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.

[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.

[acklam2017]

Acklam P.J. Acklam’s algorithm for the inverse normal cdf, 2017. https://stackedboxes.org/2017/05/01/acklams-normal-quantile-function/

[amblard2012]

Pierre-Olivier Amblard, Jean-François Coeurjolly, Frédéric Lavancier, Anne Philippe, Basic properties of the Multivariate Fractional Brownian Motion, pdf

[arnold2008]

Arnold B.C, Balakrishnan N., Nagaraja H. N., A First Course in Order Statistics, SIAM, 2008

[au2001]

Au, S. K. Estimation of small failure probabilities in high dimensions by subset simulation. Prob. Eng. Mech., 2001, 16(4), 263-277. pdf

[baudin2015]

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

[baron2014]

Baron, M. (2019). Probability and statistics for computer scientists. CRC press.

[beirlant2004]

Beirlant J., Goegebeur Y., Teugels J., Segers J., Statistics of extremes: theory and applications, Wiley, 2004

[benton2003]

Benton D. and Krishnamoorthy K. (2003). Computing discrete mixtures of continuous distributions: noncentral chisquare, noncentral t and the distribution of the square of the sample multiple correlation coefficient. Computational Statistics and Data Analysis, 43 (2003) pp 249-267, https://www.sciencedirect.com/science/article/abs/pii/S0167947302002839

[bhattacharyya1997]

Bhattacharyya G.K., and R.A. Johnson, Statistical Concepts and Methods, John Wiley and Sons, New York, 1997.

[bjork1996]

A. Bjorck (1996), Numerical methods for least squares problems, SIAM Press, Philadelphia.

[blatman2009]

Blatman, G. Adaptive sparse polynomial chaos expansions for uncertainty propagation and sensitivity analysis., PhD thesis. Blaise Pascal University-Clermont II, France, 2009. pdf

[blatman2011]

Blatman, G., and Sudret, B.. Adaptive sparse polynomial chaos expansion based on least angle regression. Journal of Computational Physics 230 (2011) 2345–2367.

[borgonovo2017]

Borgonovo, E. (2017). Sensitivity analysis. An Introduction for the Management Scientist. International Series in Operations Research and Management Science. Cham, Switzerland : Springer.

[burman1989]

P. Burman. Comparative study of Ordinary Cross-Validation, v-Fold Cross-Validation and the repeated Learning-Testing Methods. Biometrika, 76(3):503–514, 1989.

[burnham2002]

Burnham, K.P., and Anderson, D.R. Model Selection and Multimodel Inference: A Practical Information Theoretic Approach, Springer, 2002.

[bingham2010]

Bingham, N. H., & Fry, J. M. (2010). Regression: Linear models in statistics. Springer.

[Bjorck1996]

Björck, Å. (1996). Numerical methods for least squares problems. Society for Industrial and Applied Mathematics.

[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

[chacon2018]

Chacón, J. E., & Duong, T. (2018). Multivariate kernel smoothing and its applications. CRC Press.

[charpentier2015]

Charpentier, A., & Flachaire, E. (2014). Log-Transform Kernel Density Estimation of Income Distribution WP 2015-Nr 6, AMSE Aix Marseille School of Economics. pdf

[chihara1978]

Chihara, T. S. (1978). An introduction to orthogonal polynomials. Dover publications.

[chapelle2002]

Chapelle, O., Vapnik, V., & Bengio, Y. (2002). Model selection for small sample regression. Machine Learning, 48(1-3), 9.

[cminpack2007]

Devernay, F. C/C++ Minpack, 2007. http://devernay.free.fr/hacks/cminpack

[coles2001]

Coles, S. G., An Introduction to Statistical Modelling of Extreme Values. Springer, 2001.

[dagostino1986]

D’Agostino, R.B. and Stephens, M.A. Goodness-of-Fit Techniques, Marcel Dekker, Inc., New York, 1986.

[dahlquist2008]

Dahlquist, G. and Björck, A. Numerical methods in scientific computing, volume I. Society for Industrial and Applied Mathematics. 2008

[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

[daveiga2015]

Da Veiga, S. (2015). Global sensitivity analysis with dependence measures. Journal of Statistical Computation and Simulation, 85(7), 1283-1305.

