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All issues Volume 30 (2026) ESAIM: PS, 30 (2026) 285-341 References
Issue
ESAIM: PS
Volume 30, 2026
SAMO 2025 - Uncertainty Quantification and Sensitivity Analysis, from Theory to App
Page(s) 285 - 341
DOI https://doi.org/10.1051/ps/2026004
Published online 25 May 2026
  1. T.J. Santner, B.J. Williams, W.I. Notz and B.J. Williams, The Design and Analysis of Computer Experiments, vol. 1. Springer (2003). [Google Scholar]
  2. K. Campbell, Statistical calibration of computer simulations. Reliabil. Eng. Syst. Saf. 91 (2006) 1358–1363. [Google Scholar]
  3. T.G. Trucano, L.P. Swiler, T. Igusa, W.L. Oberkampf and M. Pilch, Calibration, validation, and sensitivity analysis: What's what. Reliabil. Eng. Syst. Saf. 91 (2006) 1331–1357. [Google Scholar]
  4. E. de Rocquigny, N. Devictor and S. Tarantola, Uncertainty in Industrial Practice: A Guide to Quantitative Uncertainty Management. John Wiley & Sons (2008). [Google Scholar]
  5. A. Boulore, Importance of uncertainty quantification in nuclear fuel behaviour modelling and simulation. Nucl. Eng. Des. 355 (2019) 110311. [Google Scholar]
  6. M. Gu and L. Wang, Scaled Gaussian stochastic process for computer model calibration and prediction. SIAM/ASA J. Uncertainty Quantif. 6 (2018) 1555–1583. [Google Scholar]
  7. R.K. Wong, C.B. Storlie and T.C. Lee, A frequentist approach to computer model calibration. J. Roy. Statist. Soc. B Statist. Methodol. 79 (2017) 635–648. [Google Scholar]
  8. M.C. Kennedy and A. O'Hagan, Bayesian calibration of computer models. J. Roy. Statist. Soc. B (Statist. Methodol.) 63 (2001) 425–464. [Google Scholar]
  9. X. Wu, T. Kozlowski, H. Meidani and K. Shirvan, Inverse uncertainty quantification using the modular Bayesian approach based on Gaussian process. Part 1. Theory. Nucl. Eng. Des. 335 (2018) 339–355. [Google Scholar]
  10. R.E. Kass and L. Wasserman, The selection of prior distributions by formal rules. J. Am. Statist. Assoc. 91 (1996) 1343–1370. [Google Scholar]
  11. S. Chib and E. Greenberg, Understanding the Metropolis-Hastings algorithm. Am. Statist. 49 (1995) 327–335. [Google Scholar]
  12. B. Currin, T. Mitchell, M. Morris and D. Ylvisaker, Bayesian prediction of deterministic functions, with applications to the design and analysis of computer experiments. J. Am. Statist. Assoc. 86 (1991) 953–963. [Google Scholar]
  13. J. Sacks, W.J. Welch, T.J. Mitchell and H.P. Wynn, Design and analysis of computer experiments. Statist. Sci. 4 (1989) 409–423. [Google Scholar]
  14. C. Andrieu and J. Thoms, A tutorial on adaptive MCMC. Statist. Comput. 18 (2008) 343–373. [Google Scholar]
  15. V.V. Dighe, M. Becker, T. Göcmen, B. Sanderse and J.-W. van Wingerden, Sensitivity analysis and Bayesian calibration of a dynamic wind farm control model: FLORIDyn, in Journal of Physics: Conference Series, vol. 2265. IOP Publishing (2022) 022062. [Google Scholar]
  16. J. Gou, C. Miao, Q. Duan, Q. Tang, Z. Di, W. Liao, J. Wu@ and R. Zhou, Sensitivity analysis-based automatic parameter calibration of the VIC model for streamflow simulations over China. Water Resources Res. 56 (2020) e2019WR025968. [Google Scholar]
  17. J.B. Nagel, J. Rieckermann and B. Sudret, Principal component analysis and sparse polynomial chaos expansions for global sensitivity analysis and model calibration: application to urban drainage simulation. Reliabil. Eng. Syst. Saf. 195 (2020) 106737. [Google Scholar]
  18. G. Perret, D. Wicaksono, I.D. Clifford and H. Ferroukhi, Global sensitivity analysis and Bayesian calibration on a series of reflood experiments with varying boundary conditions. Nucl. Technol. 208 (2022) 711–722. [Google Scholar]
