.. _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.
.. [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 <http://www.columbia.edu/~ww2040/Fourier-series.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 <https://arxiv.org/pdf/1007.0828.pdf>`__
.. [angelis2015] Angelis M., Patelli E., Beer M., *Advanced line sampling for efficient robust reliability analysis*,
    Structural safety, 52 :170-182, 2015.
    `pdf <https://livrepository.liverpool.ac.uk/2010225/1/sissue_mda_ep_mb.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 <http://jimbeck.caltech.edu/papers_pdf/estimation_of_small_failure_probabilities.pdf>`__
.. [Motoyama2025] Hitoshi Motoyama (2025) *The Bahadur representations of quantile estimators in general unequal probability sampling*,
     Communications in Statistics - Theory and Methods, 54:13, 3820-3836, DOI: 10.1080/03610926.2024.2406382
     `pdf <https://www.tandfonline.com/doi/epdf/10.1080/03610926.2024.2406382?needAccess=true>`__
.. [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 <https://arxiv.org/pdf/1501.05242>`__
.. [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 <https://tel.archives-ouvertes.fr/tel-00440197/document>`__
.. [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 <https://arxiv.org/pdf/1508.03483.pdf>`__
.. [caniou2012] Caniou, Y. *Global sensitivity analysis for nested and
    multiscale modelling.* PhD thesis. Blaise Pascal University-Clermont II,
    France, 2012.
    `pdf <https://tel.archives-ouvertes.fr/tel-00864175/document>`__
.. [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 <https://www.amse-aixmarseille.fr/sites/default/files/_dt/2012/wp_2015_-_nr_06.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.
.. [clouvel2025] Clouvel, L., Iooss, B., Chabridon, V., Il Idrissi, M. & Robin, F. (2025).
    *An overview of variance-based importance measures in the linear regression context: comparative analyses and numerical tests*,
    Socio-Environmental Systems Modeling, vol. 7, 18681, doi:10.18174/sesmo.18681
    `pdf <https://sesmo.org/article/view/18681/18319>`__
.. [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.
.. [crombecq2011] Crombecq, K., *Surrogate Modelling of Computer Experiments with Sequential Experimental Design*,
    PhD thesis, Universiteit Gent, Belgium, 2011.
    `pdf <https://backoffice.biblio.ugent.be/download/1970716/1971191>`__
.. [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 <https://arxiv.org/pdf/1307.6835.pdf>`__
.. [david1981] David, H.A. (1981). *Order statistics.*, New-York:Wiley.
.. [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 <http://luc.devroye.org/handbooksimulation1.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 <https://www.ine.pt/revstat/pdf/rs080103.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 <https://ubt.opus.hbz-nrw.de/opus45-ubtr/frontdoor/deliver/index/docId/758/file/DissertationDimitriadis.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 <https://ajmaa.org/searchroot/files/pdf/v11n1/v11i1p2.pdf>`__
.. [doornik2005] Doornik, J.A. *An Improved Ziggurat Method to Generate Normal Random Samples*,
    mimeo, Nuffield College, University of Oxford, 2005.
    `pdf <https://www.doornik.com/research/ziggurat.pdf>`__
.. [dubourg2011] Dubourg, V. *Adaptative surrogate models for reliability and reliability-based design optimization*,
    University Blaise Pascal - Clermont II, 2011.
    `pdf <https://tel.archives-ouvertes.fr/tel-00697026v2/document>`__
.. [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.
.. [feller1970] Feller W.,
    *An Introduction to Probability Theory and Its Application*, John Wiley \& Sons,
    2nd edition, Vol. 2.
.. [fischer2017] Fischer, R. (2017). *Modelling the dependence of order
   statistics and nonparametric estimation*.
   `pdf <https://pastel.hal.science/tel-01526823/file/TH2016PESC1039.pdf>`__
.. [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 <https://arxiv.org/pdf/1311.1797.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 <https://hal.science/hal-02474902v4/file/New_Look_Bernoulli_4.pdf>`__
.. [garnier2008] Garnier, J. *Quantile estimation* ECODOQUI 2008
.. [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 <https://www.researchgate.net/publication/220492882_An_adaptive_numerical_cubature_algorithm_for_simplices>`__
.. [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 <https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.33.3141&rep=rep1&type=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.
