.. _bibliography: ============ Bibliography ============ .. [aas2004] 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 `__ .. [abate1992] 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 `__ .. [AbdiMolinSalkind2007] Hervé Abdi, Paul Molin. Neil Salkind (Ed.) *Lilliefors/Van Soest’s test of normality.*. Encyclopedia of Measurement and Statistics, 2007. .. [AbdiMolin1998] Hervé Abdi, Paul Molin. *New table and numerical approximations for approximations for Kolmogorov-Smirnov / Lillifors / Van Soest normality test.*, 1998. .. [amblard2012] Pierre-Olivier Amblard, Jean-François Coeurjolly, Frédéric Lavancier, Anne Philippe, *Basic properties of the Multivariate Fractional Brownian Motion*, `pdf `__ .. [au2001] Au, S. K. *Estimation of small failure probabilities in high dimensions by subset simulation*. Prob. Eng. Mech., 2001, 16(4), 263-277. `pdf `__ .. [bhattacharyya1997] Bhattacharyya G.K., and R.A. Johnson, *Statistical Concepts and Methods*, John Wiley and Sons, New York, 1997. .. [blatman2009] Blatman, G. *Adaptive sparse polynomial chaos expansions for uncertainty propagation and sensitivity analysis.*, PhD thesis. Blaise Pascal University-Clermont II, France, 2009. `pdf `__ .. [burnham2002] Burnham, K.P., and Anderson, D.R. *Model Selection and Multimodel Inference: A Practical Information Theoretic Approach*, Springer, 2002. .. [cambou2017] Mathieu Cambou, Marius Hofert, Christiane Lemieux, *Quasi-Random numbers for copula models*, Stat. Comp., 2017, 27(5), 1307-1329. `pdf `__ .. [caniou2012] Caniou, Y. *Global sensitivity analysis for nested and multiscale modelling.* PhD thesis. Blaise Pascal University-Clermont II, France, 2012. `pdf `__ .. [ceres2012] Sameer Agarwal and Keir Mierle and Others, *Ceres Solver*, http://ceres-solver.org .. [cminpack2007] Devernay, F. *C/C++ Minpack*, 2007. http://devernay.free.fr/hacks/cminpack .. [dagostino1986] D'Agostino, R.B. and Stephens, M.A. *Goodness-of-Fit Techniques*, Marcel Dekker, Inc., New York, 1986. .. [damblin2013] 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 `__ .. [devroye1986] Devroye L, *Non-Uniform RandomVariate Generation*, Springer-Verlag, New York, 1986 `pdf `__ .. [devroye1986b] Devroye L, *Non-Uniform RandomVariate Generation - Errata*, `pdf `__ .. [dimitriadis2016] 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 `__ .. [dixon1983] Dixon, W.J., Massey, F.J, *Introduction to statistical analysis* 4th ed., McGraw-Hill, 1983 .. [dlib2009] Davis E. King, *Dlib-ml: A Machine Learning Toolkit*, Journal of Machine Learning Research, 10:1755-1758, 2009. .. [doornik2005] Doornik, J.A. *An Improved Ziggurat Method to Generate Normal Random Samples*, mimeo, Nuffield College, University of Oxford, 2005. `pdf `__ .. [dubourg2011] Dubourg, V. *Adaptative surrogate models for reliability and reliability-based design optimization*, University Blaise Pascal - Clermont II, 2011. `pdf `__ .. [fang2006] K-T. Fang, R. Li, and A. Sudjianto. *Design and modeling for computer experiments.* Chapman & Hall CRC, 2006. .. [freedman1981] David Freedman, Persi Diaconis, *On the histogram as a density estimator: L2 theory*, December 1981, Probability Theory and Related Fields. 57 (4): 453–476. .. [gamboa2013] Gamboa, F., Janon, A., Klein, T. & Lagnoux, A. *Sensitivity analysis for multidimensional and functional outputs.* 2013. `pdf `__ .. [hormann1993] Hormann W., *The generation of Binomial Random Variates* Journal of Statistical Computation and Simulation 46, pp. 101-110, 1993. `pdf `__ .. [halko2010] Nathan Halko, Per-Gunnar Martinsson, Joel A. Tropp, *Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions*, `pdf `__ .. [halko2011] Nathan Halko, Per-Gunnar Martisson, Yoel Shkolnisky and Mark Tygert, *An algorithm for the principal component analysis of large data sets*, `pdf `__ .. [janon2014] 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 `__ .. [jansen1999] Jansen, M.J.W. *Analysis of variance designs for model output*, Computer Physics Communication, 1999, 117, 35-43. `pdf `__ .. [jin2005] 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 `__ .. [johnson1990] Johnson M, Moore L and Ylvisaker D (1990). *Minimax and maximin distance design.* Journal of Statistical Planning and Inference 26(2): 131-148. .. [jones1998] 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 `__ .. [Keutelian1991] Hovhannes Keutelian. *The Kolmogorov-Smirnov test when parameters are estimated from data*, 30 April 1991, Fermilab. .. [kiureghian1998] Kiureghian A., Dakessian T., *Multiple design points in first and second-order reliability* Structural Safety, Volume 20, Issue 1, 1998, Pages 37-49 `pdf `__ .. [knight1966] 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 `__ .. [koay2006] 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. .. [koehler1996] 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. .. [lebrun2009a] Lebrun, R. & Dutfoy, A. *An innovating analysis of the Nataf transformation from the copula viewpoint.