Latin hypercube sampling with inequality constraints

Asserin, O., Loredo, A., Petelet, M., Iooss, B.: Global sensitivity analysis in welding simulations—What are the material data you really need? Finite Elem. Anal. Des. (2009, submitted). Available at URL: http://hal.archives-ouvertes.fr/hal-00419162/fr/

Borgonovo, E.: Sensitivity analysis of model output with input constraints: A generalized rationale for local methods. Risk Anal. 28, 667–680 (2008)

Bursztyn, D., Steinberg, D.: Comparison of designs for computer experiments. J. Stat. Plan. Inference 136, 1103–1119 (2006)

De Rocquigny, E., Devictor, N., Tarantola, S. (eds.): Uncertainty in Industrial Practice. Wiley, New York (2008)

Fang, K.-T., Li, R., Sudjianto, A.: Design and Modeling for Computer Experiments. Chapman & Hall/CRC, London (2006)

Gentle, J.: Random Number Generation and Monte Carlo Methods. Springer, Berlin (2003)

Helton, J., Davis, F.: Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems. Reliab. Eng. Syst. Saf. 81, 23–69 (2003)

Iman, R., Conover, W.: A distribution-free approach to inducing rank correlation among input variables. Commun. Stat. 11(3), 311–334 (1982)

Iooss, B., Boussouf, L., Feuillard, V., Marrel, A.: Numerical studies of the metamodel fitting and validation processes. Int. J. Adv. Syst. Meas. 3, 11–21 (2010)

Jourdan, A., Franco, J.: Optimal Latin hypercube designs for the Kullback-Leibler criterion. Adv. Stat. Anal. 94(4), 341–351 (2010)

Kleijnen, J.: Design and Analysis of Simulation Experiments. Springer, Berlin (2008)

Kurowicka, D., Cooke, R.: Uncertainty Analysis with High Dimensional Dependence Modelling. Wiley, New York (2006)

Levy, S., Steinberg, D.: Computer experiments: A review. Adv. Stat. Anal. 94(4), 311–324 (2010)

McKay, M., Beckman, R., Conover, W.: A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 21, 239–245 (1979)

Owen, A.: A central limit theorem for Latin hypercube sampling. J. R. Stat. Soc. B 16, 140–149 (1992)

Park, J.-S.: Optimal Latin-hypercube designs for computer experiments. J. Stat. Plan. Inference 39, 95–111 (1994)

Petelet, M.: Analyse de sensibilité globale de modèles thermomécaniques de simulation numérique du soudage. Thèse de l’Université de Bourgogne (2007)

Petelet, M., Asserin, O., Iooss, B., Loredo, A.: Echantillonnage LHS des propriétés matériau des aciers pour l’analyse de sensibilité globale en simulation numérique du soudage. In: Actes de MATERIAUX, Dijon, France, 2006

Pistone, G., Vicario, G.: Comparing and generating Latin Hypercube designs in Kriging models. Adv. Stat. Anal. 94(4), 353–366 (2010)

Saltelli, A., Chan, K., Scott, E. (eds.): Sensitivity Analysis. Wiley Series in Probability and Statistics. Wiley, New York (2000)

Simpson, T., Lin, D., Chen, W.: Sampling strategies for computer experiments: Design and analysis. Int. J. Reliab. Appl. 2, 209–240 (2001a)

Simpson, T., Peplinski, J., Kock, P., Allen, J.: Metamodel for computer-based engineering designs: Survey and recommendations. Eng. Comput. 17, 129–150 (2001b)

Sobol, I.: Uniformly distributed sequences with additional uniformity property. USSR Comput. Math. Math. Phys. 16, 236–242 (1976)

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

Volkova, E., Iooss, B., Van Dorpe, F.: Global sensitivity analysis for a numerical model of radionuclide migration from the RRC “Kurchatov Institute” radwaste disposal site. Stoch. Environ. Res. Risk Assess. 22, 17–31 (2008)