.. [gobet2016] Gobet, E., 2016, *Monte-Carlo Methods and Stochastic Processes: From Linear to Non-Linear*,
    Chapman \& Hall/CRC.
.. [ginsbourger2018] Ginsbouger, D., 2018 *Sequential Design of Computer Experiments*,
    Wiley StatsRef: Statistics Reference Online, Wiley
.. [hormann1993] Hormann W., *The generation of Binomial Random Variates* Journal
    of Statistical Computation and Simulation 46, pp. 101-110, 1993.
    `pdf <https://epub.wu.ac.at/1242/1/document.pdf>`__
.. [hahn2005] Thomas Hahn, *Cuba - a library for multidimensional numerical integration*
    Computer Physics Communications, 168(2), 78-95.
    `pdf <https://arxiv.org/pdf/hep-ph/0404043>`__
.. [halko2010] Nathan Halko, Per-Gunnar Martinsson, Joel A. Tropp, *Finding
    structure with randomness: Probabilistic algorithms for constructing
    approximate matrix decompositions*,
    `pdf <https://arxiv.org/pdf/0909.4061.pdf>`__
.. [halko2011] Nathan Halko, Per-Gunnar Martisson, Yoel Shkolnisky and Mark Tygert,
    *An algorithm for the principal component analysis of large data sets*,
    `pdf <https://arxiv.org/pdf/1007.5510.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 <https://web.archive.org/web/20141222122431id_/http://www.stat.unm.edu:80/~storlie/st579/articles/RESS_2003_LHS.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 <https://arxiv.org/pdf/1404.2405>`__
.. [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 <https://hal.inria.fr/hal-00665048/document>`__
.. [jansen1999] Jansen, M.J.W. *Analysis of variance designs for model output*,
    Computer Physics Communication, 1999, 117, 35-43.
    `pdf <https://openturns.github.io/openturns/papers/jansen1999.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 <https://openturns.github.io/openturns/papers/jin2005.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 <https://openturns.github.io/openturns/papers/jones1998.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
.. [kallenberg2021] Kallenberg, O.
    *Fundations of Modern Probability*,
    Springer, 3rd edition, 2021.
.. [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 <https://openturns.github.io/openturns/papers/kiureghian1998.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 <https://www.osti.gov/servlets/purl/5004>`__
.. [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 <https://openturns.github.io/openturns/papers/knight1966.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.
.. [koutsourelakis2004] Koutsourelakis, H. Pradlwarter, G. Schueller,
    *Reliability of structures in high dimensions, part i: algorithms and applications*,
    Probabilistic Engineering Mechanics 19 (4) (2004) 409–417
.. [lebrun2009a] Lebrun, R. & Dutfoy, A. *An innovating analysis of the Nataf
    transformation from the copula viewpoint.* Prob. Eng. Mech., 2009, 24,
    312-320.
    `pdf <https://www.researchgate.net/profile/Regis_Lebrun/publication/245186106_An_innovating_analysis_of_the_Nataf_transformation_from_the_copula_viewpoint/links/5ab4ac1faca272171004264f/An-innovating-analysis-of-the-Nataf-transformation-from-the-copula-viewpoint.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 <https://www.researchgate.net/profile/Regis_Lebrun/publication/229410827_A_generalization_of_the_Nataf_transformation_to_distribution_with_copula/links/59e47955458515393d60e7f1/A-generalization-of-the-Nataf-transformation-to-distribution-with-copula.pdf>`__
.. [lebrun2009c] Lebrun, R. & Dutfoy, A. *Do Rosenblatt and Nataf
    isoprobabilistic transformations really differ?* Prob. Eng. Mech., 2009,
    24, 577-584.
