Further results on orthogonal arrays for the estimation of global sensitivity indices based on alias matrix

Journal of the Italian Statistical Society - Tập 24 Số 3 - Trang 411-426 - 2015
Xueping Chen1,2, Jin-Guan Lin2, Xiaodi Wang3, Xing-Fang Huang2
1Department of Mathematics, Jiangsu University of Technology, Changzhou, China
2Department of Mathematics, Southeast University, Nanjing, China
3School of Statistics, Central University of Finance and Economics, Beijing, China

Tóm tắt

Từ khóa


Tài liệu tham khảo

Box G, Wilson K (1951) On the experimental attainment of optimum condition. J R Stat Soc Ser B 13:1–38

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

Dimov I, Georgieva R (2010) Monte Carlo algorithms for evaluating Sobol’ sensitivity indices. Math Comput Simul 81:506–514

Hall M (1961) Hadamard matrix of order 16. Jet propulsion laboratory. Res Summ 1:21–36

Hedayat A, Raktoe B, Federer W (1974) On a measure of aliasing due to fitting an incomplete model. Ann Stat 2:650–660

Homma T, Saltelli A (1996) Importance measures in global sensitivity analysis of nonlinear models. Reliab Eng Syst Saf 52:1–17

Jone B, Nachtsheim C (2011) Efficient designs with minimal aliasing. Technometrics 53:62–71

Mitchell T (1974) Computer construction of D-optimal first-order designs. Technometrics 16:211–220

Morris M, Moore L, McKay M (2006) Sampling plans based on balanced incomplete block designs for evaluating the important of computer model inputs. J Stat Plan Inference 136:3203–3220

Morris M, Moore L, McKay M (2008) Using orthogonal arrays in the sensitivity analysis of computer models. Technometrics 2:205–215

Owen AB (1992) Orthogonal arrays for computer experiments, integration and visualization. Stat Sin 2:439–452

Pang SQ, Liu SY, Zhang YS (2002) Satisfactory orthogonal array and its checking method. Stat Probab Lett 59:17–22

Pang SQ, Zhang YS, Liu SY (2004) Further results on the orthogonal arrays obtained by generalized Hadamard product. Stat Probab Lett 68:17–25

Saltelli A, Annoni P, Azzini I, Campolongo F, Ratto M, Tarantola S (2010) Variance based sensitivity analysis of model output. Design and estimator for the total sensitivity index. Comput Phys Commun 181:259–270

Saltelli A, Ratto M, Andres T, Campolongo F, Cariboni J, Gatelli D, Sisana M, Tarantola S (2008) Global sensitivity analysis: the primer. Wiley, New York

Sobol IM (1993) Sensitivity analysis for nonlinear mathematical models. Math Model Comput Exp 1:407–414

Sobol IM (2001) Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Math Comput Simul 55:271–280

Sobol IM, Levitan YL (1999) On the use of variance reducing multipliers in Monte Carlo computations of a global sensitivity index. Comput Phys Commun 117:52–61

Sobol IM, Myshetskaya EE (2008) Monte Carlo estimators for small sensitivity indices. Monte Carlo Methods Appl 13:455–465

Tarantola S, Gatelli T, Mara TA (2006) Random balance designs for the estimator of first order global sensitivity indices. Reliab Eng Syst Saf 91:717–727

Wang XD, Tang YC, Chen XP, Zhang YS (2010) Design of experiment in global sensitivity analysis based on ANOVA high-dimensional model representation. Commun Stat Simul Comput 39:1183–1195

Wang XD, Tang YC, Zhang YS (2011) Orthogonal arrays for the estimation of global sensititity indices based on ANOVA high-dimensional model representation. Commun Stat Simul Comput 40:1801–1812

Wang XD, Tang YC, Zhang YS (2012) Orthogonal arrays for estimating global sensitivity indices of non-parametric models based on ANOVA high-dimensional model representation. J Stat Plan Inference 142:1324–1341

Zhang YS, Lu YQ, Pang SQ (1999) Orthogonal arrays obtained by orthogonal decomposition of projection matrices. Stat Sin 9:595–604

Zhang YS, Pang SQ, Wang YP (2001) Orthogonal arrays obtained by generalized Hadamard product. Discret Math 238:151–170