameer Agarwal and Keir Mierle and Others, Ceres Solver, http://ceres-solver.org
Devernay, F. C/C++ Minpack, 2007. http://devernay.free.fr/hacks/cminpack
Coles, S. G., An Introduction to Statistical Modelling of Extreme Values. Springer, 2001.
D’Agostino, R.B. and Stephens, M.A. Goodness-of-Fit Techniques, Marcel Dekker, Inc., New York, 1986.
G. Damblin, M. Couplet and B. Iooss. Numerical studies of space filling designs: optimization of Latin hypercube samples and subprojection properties. Journal of Simulation, 7:276-289, 2013. pdf
Da Veiga, S. (2015). Global sensitivity analysis with dependence measures. Journal of Statistical Computation and Simulation, 85(7), 1283-1305.
Da Veiga, S., Gamboa, F., Iooss, B., and Prieur, C. (2021). Basics and trends in sensitivity analysis: theory and practice in R. Society for Industrial and Applied Mathematics.
Devroye L, Non-Uniform RandomVariate Generation, Springer-Verlag, New York, 1986 pdf
Devroye L, Non-Uniform RandomVariate Generation - Errata, pdf
Diebolt J., Improving probability-weighted moment methods for the generalized extreme value distribution, REVSTAT Statistical Journal, 2008. pdf
Dimitriadis J., On the Accuracy of Loader’s Algorithm for the Binomial Density and Algorithms for Rectangle Probabilities for Markov Increments, PhD thesis. Trier University, 2016. pdf
Dixon, W.J., Massey, F.J, Introduction to statistical analysis 4th ed., McGraw-Hill, 1983
Davis E. King, Dlib-ml: A Machine Learning Toolkit, Journal of Machine Learning Research, 10:1755-1758, 2009.
Doornik, J.A. An Improved Ziggurat Method to Generate Normal Random Samples, mimeo, Nuffield College, University of Oxford, 2005. pdf
Dubourg, V. Adaptative surrogate models for reliability and reliability-based design optimization, University Blaise Pascal - Clermont II, 2011. pdf
K-T. Fang, R. Li, and A. Sudjianto. Design and modeling for computer experiments. Chapman & Hall CRC, 2006.
David Freedman, Persi Diaconis, On the histogram as a density estimator: L2 theory, December 1981, Probability Theory and Related Fields. 57 (4): 453–476.
Gamboa, F., Janon, A., Klein, T. & Lagnoux, A. Sensitivity analysis for multidimensional and functional outputs. 2013. pdf
Gerstner, T., & Griebel, M. (1998). Numerical integration using sparse grids. Numerical algorithms, 18 (3), 209-232. pdf
Gretton, A., Bousquet, O., Smola, A., & Schölkopf, B. (2005, October). Measuring statistical dependence with Hilbert-Schmidt norms. In International conference on algorithmic learning theory (pp. 63-77). Springer, Berlin, Heidelberg.
Hormann W., The generation of Binomial Random Variates Journal of Statistical Computation and Simulation 46, pp. 101-110, 1993. pdf
Nathan Halko, Per-Gunnar Martinsson, Joel A. Tropp, Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions, pdf
Nathan Halko, Per-Gunnar Martisson, Yoel Shkolnisky and Mark Tygert, An algorithm for the principal component analysis of large data sets, pdf
Helton, J.C., and Davis, F. J., Latin Hypercube sampling and the propagation of uncertainty analyses of complex systems, Reliability Engineering and System Safety 81, 23-69. pdf
Iooss B., Lemaître P. (2015) A review on global sensitivity analysis methods. In: Meloni C., Dellino G. (eds) Uncertainty management in Simulation-Optimization of Complex Systems: Algorithms and Applications, Springer. pdf
Janon A., Klein T., Lagnoux-Renaudie A., Prieur C., Asymptotic normality and efficiency of two Sobol index estimators, ESAIM: Probability and Statistics, EDP Sciences, 2014, 18, pp.342-364. pdf
Jansen, M.J.W. Analysis of variance designs for model output, Computer Physics Communication, 1999, 117, 35-43. pdf
R. Jin, W. Chen, and A. Sudjianto. An efficient algorithm for constructing optimal design of computer experiments. Journal of Statistical Planning and Inference, 134 :268-287, 2005. pdf
Johnson M, Moore L and Ylvisaker D (1990). Minimax and maximin distance design. Journal of Statistical Planning and Inference 26(2): 131-148.
Donald R. Jones, Matthias Schonlau and William J Welch. Global optimization of expensive black-box functions, Journal of Global Optimization, 13(4), 455-492, 1998. pdf
Hovhannes Keutelian. The Kolmogorov-Smirnov test when parameters are estimated from data, 30 April 1991, Fermilab.
