[Construction de plans répliqués à partir de séquences de Sobol']
Dans l'objectif d'estimer les effets principaux des paramètres d'un modèle, nous proposons d'étudier deux approches pour construire itérativement des plans répliqués à partir de séquences de Sobol'. Les propriétés de remplissement de l'espace des plans construits sont étudiées sur la base de deux critères.
In the perspective of estimating main effects of model inputs, two approaches are studied to iteratively construct replicated designs based on Sobol' sequences. Space-filling properties of the resulting designs are studied based on two criteria.
Accepté le :
Publié le :
@article{CRMATH_2017__355_1_10_0,
author = {Gilquin, Laurent and Jim\'enez Rugama, Llu{\'\i}s Antoni and Arnaud, \'Elise and Hickernell, Fred J. and Monod, Herv\'e and Prieur, Cl\'ementine},
title = {Iterative construction of replicated designs based on {Sobol'} sequences},
journal = {Comptes Rendus. Math\'ematique},
pages = {10--14},
publisher = {Elsevier},
volume = {355},
number = {1},
year = {2017},
doi = {10.1016/j.crma.2016.11.013},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2016.11.013/}
}
TY - JOUR AU - Gilquin, Laurent AU - Jiménez Rugama, Lluís Antoni AU - Arnaud, Élise AU - Hickernell, Fred J. AU - Monod, Hervé AU - Prieur, Clémentine TI - Iterative construction of replicated designs based on Sobol' sequences JO - Comptes Rendus. Mathématique PY - 2017 SP - 10 EP - 14 VL - 355 IS - 1 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2016.11.013/ DO - 10.1016/j.crma.2016.11.013 LA - en ID - CRMATH_2017__355_1_10_0 ER -
%0 Journal Article %A Gilquin, Laurent %A Jiménez Rugama, Lluís Antoni %A Arnaud, Élise %A Hickernell, Fred J. %A Monod, Hervé %A Prieur, Clémentine %T Iterative construction of replicated designs based on Sobol' sequences %J Comptes Rendus. Mathématique %D 2017 %P 10-14 %V 355 %N 1 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2016.11.013/ %R 10.1016/j.crma.2016.11.013 %G en %F CRMATH_2017__355_1_10_0
Gilquin, Laurent; Jiménez Rugama, Lluís Antoni; Arnaud, Élise; Hickernell, Fred J.; Monod, Hervé; Prieur, Clémentine. Iterative construction of replicated designs based on Sobol' sequences. Comptes Rendus. Mathématique, Tome 355 (2017) no. 1, pp. 10-14. doi : 10.1016/j.crma.2016.11.013. http://www.numdam.org/articles/10.1016/j.crma.2016.11.013/
[1] Constructing Sobol sequences with better two-dimensional projections, SIAM J. Sci. Comput., Volume 30 (2008) no. 8, pp. 2635-2654
[2] Comparison of some efficient methods to evaluate the main effect of computer model factors, J. Stat. Comput. Simul., Volume 78 (2008) no. 2, pp. 167-178
[3] On the L2-discrepancy for anchored boxes, J. Complexity, Volume 14 (1998), pp. 527-556
[4] A comparison of three methods for selecting values of input variables in the analysis of output from a computer code, Technometrics, Volume 21 (1979), pp. 239-245
[5] Quasi-random sequences and their discrepancies, SIAM J. Sci. Comput., Volume 15 (1994), pp. 1251-1279
[6] Random number generation and quasi-Monte Carlo methods, CBMS-NSF Reg. Conf. Ser. Appl. Math., vol. 63, SIAM, Philadelphia, PA, USA, 1992
[7] Low-discrepancy sequences and global function fields with many rational places, Finite Fields Appl., Volume 2 (1996) no. 3, pp. 241-273
[8] Scrambling Sobol' and Niederreiter–Xing points, J. Complex., Volume 14 (1998) no. 4, pp. 466-489
[9] Making best use of model evaluations to compute sensitivity indices, Comput. Phys. Commun., Volume 145 (2002) no. 2, pp. 280-297
[10] On the distribution of points in a cube and the approximate evaluation of integrals, USSR Comput. Math. Math. Phys., Volume 7 (1967) no. 4, pp. 86-112
[11] Sensitivity indices for nonlinear mathematical models, Math. Model. Comput. Exp., Volume 1 (1993), pp. 407-414
[12] A randomized orthogonal array-based procedure for the estimation of first- and second-order Sobol' indices, J. Stat. Comput. Simul., Volume 85 (2014), pp. 1358-1381
Cité par Sources :