[daveiga2022]

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.

[davis1975]

Davis, P.-J. and P.Rabinowitz, P. (1975). Methods of numerical integration, Academic Press.

[delmas2006]

Delmas, J.F. and Jourdain, B. Modèles aléatoires: Applications aux sciences de l’ingénieur et du vivant , Berlin, Heidelberg: Springer Berlin Heidelberg (2006). La maîtrise des incertitudes dans un contexte industriel. 1re partie: une approche méthodologique globale basée sur des exemples. Journal de la Société française de statistique, 147 (3), 33-71.

[deRocquigny2006]

De Rocquigny, É. (2006). La maîtrise des incertitudes dans un contexte industriel. 1re partie: une approche méthodologique globale basée sur des exemples. Journal de la Société française de statistique, 147 (3), 33-71.

[deRocquigny2012]

De Rocquigny, E. (2012). Modelling under risk and uncertainty. John Wiley & Sons.

[deisenroth2020]

Deisenroth, M. P., Faisal, A. A., and Ong, C. S. (2020). Mathematics for machine learning. Cambridge University Press.

[devroye1986]

Devroye L, Non-Uniform RandomVariate Generation, Springer-Verlag, New York, 1986 pdf

[devroye1986b]

Devroye L, Non-Uniform RandomVariate Generation - Errata

[diebolt2008]

Diebolt J., Improving probability-weighted moment methods for the generalized extreme value distribution, REVSTAT Statistical Journal, 2008. 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.

[dobrolowski2014]

Dobrolowski, E. and Kumar, P., Some properties of the Marshall-Olkin and generalized Cuadras-Augé families of copulas, The Australian Journal of Mathematical Analysis and Applications, 11(1), 1-13, 2014. pdf

[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

[ernst2012]

Ernst, O. G., Mugler, A., Starkloff, H. J., & Ullmann, E. (2012). On the convergence of generalized polynomial chaos expansions. ESAIM: Mathematical Modelling and Numerical Analysis, 46(2), 317-339.

[fang2006]

K-T. Fang, R. Li, and A. Sudjianto. Design and modeling for computer experiments. Chapman & Hall CRC, 2006.

[faraway2014]

Faraway, J. J. (2014). Linear models with R. Second Edition CRC press.

[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

[gamboa2022]

Gamboa, F., Gremaud, P., Klein, T. & Lagnoux, A. Global sensitivity analysis: A novel generation of mighty estimators based on rank statistics Bernoulli 28(4): 2345-2374, 2022. pdf

[gautschi2004]

Gautschi, W. (2004). Orthogonal polynomials: computation and approximation. OUP Oxford.

[genz2003]

Genz A., Cools R., An adaptive numerical cubature algorithm for simplices, ACM Transactions on Mathematical Software 29(3):297-308, September 2003. pdf

[ghanem1991]

Ghanem R. and P. Spanos, 1991, Stochastic finite elements - A spectral approach, Springer Verlag. (Reedited by Dover Publications, 2003).

[gerstner1998]

Gerstner, T., & Griebel, M. (1998). Numerical integration using sparse grids. Numerical algorithms, 18 (3), 209-232. pdf

[girardin2018]

Girardin, V., & Limnios, N. (2018). Applied probability. From Random Sequences to Stochastic Processes (Springer, Cham).

[gretton2005]

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.

[hormann1993]

Hormann W., The generation of Binomial Random Variates Journal of Statistical Computation and Simulation 46, pp. 101-110, 1993. pdf

[hahn2005]

Thomas Hahn, Cuba - a library for multidimensional numerical integration Computer Physics Communications, 168(2), 78-95. 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

[hammersley1961]

Hammersley, J. M., & Handscomb, D. C. (1961). Monte Carlo Methods. Chapman and Hall. Monographs on Statistics and Applied Probability.

[hastie2009]

Hastie, T., Tibshirani, R., Friedman, J. H., & Friedman, J. H. (2009). The elements of statistical learning: data mining, inference, and prediction. New York: springer.

