P. Abrahamsen and F. E. Benth, Kriging with inequality constraints, Mathematical Geology, vol.33, issue.6, pp.719-744, 2001.
DOI : 10.1023/A:1011078716252

J. Aza¨?saza¨?s and M. Wschebor, Level sets and extrema of random processes and fields, 2009.

J. Bigot and S. Gadat, Smoothing under Diffeomorphic Constraints with Homeomorphic Splines, SIAM Journal on Numerical Analysis, vol.48, issue.1, pp.224-243, 2010.
DOI : 10.1137/080727555

URL : https://hal.archives-ouvertes.fr/hal-00629301

N. Chopin, Fast simulation of truncated Gaussian distributions, Statistics and Computing, vol.82, issue.398, pp.275-288, 2011.
DOI : 10.1007/s11222-009-9168-1

URL : http://arxiv.org/abs/1201.6140

F. Cozman and E. Krotkov, Truncated Gaussians as Tolerance Sets, Fifth Workshop on Artificial Intelligence and Statistics, 1995.

H. Cramér and M. R. Leadbetter, Stationary and Related Stochastic Processes: Sample Function Properties and Their Applications, 1967.

D. Veiga, S. Wahl, F. Gamboa, and F. , Local Polynomial Estimation for Sensitivity Analysis on Models With Correlated Inputs Technometrics, pp.452-463, 2009.

D. Veiga, S. Marrel, and A. , Gaussian process modeling with inequality constraints, Annales de la Faculté des Sciences de Toulouse, pp.529-555, 2012.
DOI : 10.5802/afst.1344

H. Dette and R. Scheder, Strictly monotone and smooth nonparametric regression for two or more variables, Canadian Journal of Statistics, vol.73, issue.4, pp.535-561, 2006.
DOI : 10.1002/cjs.5550340401

URL : http://dx.doi.org/10.17877/DE290R-6670

N. Ellis and R. Maitra, Multivariate Gaussian Simulation Outside Arbitrary Ellipsoids, Journal of Computational and Graphical Statistics, vol.16, issue.3, pp.692-798, 2007.
DOI : 10.1198/106186007X238431

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.643.1697

K. Fang, R. Li, and A. Sudjianto, Design and modeling for computer experiments, 2006.
DOI : 10.1201/9781420034899

P. J. Fernandez, P. A. Ferrari, and S. P. Grynberg, Perfectly random sampling of truncated multinormal distributions, Advances in Applied Probability, vol.89, issue.04, pp.973-990, 2007.
DOI : 10.1111/1467-9868.00175

A. Genz, Numerical Computation of Multivariate Normal Probabilities, Journal of Computational and Graphical Statistics, vol.1, issue.2, pp.141-149, 1992.
DOI : 10.1007/978-1-4613-9655-0

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.33.7726

A. Genz, Comparison of Methods for the Computation of Multivariate Normal Probabilities, Computing Science and Statistics, vol.25, pp.400-405, 1993.

A. Genz and F. Bretz, Computation of Multivariate Normal and t Probabilities, Lecture Notes in Statistics, vol.195, 2009.
DOI : 10.1007/978-3-642-01689-9

J. Geweke, Efficient simulation from the multivariate normal and student t-distribution subject to linear constraints, Computing Science and Statistics: Proceedings of the Twenty-Third Symposium on the Interface, pp.571-578, 1991.

W. Griffiths, A Gibbs' sampler for the parameters of a truncated multivariate normal distribution. Working Paper, 2002.

P. Hall and L. Huang, Nonparametric kernel regression subject to monotonicity constraints, The Annals of Statistics, vol.29, issue.3, pp.624-647, 2001.

M. L. Hazelton and B. A. Turlach, Semiparametric regression with shape-constrained penalized splines, Computational Statistics & Data Analysis, vol.55, issue.10, pp.2871-2879, 2011.
DOI : 10.1016/j.csda.2011.04.018

W. C. Horrace, Some results on the multivariate truncated normal distribution, Journal of Multivariate Analysis, vol.94, issue.1, pp.209-221, 2005.
DOI : 10.1016/j.jmva.2004.10.007

URL : http://doi.org/10.1016/j.jmva.2004.10.007

M. E. Johnson, L. M. Moore, and D. Ylvisaker, Minimax and maximin distance designs, Journal of Statistical Planning and Inference, vol.26, issue.2, pp.131-148, 1990.
DOI : 10.1016/0378-3758(90)90122-B

J. P. Kleijnen and W. C. Van-beers, Monotonicity-preserving bootstrapped Kriging metamodels for expensive simulations, Working Paper, 2010.
DOI : 10.2139/ssrn.1477896