  19. D.M. Hamby, A review of techniques for parameter sensitivity analysis of environmental models. Environ. Monitor. Assessment 32 (1994) 135–154. [Google Scholar]
  20. M.D. Morris, Factorial sampling plans for preliminary computational experiments. Technometrics 33 (1991) 161174. [Google Scholar]
  21. J. Morio, Global and local sensitivity analysis methods for a physical system. Eur. J. Phys. 32 (2011) 1577. [Google Scholar]
  22. A. Saltelli, Making best use of model evaluations to compute sensitivity indices. Comput. Phys. Commun. 145 (2002) 280–297. [CrossRef] [Google Scholar]
  23. I.M. Sobol, Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Math. Comput. Simul. 55 (2001) 271–280. [Google Scholar]
  24. S. Kucherenko, M. Rodriguez-Fernandez, C. Pantelides and N. Shah, Monte Carlo evaluation of derivative-based global sensitivity measures. Reliabil. Eng. Syst. Saf. 94 (2009) 1135–1148. [Google Scholar]
  25. L. Clouvel, B. Iooss, V. Chabridon, M.I. Idrissi and F. Robin, An overview of variance-based importance measures in the linear regression context: comparative analyses and numerical tests. Socioenviron. Syst. Model. 7 (2025) 18681–18681. [Google Scholar]
  26. B. Iooss and C. Prieur, Shapley effects for sensitivity analysis with correlated inputs: Comparisons with Sobol' indices, numerical estimation and applications. Int. J. Uncertain. Quantif. 9 (2019) 493–514. [Google Scholar]
  27. A.B. Owen and C. Prieur, On Shapley value for measuring importance of dependent inputs. SIAM/ASA J. Uncertain. Quantif. 5 (2017) 986–1002. [Google Scholar]
  28. S. Da Veiga, Global sensitivity analysis with dependence measures. J. Statist. Computat. Simul. 85 (2015) 12831305. [Google Scholar]
  29. M. De Lozzo and A. Marrel, New improvements in the use of dependence measures for sensitivity analysis and screening. J. Statist. Computat. Simul. 86 (2016) 3038–3058. [Google Scholar]
  30. A. Gretton, K. Fukumizu, C. Teo, L. Song, B. Schölkopf and A. Smola, A kernel statistical test of independence. Adv. Neural Inform. Process. Syst. 20 (2007) 585–592. [Google Scholar]
  31. C. Introöni, I. Ramiere, J. Sercombe, B. Michel, T. Helfer and J. Fauque, ALCYONE: the fuel performance code of the PLEIADES platform dedicated to PWR fuel rods behavior. Ann. Nucl. Energy 207 (2024) 110711. [Google Scholar]
  32. A. Boulore, C. Struzik, V. Bouineau, F. Gaudier, G. Damblin and S. Bernaud, Modelling of UO2 thermal conductivity: improvement of the irradiation defects contribution and uncertainty quantification. Nucl. Eng. Des. 407 (2023) 112304. [Google Scholar]
  33. G. Damblin, P. Barbillon, M. Keller, A. Pasanisi and E. Parent, Adaptive numerical designs for the calibration of computer codes. SIAM/ASA J. Uncertain. Quantif. 6 (2018) 151–179. [Google Scholar]
  34. C.P. Robert, G. Casella and G. Casella, Monte Carlo Statistical Methods, vol. 2. Springer (1999). [Google Scholar]
  35. G. Damblin and P. Gaillard, Bayesian inference and non-linear extensions of the CIRCE method for quantifying the uncertainty of closure relationships integrated into thermal-hydraulic system codes. Nucl. Eng. Des. 359 (2020) 110391. [Google Scholar]
  36. S. Barde, Bayesian estimation of large-scale simulation models with Gaussian process regression surrogates. Computat. Statist. Data Anal. 196 (2024) 107972. [Google Scholar]
  37. M. Van Oijen, D. Cameron, K. Butterbach-Bahl, N. Farahbakhshazad, P.-E. Jansson, R. Kiese, K.H. Rahn, C. Werner and J. Yeluripati. A Bayesian framework for model calibration, comparison and analysis: application to four models for the biogeochemistry of a Norway spruce forest. Agric. For. Meteorol. 151 (2011) 1609–1621. [Google Scholar]
  38. X. Wu, T. Mui, G. Hu, H. Meidani and T. Kozlowski, Inverse uncertainty quantification of TRACE physical model parameters using sparse gird stochastic collocation surrogate model. Nucl. Eng. Des. 319 (2017) 185–200. [Google Scholar]