[helton2003]

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

[hotelling1933]

Hotelling, H. (1933). Analysis of a complex of statistical variables into principal components. Journal of educational psychology, 24(6):417.

[iooss2015]

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

[jackson1991]

Jackson, J. E. (1991). A user’s guide to principal components. John Wiley & Sons.

[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.

[jolliffe2002]

Jolliffe, I. T. (2002). Principal component analysis. Springer.

[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

[jones1993]

M.C. Jones, Simple boundary correction for kernel density estimation, Statistics and Computing. Vol. 3, Issue 3, 1993, pp. 135-146, https://doi.org/10.1007/BF00147776

[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

[kleijnen1999]

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

[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

[knio2006]

Knio, O. M., & Le Maitre, O. P. (2006). Uncertainty propagation in CFD using polynomial chaos decomposition. Fluid dynamics research, 38 (9), 616.

[knio2010]

Le Maître, O., & Knio, O. M. (2010). Spectral methods for uncertainty quantification: with applications to computational fluid dynamics. Springer Science & Business Media.

[ko1994]

William L. Ko, Raymond H. Jackson, Share Buckling Analysis of a Hat-Stiffend Panel, NASA Technical Memorandum 4644 (November 1994).

[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

[legratiet2017]

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.

[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.

[lemaitre2010]

Le Maître, O., & Knio, O. M. (2010). Spectral methods for uncertainty quantification: with applications to computational fluid dynamics. Springer Science & Business Media.

[lemieux2009]

Lemieux, C. (2009). Monte Carlo and Quasi-Monte Carlo Sampling. Springer. Springer Series in Statistics.

[leriche2021]

Le Riche, R., & Picheny, V. (2021). Revisiting Bayesian optimization in the light of the COCO benchmark. Structural and Multidisciplinary Optimization, 64, 3063-3087.

[liu2006]

Liu, R., & Owen, A. B. (2006). Estimating mean dimensionality of analysis of variance decompositions. Journal of the American Statistical Association, 101 (474), 712-721.

[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

[Limbourg2010]

Limbourg, P., & De Rocquigny, E. (2010). Uncertainty analysis using evidence theory–confronting level-1 and level-2 approaches with data availability and computational constraints. Reliability Engineering & System Safety, 95(5), 550-564.

[loader2000]

Loader C. Fast and Accurate Computation of Binomial Probabilities, pdf

[luke]

Luke Gustafson. The Spearman Rho null distribution. https://www.luke-g.com/math/spearman/index.html

[luo2018]

Zhendong Luo, Goong Chen Proper Orthogonal Decomposition Methods for Partial Differential Equations. (2018) Academic Press.

[marelli2018]

S. Marelli, B. Sudret, An active-learning algorithm that combines sparse polynomial chaos expansions and bootstrap for structural reliability analysis, Structural Safety, 2018. pdf

[marrel2021]

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.

[marsaglia1993]

Marsaglia G. and Tsang W. W. A Simple Method for Generating Gamma, Journal of Statistical Computational and Simulation, vol 46, pp101 - 110,1993. https://www.researchgate.net/publication/220492850_A_simple_method_for_generating_Gamma_Variables

[marsaglia2000]

Marsaglia G. and Tsang W.W. A simple method for generating gamma variables, ACM Transactions on Mathematical Software, Vol. 26, No. 3, September 2000, Pages 363-372 https://dl.acm.org/doi/10.1145/358407.358414

[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

[melchers1990]

Melchers, R. E. (1990). Radial importance sampling for structural reliability. Journal of engineering mechanics, 116(1), 189-203.

[minka2012]

Thomas P. Minka, Estimating a Dirichlet distribution, Microsoft Research report, 2000 (revised 2003, 2009, 2012). pdf

[morio2015]

Morio J., Balesdent M., Estimation of Rare Event Probabilities in Complex Aerospace and Other Systems, A Practical Approach, Elsevier, 2015.