Kiureghian A., Dakessian T., Multiple design points in first and second-order reliability Structural Safety, Volume 20, Issue 1, 1998, Pages 37-49 pdf
Kleijnen J. P. C., Helton J. C., Statistical analyses of scatterplots to identify factors in large-scale simulations, 1: Review and comparison of techniques. Reliability Engineering and System Safety 65, 147-185 pdf
Knight, W. R. A Computer Method for Calculating Kendall’s Tau with Ungrouped Data. Journal of the American Statistical Association, 1966, 61(314, Part 1), 436-439. pdf
Knio, O. M., & Le Maitre, O. P. (2006). Uncertainty propagation in CFD using polynomial chaos decomposition. Fluid dynamics research, 38 (9), 616.
Le Maître, O., & Knio, O. M. (2010). Spectral methods for uncertainty quantification: with applications to computational fluid dynamics. Springer Science & Business Media.
Koay C.G., Basser P.J., Analytically exact correction scheme for signal extraction from noisy magnitude MR signals, Journal of magnetics Resonance 179, 317-322, 2006.
J.R. Koehler and A.B. Owen. Computer experiments. In S. Ghosh and C.R. Rao, editors, Design and analysis of experiments, volume 13 of Handbook of statistics. Elsevier, 1996.
Lebrun, R. & Dutfoy, A. An innovating analysis of the Nataf transformation from the copula viewpoint. Prob. Eng. Mech., 2009, 24, 312-320. pdf
Lebrun, R. & Dutfoy, A. A generalization of the Nataf transformation to distributions with elliptical copula. Prob. Eng. Mech., 2009, 24, 172-178. pdf
Lebrun, R. & Dutfoy, A. Do Rosenblatt and Nataf isoprobabilistic transformations really differ? Prob. Eng. Mech., 2009, 24, 577-584. pdf
Le Gratiet, L., Marelli, S., & Sudret, B. (2017). Metamodel-based sensitivity analysis: polynomial chaos expansions and Gaussian processes. In Handbook of uncertainty quantification 1289-1325. Springer, Cham.
L’Ecuyer P., Lemieux C. (2005) Recent Advances in Randomized Quasi-Monte Carlo Methods. In: Dror M., L’Ecuyer P., Szidarovszky F. (eds) Modeling Uncertainty. International Series in Operations Research & Management Science, vol 46. Springer, Boston, MA pdf
Lemaire M., Structural reliability, John Wiley & Sons, 2009.
Le Maître, O., & Knio, O. M. (2010). Spectral methods for uncertainty quantification: with applications to computational fluid dynamics. Springer Science & Business Media.
Liu, R., & Owen, A. B. (2006). Estimating mean dimensionality of analysis of variance decompositions. Journal of the American Statistical Association, 101 (474), 712-721.
On the Kolmogorov-Smirnov Test for Normality with Mean and Variance Unknown Hubert W. Lilliefors Journal of the American Statistical Association, Vol. 62, No. 318. (Jun., 1967), pp. 399-402. pdf
Loader C. Fast and Accurate Computation of Binomial Probabilities, pdf
S. Marelli, B. Sudret, An active-learning algorithm that combines sparse polynomial chaos expansions and bootstrap for structural reliability analysis, Structural Safety, 2018. pdf
Marrel, A., & Chabridon, V. (2021). Statistical developments for target and conditional sensitivity analysis: application on safety studies for nuclear reactor. Reliability Engineering & System Safety, 107711.
Marsaglia G. and Tsang W. W., A Simple Method for Generating Gamma, Journal of Statistical Computational and Simulation, vol 46, pp101 - 110,1993.
Martinez, J-M., Analyse de sensibilite globale par decomposition de la variance, Presentation in the meeting of GdR Ondes and GdR MASCOT-NUM, January, 13th, 2011, Institut Henri Poincare, Paris, France
G. Matthys & J. Beirlant, Estimating the extreme value index and high quantiles with exponential regression models, Statistica Sinica, 13, 850-880, 2003. pdf
J. A. Mauricio, Exact Maximum Likelihood Estimation of Stationary Vector ARMA Models, Journal of the American Statistical Association 90, 282-291, 1995. pdf
McKay M, Beckman R and Conover W (1979). A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 21(2): 239-245. pdf
Thomas P. Minka, Estimating a Dirichlet distribution, Microsoft Research report, 2000 (revised 2003, 2009, 2012). pdf
Morio J., Balesdent M., Estimation of Rare Event Probabilities in Complex Aerospace and Other Systems, A Practical Approach, Elsevier, 2015.
D. Morris and J. Mitchell. Exploratory designs for computational experiments. Journal of Statistical Planning and Inference, 43 :381-402, 1995. pdf
Morokoff, W. J., & Caflisch, R. E. (1995). Quasi-Monte Carlo integration. Journal of computational physics, 122(2), 218-230. pdf
Müller, A. C., & Guido, S. (2016). Introduction to machine learning with Python: a guide for data scientists. “ O’Reilly Media, Inc.”.
M. Munoz Zuniga, J. Garnier, E. Remy and E. de Rocquigny, Adaptative Directional Stratification for controlled estimation of the probability of a rare event, Reliability Engineering and System Safety, 2011. pdf
Nataf, A. Determination des distributions dont les marges sont donnees. C. R. Acad. Sci. Paris, 1962, 225, 42-43. pdf
Stephen G. Nash, 1999, A survey of Truncated-Newton methods, Systems Engineering and Operations Research Dept., George Mason University, Fairfax, VA 22030. pdf
Roger B. Nelsen, An Introduction to Copulas 2nd Edition, Springer, 2006.