    `pdf <https://openturns.github.io/openturns/papers/lebrun2009c.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 <https://www.researchgate.net/profile/Pierre_LEcuyer/publication/226670289_Recent_Advances_in_Randomized_Quasi-Monte_Carlo_Methods/links/0deec52dd9d449512b000000/Recent-Advances-in-Randomized-Quasi-Monte-Carlo-Methods.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 <http://www.bios.unc.edu/~mhudgens/bios/662/2008fall/Backup/lilliefors1967.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 <https://www.r-project.org/doc/reports/CLoader-dbinom-2002.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 <https://arxiv.org/pdf/1709.01589.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 <http://www3.stat.sinica.edu.tw/statistica/oldpdf/A13n316.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 <https://openturns.github.io/openturns/papers/mauricio1995.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 <https://www.asc.ohio-state.edu/statistics/comp_exp/jour.club/McKayConoverBeckman.pdf>`__
.. [meeker2017] Meeker, W. Q. Hahn, G. J., and Escobar, L.A. (2017).
    *Statistical intervals : a guide for practitioners and researchers*, John Wiley & Sons
.. [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 <http://research.microsoft.com/en-us/um/people/minka/papers/dirichlet/minka-dirichlet.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 <https://www.osti.gov/servlets/purl/10184343>`__
.. [morokoff1995] Morokoff, W. J., & Caflisch, R. E. (1995). *Quasi-Monte Carlo
    integration.* Journal of computational physics, 122(2), 218-230.
    `pdf <https://www.math.ucla.edu/~caflisch/Pubs/Pubs1995-1999/actaNumerica1998.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 <https://josselin-garnier.org/wp-content/uploads/2013/12/munoz_ress.pdf>`__
.. [nataf1962] Nataf, A. *Determination des distributions dont les marges sont
    donnees.* C. R. Acad. Sci. Paris, 1962, 225, 42-43.
    `pdf <https://openturns.github.io/openturns/papers/nataf1962.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 <https://core.ac.uk/download/pdf/82362441.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 <https://sas.uwaterloo.ca/~wang/papers/2014PW(Variance).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 <https://openturns.github.io/openturns/papers/RT-PMFRE-01116-001C_-_Rapport_loi_estimateur_sobol.pdf>`__
.. [pronzato2012] Pronzato L and Muller W (2012).
    *Design of computer experiments: Space filling and beyond.*
    Statistics and Computing 22(3): 681-701.
    `pdf <https://hal.archives-ouvertes.fr/hal-00685876/document>`__
.. [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 <https://arxiv.org/pdf/1504.01896.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 <https://www.diva-portal.org/smash/get/diva2:1865473/FULLTEXT01.pdf>`__
.. [rosenblatt1952] Rosenblatt, M. *Remarks on a multivariate transformation.*
    Ann. Math. Stat., 1952, 23, 470-472.
    `pdf <https://projecteuclid.org/download/pdf_1/euclid.aoms/1177729394>`__
.. [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 <https://kgut.ac.ir/useruploads/1509987964985oqk.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 <http://www.andreasaltelli.eu/file/repository/Saltelli_Technom.pdf>`__
.. [saltelli2000] Saltelli, A., Chan, K. and Scott, M. *Sensitivity analysis.*
    John Wiley and Sons publishers, Probability and statistics series, 2000.
    `pdf <http://www.andreasaltelli.eu/file/repository/Saltelli_Technom.pdf>`__
.. [saltelli2002] Saltelli, A. *Making best use of model evaluations to compute
    sensitivity indices.* Computer Physics Communication, 2002, 145, 580-297.
    `pdf <http://www.andreasaltelli.eu/file/repository/Making_best_use.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 <https://arxiv.org/pdf/1607.04430>`__
.. [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 <https://www.jstatsoft.org/article/view/v039i11/v39i11.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 <https://openturns.github.io/openturns/papers/sobol1993.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 <https://openturns.github.io/openturns/papers/sobol2007.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 <https://hal.archives-ouvertes.fr/hal-00686211/document>`__
.. [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 <https://openturns.github.io/openturns/papers/stadlober1990.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 <https://zhilin.math.ncsu.edu/TEACHING/MA580/Stoer_Bulirsch.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.
.. [wilks1948] Wilks, S. S. (1948). Order statistics. Bulletin of the American Mathematical Society, 54(1) :6–50.
.. [robert2004] Robert C.P., Casella G. *Monte-Carlo Statistical Methods*, Springer, ISBN 0-387-21239-6, 2nd ed, 2004.
.. [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.