[morris1995]

D. Morris and J. Mitchell. Exploratory designs for computational experiments. Journal of Statistical Planning and Inference, 43 :381-402, 1995. pdf

[morokoff1995]

Morokoff, W. J., & Caflisch, R. E. (1995). Quasi-Monte Carlo integration. Journal of computational physics, 122(2), 218-230. pdf

[muller2016]

Müller, A. C., & Guido, S. (2016). Introduction to machine learning with Python: a guide for data scientists. “ O’Reilly Media, Inc.”.

[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

[johnson1995]

Johnson, N. L. and Kotz, S; and Balakrishnan, N., Continuous univariate distributions volume 2, second edition, 1995, Wiley Inter-Science.

[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

[novak1999]

Novak, E., & Ritter, K. (1999). Simple cubature formulas with high polynomial exactness. Constructive approximation, 15, 499-522.

[park1990]

Byeong U. Park and J. S. Marron. Comparison of data-driven bandwidth selectors. Journal of the American Statistical Association, 85(409) :66–72, 1990.

[pearson1907]

Pearson, K. (1901). On lines and planes of closest fit to systems of points in space. The London, Edinburgh, and Dublin philosophical magazine and journal of science, 2(11):559–572.

[pelamatti2020]

Pelamatti, J., Brevault, L., Balesdent, M., Talbi, E. G., & Guerin, Y. (2020). Overview and comparison of gaussian process-based surrogate models for mixed continuous and discrete variables: Application on aerospace design problems. High-Performance Simulation-Based Optimization, 189-224.

[peng2014]

L. Peng, R. Wang, Interval Estimation for Bivariate t-Copulas via Kendall’s Tau Casualty Actuarial Society, Volume 8/Issue 1, 2014. pdf

[peter2019]

Jacques Peter, Eric Savin, Itham Salah el Din. Generalized polynomial chaos and stochastic collocation methods for uncertainty quantification in aerodynamics. STO-AVT-326 Uncertainty Quantification in Computational Fluid Dynamics.

[petras2003]

Petras, K. (2003). Smolyak cubature of given polynomial degree with few nodes for increasing dimension. Numerische Mathematik, 93 (4), 729-753.

[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

[raykar2006]

Vikas Chandrakant Raykar, Ramani Duraiswami Very Fast optimal bandwidth selection for univariate kernel density estimation. CS-TR-4774. University of Maryland, College Park, MD 20783, 2006

[rawlings2001]

Rawlings, J. O., Pantula, S. G., and Dickey, D. A. Applied regression analysis: a research tool. Springer Science and Business Media, 2001.

[robert2015]

Robert, C. P. The Metropolis-Hastings algorithm. arXiv preprint arXiv:1504.01896, 2015. pdf

[robertson2024]

Robertson, G., Sjöstrand, H., Andersson, P., Göök, A. and Blair, P. Addressing model inadequacy in fuel performance model calibration using MH-within-gibbs sampling. Best Estimate Plus Uncertainty International Conference (BEPU 2024), Real Collegio, Lucca, Tuscany, Italy, May 19–24, 2024. Nuclear and Industrial Engineering (NINE) pdf

[rosenblatt1952]

Rosenblatt, M. Remarks on a multivariate transformation. Ann. Math. Stat., 1952, 23, 470-472. pdf

[rota1964]

Rota, G. C. (1964). On the foundations of combinatorial theory I. Theory of Möbius functions.. Z. Wahrseheinlichkeitstheorie, volume 2, pages 340-368.

[rubinstein2017]

Rubinstein, R. Y., & Kroese, D. P. (2017). Simulation and the Monte Carlo method. John Wiley & Sons. pdf

[rudin1987]

Rudin, W. Real and complex analysis 1987.

[saltelli1999]

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

[saltelli2000]

Saltelli, A., Chan, K. and Scott, M. Sensitivity analysis. John Wiley and Sons publishers, Probability and statistics series, 2000. pdf

[saltelli2002]

Saltelli, A. Making best use of model evaluations to compute sensitivity indices. Computer Physics Communication, 2002, 145, 580-297. pdf

[sankararaman2012]

Sankararaman, S. and Mahadevan, S. Likelihood-based approach to multidisciplinary analysis under uncertainty. Journal of Mechanical Design, 134(3):031008, 2012.

