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.