J. H. Kotecha and P. M. Djuric, Gibbs sampling approach for generation of truncated multivariate Gaussian random variables, 1999 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings. ICASSP99 (Cat. No.99CH36258), pp.1757-1760, 1999.
DOI : 10.1109/ICASSP.1999.756335

S. Kotz, N. Balakrishnan, and N. L. Johnson, Continuous multivariate distributions, 2000.
DOI : 10.1002/0471722065

L. Lee, On the first and second moments of the truncated multi-normal distribution and a simple estimator, Economics Letters, vol.3, issue.2, pp.165-169, 1979.
DOI : 10.1016/0165-1765(79)90111-3

L. Lee, The determination of moments of the doubly truncated multivariate normal tobit model, Economics Letters, vol.11, issue.3, pp.245-250, 1983.
DOI : 10.1016/0165-1765(83)90143-X

H. Maatouk and X. Bay, A new rejection sampling method for truncated multivariate Gaussian random variables, Eleventh International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, 2014.
DOI : 10.1007/978-3-319-33507-0_27

URL : https://hal.archives-ouvertes.fr/emse-01097026

A. Marrel, B. Iooss, F. Van-dorpe, and E. Volkova, An efficient methodology for modeling complex computer codes with Gaussian processes, Computational Statistics & Data Analysis, vol.52, issue.10, pp.4731-4744, 2008.
DOI : 10.1016/j.csda.2008.03.026

URL : https://hal.archives-ouvertes.fr/hal-00239492

A. M. Michalak, A Gibbs sampler for inequality-constrained geostatistical interpolation and inverse modeling, Water Resources Research, vol.8, issue.8, pp.10-1029, 2008.
DOI : 10.1007/s10109-006-0036-7

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.600.7330

B. Muthén, Moments of the censored and truncated bivariate normal distribution, British Journal of Mathematical and Statistical Psychology, vol.43, issue.1, pp.131-143, 1990.
DOI : 10.1111/j.2044-8317.1990.tb00930.x

J. Oakley, O. Hagan, and A. , Probabilistic sensitivity analysis of complex models: a Bayesian approach, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.34, issue.3, pp.751-769, 2004.
DOI : 10.1214/ss/1009213004

A. Philippe and C. Robert, Perfect simulation of positive Gaussian distributions, Statistics and Computing, vol.13, issue.2, pp.179-186, 2003.
DOI : 10.1023/A:1023264710933

J. S. Racine, C. F. Parmeter, and P. Du, Constrained nonparametric kernel regression: Estimation and inference. Working Paper, http:/economics, 2009.

J. O. Ramsay and B. W. Silverman, Functional Data Analysis, 2005.

C. E. Rasmussen and C. K. Williams, Gaussian Processes in Machine Learning, 2006.
DOI : 10.1162/089976602317250933

URL : http://hdl.handle.net/11858/00-001M-0000-0013-F365-A

J. Riihimäki and A. Vehtari, Gaussian processes with monotonicity information, International Conference on Artificial Intelligence and Statistics, pp.645-652, 2010.

C. P. Robert, Simulation of truncated normal variables, Statistics and Computing, vol.82, issue.2, pp.121-125, 1995.
DOI : 10.1007/BF00143942

URL : https://hal.archives-ouvertes.fr/hal-00431310

J. Sacks, W. Welch, T. Mitchell, and H. Wynn, Design and Analysis of Computer Experiments, Statistical Science, vol.4, issue.4, pp.409-435, 1989.
DOI : 10.1214/ss/1177012413

A. Saltelli, K. Chan, and E. M. Scott, Sensitivity Analysis, 2000.
URL : https://hal.archives-ouvertes.fr/inria-00386559

T. Santner, B. Williams, and W. Notz, The design and analysis of computer experiments, 2003.
DOI : 10.1007/978-1-4757-3799-8

M. Scheuerer and M. Schlather, Covariance models for divergence-free and curl-free random vector fields. Stochastic Models, pp.433-451, 2012.
DOI : 10.1080/15326349.2012.699756

G. M. Tallis, The moment generating function of the truncated multinormal distribution, Journal of the Royal Statistical Society, Series B, vol.23, issue.1, pp.223-229, 1961.

G. M. Tallis, Elliptical and Radial Truncation in Normal Populations, The Annals of Mathematical Statistics, vol.34, issue.3, pp.940-944, 1963.
DOI : 10.1214/aoms/1177704016

G. M. Tallis, Plane truncation in normal populations, Journal of the Royal Statistical Society, Series B, vol.27, issue.2, pp.301-307, 1965.
DOI : 10.1214/aoms/1177704016

E. Yoo and P. C. Kyriakidis, Area-to-point Kriging with inequality-type data, Journal of Geographical Systems, vol.33, issue.8, p.357, 2006.
DOI : 10.1007/s10109-006-0036-7

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.528.3617