ANOVA decomposition of conditional Gaussian processes for sensitivity analysis with dependent inputs

References

• Saltelli A, Chan K, Scott E. Sensitivity analysis. West Sussex: Wiley; 2000.
   Google Scholar
• Saltelli A, Ratto M, Andres T, Campolongo F, Cariboni J, Gatelli D, Saisana M, Tarantola S. Global sensitivity analysis: the primer. West Sussex: Wiley-Interscience; 2008.
   Google Scholar
• Cacuci D, Ionescu-Bujor M, Navon I. Sensitivity and uncertainty analysis, Volume II: applications to large-scale systems. Vol. 2. Boca Raton, FL: Chapman & Hall/CRC; 2005.
   Google Scholar
• Hoeffding W. A class of statistics with asymptotically normal distribution. Ann Math Statist. 1948;19(3):293–325. doi: 10.1214/aoms/1177730196
   Google Scholar
• Sobol I. Sensitivity estimates for nonlinear mathematical models. Math Model Comput Exp. 1993;1(4):407–414.
   Google Scholar
• Mara T, Tarantola S. Variance-based sensitivity analysis of computer models with dependent inputs. Reliab Eng Syst Saf. 2012;107:115–121. doi: 10.1016/j.ress.2011.08.008
   Web of Science ®Google Scholar
• Xu C, Gertner G. Uncertainty and sensitivity analysis for models with correlated parameters. Reliab Eng Syst Saf. 2008;93:1563–1573. doi: 10.1016/j.ress.2007.06.003
   Web of Science ®Google Scholar
• Li G, Rabitz H, Yelvington P, Oluwole O, Bacon F, CE K, Schoendorf J. Global sensitivity analysis with independent and/or correlated inputs. J Phys Chem A. 2010;114:6022–6032. doi: 10.1021/jp9096919
   PubMed Web of Science ®Google Scholar
• Li G, Rosenthal C, Rabitz H. High dimensional model representations. J Phys Chem A. 2001;105(33):7765–7777. doi: 10.1021/jp010450t
   Web of Science ®Google Scholar
• Caniou Y. Analyse de sensibilité globale pour les modèles imbriqués et multiéchelles [Ph.D. thesis]. Université Blaise Pascal – Clermont II; 2012.
   Google Scholar
• Wiener N. The homogeneous chaos. Amer J Math. 1938;60(4):897–936. doi: 10.2307/2371268
   Google Scholar
• Sudret B. Global sensitivity analysis using polynomial chaos expansion. Reliab Eng Syst Saf. 2008;93(7):964–979. doi: 10.1016/j.ress.2007.04.002
   Web of Science ®Google Scholar
• Chastaing G, Gamboa F, Prieur C. Generalized Hoeffding-Sobol decomposition for dependent variables – application to sensitivity analysis. Electron J Stat. 2012;6:2420–2448. doi: 10.1214/12-EJS749
   Web of Science ®Google Scholar
• Stone C. The use of polynomial splines and their tensor products in multivariate function estimation. Ann Statist. 1994;22(1):118–171. doi: 10.1214/aos/1176325361
   Web of Science ®Google Scholar
• Chastaing G, Gamboa F, Prieur C. Generalized Sobol sensitivity indices for dependent variables: numerical methods; 2013. Available from: http://arxiv.org/abs/1303.4372.
   Google Scholar
• Santner T, Williams B, Notz W. The design and analysis of computer experiments. New York: Springer Verlag; 2003.
   Google Scholar
• Rasmussen C, Williams C. Gaussian processes for machine learning. Cambridge: MIT Press; 2006.
   Google Scholar
• Sacks J, Welch W, Mitchell T, Wynn H. Design and analysis of computer experiments. Statist Sci. 1989;4(4):409–423. doi: 10.1214/ss/1177012413
   Google Scholar
• Chen W, Jin R, Sudjianto A. Analytical variance-based global sensitivity analysis in simulation-based design under uncertainty. J Mech Des. 2005;127(5):875–886. doi: 10.1115/1.1904642
   Web of Science ®Google Scholar
• Oakley J, O'Hagan A. Probabilistic sensitivity analysis of complex models: a Bayesian approach. J R Stat Soc Ser B. 2004;66(3):751–769. doi: 10.1111/j.1467-9868.2004.05304.x
   Google Scholar
• Marrel A, Iooss B, Laurent B, Roustant O. Calculations of Sobol indices for the Gaussian process metamodel. Reliab Eng Syst Saf. 2009;94(3):742–751. doi: 10.1016/j.ress.2008.07.008
   Web of Science ®Google Scholar
• Durrande N, Ginsbourger D, Roustant O, Carraro L. Reproducing kernels for spaces of zero mean functions. Application to sensitivity analysis. J Multivariate Anal. 2013;115:57–67. doi: 10.1016/j.jmva.2012.08.016
   Web of Science ®Google Scholar
• Berlinet A, Thomas-Agnan C. Reproducing kernel Hilbert spaces in probability and statistics. Boston: Kluwer Academic Publishers; 2004.
   Google Scholar
• Cameron R, Martin W. The orthogonal development of non-linear functionals in series of Fourier-Hermite functionals. Ann Math. 1947;48(2):385–392. doi: 10.2307/1969178
   Web of Science ®Google Scholar
• Fang KT, Li R, Sudjianto A. Design and modeling for computer experiments. London: Chapman & Hall – Computer Science and Data Analysis Series; 2006.
   Google Scholar
• Stein ML. Interpolation of spatial data. Springer Series in Statistics. New York: Springer; 1999.
   Google Scholar
• Chilès J, Delfiner P. Geostatistics: modeling spatial uncertainty. Wiley series in probability and statistics (Applied probability and statistics section). Toronto: Wiley Publications; 1999.
   Google Scholar
• Van Der Vaart A. Asymptotic statistics. Cambridge: Cambridge University Press; 1998.
   Google Scholar
• Avriel M. Nonlinear programming: analysis and methods. New York: Dover Publications; 2003.
   Google Scholar
• Stein ML. Large sample properties of simulations using Latin hypercube sampling. Technometrics. 1987;29:143–151. doi: 10.1080/00401706.1987.10488205
   Web of Science ®Google Scholar
• Bowman AW, Azzalini A. Applied smoothing techniques for data analysis. New York: Oxford University Press; 1997.
   Google Scholar
• Nelsen R. An introduction to copulas. New York: Springer; 2006.
   Google Scholar
• Fang KT, Kotz S, Ng KW. Symmetric multivariate and related distributions-monographs on statistics and applied probability. London: Chapman and Hall; 1990.
   Google Scholar
• Faivre R, Iooss B, Mahévas S, Makowski D, Monod H. Analyse de sensibilité et exploration de modèles. Versailles: Quae; 2013.
   Google Scholar
• De Rocquigny E. La maîtrise des incertitudes dans un contexte industriel-1ere partie: une approche méthodologique globale basée sur des exemples. J Soc Fr Stat. 2006;147(2):33–71.
   Google Scholar