* Prob. Eng. Mech., 2009, 24, 312-320. `pdf `__ .. [lebrun2009b] Lebrun, R. & Dutfoy, A. *A generalization of the Nataf transformation to distributions with elliptical copula.* Prob. Eng. Mech., 2009, 24, 172-178. `pdf `__ .. [lebrun2009c] Lebrun, R. & Dutfoy, A. *Do Rosenblatt and Nataf isoprobabilistic transformations really differ?* Prob. Eng. Mech., 2009, 24, 577-584. `pdf `__ .. [lecuyer2005] 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 `__ .. [lemaire2009] Lemaire M., *Structural reliability*, John Wiley & Sons, 2009. .. [Lilliefors1967] *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 `__ .. [loader2000] Loader C. *Fast and Accurate Computation of Binomial Probabilities*, `pdf `__ .. [marsaglia1993] Marsaglia G. and Tsang W. W., *A Simple Method for Generating Gamma*, Journal of Statistical Computational and Simulation, vol 46, pp101 - 110,1993. .. [martinez2011] 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 .. [matthys2003] G. Matthys & J. Beirlant, *Estimating the extreme value index and high quantiles with exponential regression models*, Statistica Sinica, 13, 850-880, 2003. `pdf `__ .. [mauricio1995] J. A. Mauricio, *Exact Maximum Likelihood Estimation of Stationary Vector ARMA Models*, Journal of the American Statistical Association 90, 282-291, 1995. `pdf `__ .. [mckay1979] 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 `__ .. [minka2012] Thomas P. Minka, *Estimating a Dirichlet distribution*, Microsoft Research report, 2000 (revised 2003, 2009, 2012). `pdf `__ .. [morris1995] D. Morris and J. Mitchell. *Exploratory designs for computational experiments.* Journal of Statistical Planning and Inference, 43 :381-402, 1995. `pdf `__ .. [munoz2011] 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 `__ .. [nataf1962] Nataf, A. *Determination des distributions dont les marges sont donnees.* C. R. Acad. Sci. Paris, 1962, 225, 42-43. `pdf `__ .. [nash1999] Stephen G. Nash, 1999, *A survey of Truncated-Newton methods*, Systems Engineering and Operations Research Dept., George Mason University, Fairfax, VA 22030. `pdf `__ .. [nelsen2006] Roger B. Nelsen, *An Introduction to Copulas 2nd Edition*, Springer, 2006. .. [NikitinTchirina2007] 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. .. [nisthandbook] NIST/SEMATECH e-Handbook of Statistical Methods, http://www.itl.nist.gov/div898/handbook/ .. [nlopt2009] Steven G. Johnson, The NLopt nonlinear-optimization package, http://ab-initio.mit.edu/nlopt .. [pmfre01116] Dumas A., *Lois asymptotiques des estimateurs des indices de Sobol'*, Technical report, Phimeca, 2018. `pdf `__ .. [pronzato2012] Pronzato L and Muller W (2012). *Design of computer experiments: Space filling and beyond.* Statistics and Computing 22(3): 681-701. `pdf `__ .. [rai2015] Rai, P. *Sparse Low Rank Approximation of Multivariate Functions - Applications in Uncertainty Quantification.*, PhD thesis. Ecole Centrale de Nantes, France, 2015. `pdf `__ .. [rosenblatt1952] Rosenblatt, M. *Remarks on a multivariate transformation.* Ann. Math. Stat., 1952, 23, 470-472. `pdf `__ .. [saltelli1999] Saltelli, A., Tarantola, S. & Chan, K. *A quantitative, model independent method for global sensitivity analysis of model output.* Technometrics, 1999, 41(1), 39-56. `pdf `__ .. [saltelli2002] Saltelli, A. *Making best use of model evaluations to compute sensitivity indices.* Computer Physics Communication, 2002, 145, 580-297. `pdf `__ .. [saporta1990] Saporta, G. (1990). *Probabilités, Analyse de données et Statistique*, Technip .. [scott1992] David W. Scott (1992). *Multivariate density estimation*, John Wiley & Sons, Inc. .. [ScottStewart2011] 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. .. [simard2011] Simard, R. & L'Ecuyer, P. *Computing the Two-Sided Kolmogorov- Smirnov Distribution.* Journal of Statistical Software, 2011, 39(11), 1-18. `pdf `__ .. [sobol1993] Sobol, I. M. *Sensitivity analysis for non-linear mathematical model* Math. Modelling Comput. Exp., 1993, 1, 407-414. `pdf `__ .. [sobol2007] 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 `__ .. [soizeghanem2004] 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 `__ .. [sprent2001] Sprent, P., and Smeeton, N.C. *Applied Nonparametric Statistical Methods*, Third edition, Chapman & Hall, 2001. .. [stadlober1990] 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 `__ .. [stoer1993] Stoer, J., Bulirsch, R. *Introduction to Numerical Analysis*, Second Edition, Springer-Verlag, 1993. `pdf `__ .. [wand1994] Wand M.P, Jones M.C. *Kernel Smoothing* First Edition, Chapman & Hall, 1994.