Ya. Yu. Nikitin and A.V.Tchirina. Lilliefors Test for Exponentiality: Large Deviations,Asymptotic Efficiency, and Conditions of Local Optimality. Mathematical Methods of Statistics 16.1 (2007): 16-24.
NIST/SEMATECH e-Handbook of Statistical Methods, http://www.itl.nist.gov/div898/handbook/
Steven G. Johnson, The NLopt nonlinear-optimization package, http://ab-initio.mit.edu/nlopt
Petras, K. (2003). Smolyak cubature of given polynomial degree with few nodes for increasing dimension. Numerische Mathematik, 93 (4), 729-753.
Dumas A., Lois asymptotiques des estimateurs des indices de Sobol’, Technical report, Phimeca, 2018. pdf
Pronzato L and Muller W (2012). Design of computer experiments: Space filling and beyond. Statistics and Computing 22(3): 681-701. pdf
Rawlings, J. O., Pantula, S. G., and Dickey, D. A. Applied regression analysis: a research tool. Springer Science and Business Media, 2001.
Robert, C. P. The Metropolis-Hastings algorithm. arXiv preprint arXiv:1504.01896, 2015. pdf
Rosenblatt, M. Remarks on a multivariate transformation. Ann. Math. Stat., 1952, 23, 470-472. pdf
Rota, G. C. (1964). On the foundations of combinatorial theory I. Theory of Möbius functions.. Z. Wahrseheinlichkeitstheorie, volume 2, pages 340-368.
Rubinstein, R. Y., & Kroese, D. P. (2017). Simulation and the Monte Carlo method. John Wiley & Sons. pdf
Saltelli, A., Tarantola, S. and Chan, K. A quantitative, model independent method for global sensitivity analysis of model output. Technometrics, 1999, 41(1), 39-56. pdf
Saltelli, A., Chan, K. and Scott, M. Sensitivity analysis. John Wiley and Sons publishers, Probability and statistics series, 2000. pdf
Saltelli, A. Making best use of model evaluations to compute sensitivity indices. Computer Physics Communication, 2002, 145, 580-297. pdf
Sankararaman, S. and Mahadevan, S. Likelihood-based approach to multidisciplinary analysis under uncertainty. Journal of Mechanical Design, 134(3):031008, 2012.
Saporta, G. (1990). Probabilités, Analyse de données et Statistique, Technip
David W. Scott (1992). Multivariate density estimation, John Wiley & Sons, Inc.
W. F. Scott & B. Stewart. Tables for the Lilliefors and Modified Cramer–von Mises Tests of Normality., Communications in Statistics - Theory and Methods. Volume 40, 2011 - Issue 4. Pages 726-730.
Simard, R. & L’Ecuyer, P. Computing the Two-Sided Kolmogorov- Smirnov Distribution. Journal of Statistical Software, 2011, 39(11), 1-18. pdf
Sobol, I. M. Sensitivity analysis for non-linear mathematical model Math. Modelling Comput. Exp., 1993, 1, 407-414. pdf
Sobol, I.M., Tarantola, S., Gatelli, D., Kucherenko, S.S. and Mauntz, W. Estimating the approximation errors when fixing unessential factors in global sensitivity analysis, Reliability Engineering and System Safety, 2007, 92, 957-960. pdf
Soize, C., Ghanem, R. Physical systems with random uncertainties: Chaos representations with arbitrary probability measure, SIAM Journal on Scientific Computing, Society for Industrial and Applied Mathematics, 2004, 26 (2), 395-410. pdf
Sprent, P., and Smeeton, N.C. Applied Nonparametric Statistical Methods, Third edition, Chapman & Hall, 2001.
Stadlober E., The ratio of uniforms approach for generating discrete random variates. Journal of Computational and Applied Mathematics, vol. 31, no. 1, pp. 181-189, 1990. pdf
Stoer, J., Bulirsch, R. Introduction to Numerical Analysis, Second Edition, Springer-Verlag, 1993. pdf
Sudret, B. (2006). Global sensitivity analysis using polynomial chaos expansions. In. Proceedings of the 5th International Conference on Computational Stochastic Mechanics (CSM5), Rhodos (2006)
Sudret, B. (2008). Global sensitivity analysis using polynomial chaos expansions. Reliability engineering & system safety, 93 (7), 964-979.
Sullivan, T. J. (2015). Introduction to uncertainty quantification, Vol. 63. Springer.
Wand M.P, Jones M.C. Kernel Smoothing First Edition, Chapman & Hall, 1994.
Wertz, J. and Larson, W. Space Mission Analysis and Design. Microcosm, Inc. Torrance, CA.,1999.
Zaman, K. Modeling and management of epistemic uncertainty for multidisciplinary system analysis and design. PhD thesis, Vanderbilt University, USA, 2012