[santner2003]

Santner, T. J., Williams, B. J., Notz, W. I., & Williams, B. J. (2003). The design and analysis of computer experiments. New York: Springer.

[saporta1990]

Saporta, G. (1990). Probabilités, Analyse de données et Statistique, Technip

[scott1992]

Scott, D. W. (1992). Multivariate density estimation, John Wiley & Sons, Inc.

[scott2015]

Scott, D. W. (2015). Multivariate density estimation: theory, practice, and visualization. John Wiley & Sons.

[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.

[segers2016]

J. Segers & M. Sibuya & H. TsukaharaSen (2016). The Empirical Beta Copula, pdf

[sen1990]

Sen, A., & Srivastava, M. (1990). Regression analysis: theory, methods, and applications. Springer.

[shao1993]

Shao, J. (1993). Linear model selection by cross-validation. Journal of the American statistical Association. 88 (422), 486-494.

[sheather1991]

Sheather, S. J. and Jones, M. C. (1991). A reliable data-based bandwidth selection method for kernel density estimation. Journal of the Royal Statistical Society. Series B (Methodological), 53(3) :683–690.

[simard2011]

Simard, R. & L’Ecuyer, P. Computing the Two-Sided Kolmogorov- Smirnov Distribution. Journal of Statistical Software, 2011, 39(11), 1-18. pdf

[silverman1982]

B. W. Silverman Algorithm AS 176: Kernel Density Estimation Using the Fast Fourier Transform. Journal of the Royal Statistical Society. Series C (Applied Statistics), Vol. 31, No. 1 (1982), pp. 93-99 (7 pages)

[silverman1986]

Silverman, B. W. (1986). Density estimation. (Chapman Hall, London).

[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

[stein1987]

Stein, M. (1987). Large sample properties of simulations using Latin hypercube sampling. Technometrics, 29(2), 143-151.

[stone1974]

Stone, M. (1974). Cross‐validatory choice and assessment of statistical predictions. Journal of the royal statistical society: Series B (Methodological), 36 (2), 111-133.

[stoer1993]

Stoer, J., Bulirsch, R. Introduction to Numerical Analysis, Second Edition, Springer-Verlag, 1993. pdf

[sudret2006]

Sudret, B. (2006). Global sensitivity analysis using polynomial chaos expansions. In. Proceedings of the 5th International Conference on Computational Stochastic Mechanics (CSM5), Rhodos (2006)

[sudret2008]

Sudret, B. (2008). Global sensitivity analysis using polynomial chaos expansions. Reliability engineering & system safety, 93 (7), 964-979.

[sullivan2015]

Sullivan, T. J. (2015). Introduction to uncertainty quantification, Vol. 63. Springer.

[vaart2000]

Van der Vaart, A. W. (2000). Asymptotic statistics. Cambridge university press.

[suzuki2020]

Suzuki, J. (2020). Statistical Learning with Math and R. Springer, Berlin.

[wand1994]

Wand M.P, Jones M.C. Kernel Smoothing First Edition, Chapman & Hall, 1994.

[wang2012]

Wang, Y. Model selection. (2012). In Handbook of computational statistics (pp. 469-497). Springer, Berlin, Heidelberg.

[wertz1999]

Wertz, J. and Larson, W. Space Mission Analysis and Design. Microcosm, Inc. Torrance, CA.,1999.

[witkovsky2003]

Witkovsky V. A Note on Computing Extreme Tail Probabilities of the Noncentral T Distribution with Large Noncentrality Parameter. Computational Statistics & Data Analysis, 43 (2003) pp 249-267

[xiu2010]

Xiu, D. (2010). Numerical methods for stochastic computations: a spectral method approach. Princeton university press.

[zaman2012]

Zaman, K. Modeling and management of epistemic uncertainty for multidisciplinary system analysis and design. PhD thesis, Vanderbilt University, USA, 2012

[zhang2020]

Zhang, Y., Tao, S., Chen, W., & Apley, D. W. A latent variable approach to Gaussian process modeling with qualitative and quantitative factors Technometrics 62.3 (2020): 291-302.