  39. A. Marrel, B. Iooss and V. Chabridon, The ICSCREAM methodology: identification of penalizing configurations in computer experiments using screening and metamodel: applications in thermal-hydraulics. Nucl. Sci. Eng. 196 (2022) 301–321. [Google Scholar]
  40. A. Marrel and B. Iooss, Probabilistic surrogate modeling by Gaussian process: a new estimation algorithm for more robust prediction. Reliabil. Eng. Syst. Saf. 247 (2024) 110120. [Google Scholar]
  41. B. Zhou, Z. Shi, S. Kucherenko and H. Zhao, A unified approach for global sensitivity analysis based on active subspace and Kriging. Reliabil. Eng. Syst. Saf. 217 (2022) 108080. [Google Scholar]
  42. M. Binois and N. Wycoff, A survey on high-dimensional Gaussian process modeling with application to Bayesian optimization. ACM Trans. Evol. Learn. Optim. 2 (2022) 1–26. [Google Scholar]
  43. H. Haario, E. Saksman and J. Tamminen, An adaptive Metropolis algorithm. Bernoulli 7 (2001) 223–242. [CrossRef] [Google Scholar]
  44. F. Liu, M. Bayarri and J. Berger, Modularization in Bayesian analysis, with emphasis on analysis of computer models. Bayesian Anal. 4 (2009) 119–150. [Google Scholar]
  45. X. Wu, K. Shirvan and T. Kozlowski, Demonstration of the relationship between sensitivity and identifiability for inverse uncertainty quantification. J. Computat. Phys. 396 (2019) 2–30. [Google Scholar]
  46. X. Xu, C. Sun, G. Huang and B.P. Mohanty, Global sensitivity analysis and calibration of parameters for a physically-based agro-hydrological model. Environ. Model. Softw. 83 (2016) 88–102. [Google Scholar]
  47. M. Zambrano-Bigiarini, Z. Zajac and S. Tarantola, Global sensitivity analysis for the calibration of a fully-distributed hydrological model, in 7th International Conference on Sensitivity Analysis of Model Output, MASCOT-SAMO (2013). [Google Scholar]
  48. A.B. Owen, Sobol'indices and Shapley value. SIAM/ASA J. Uncertain. Quantif. 2 (2014) 245–251. [Google Scholar]
  49. M. Herin, M. Il Idrissi, V. Chabridon and B. Iooss, Proportional marginal effects for global sensitivity analysis. SIAM/ASA J. Uncertain. Quantif. 12 (2024) 667–692. [Google Scholar]
  50. F. Gamboa, A. Janon, T. Klein and A. Lagnoux, Sensitivity analysis for multidimensional and functional outputs. Electron. J. Statist. 8 (2014) 575–603. [Google Scholar]
  51. F. Gamboa, T. Klein, A. Lagnoux and L. Moreno, Sensitivity analysis in general metric spaces. Reliabil. Eng. Syst. Saf. 212 (2021) 107611. [Google Scholar]
  52. A. Janon, T. Klein, A. Lagnoux, M. Nodet and C. Prieur, Asymptotic normality and efficiency of two Sobol index estimators. ESAIM Probab. Statist. 18 (2014) 342–364. [Google Scholar]
  53. A. Marrel, B. Iooss, B. Laurent and O. Roustant, Calculations of Sobol' indices for the Gaussian process metamodel. Reliabil. Eng. Syst. Saf. 94 (2009) 742–751. [Google Scholar]
  54. S. Da Veiga, F. Gamboa, A. Lagnoux, T. Klein and C. Prieur, New estimation of Sobol' indices using kernels (2023). https://arxiv.org/pdf/2303.17832. [Google Scholar]
  55. E. Borgonovo, A new uncertainty importance measure. Reliabil. Eng. Syst. Saf. 92 (2007) 771–784. [Google Scholar]
  56. S. Rahman, The f-sensitivity index. SIAM/ASA J. Uncertain. Quantif. 4 (2016) 130–162. [Google Scholar]
  57. M.R. El Amri and A. Marrel, Optimized HSIC-based tests for sensitivity analysis: application to thermalhydraulic simulation of accidental scenario on nuclear reactor. Qual. Reliabil. Eng. Int. 38 (2022) 1386–1403. [Google Scholar]
  58. M.R. El Amri and A. Marrel, More powerful HSIC-based independence tests, extension to space-filling designs and functional data. Int. J. Uncertain. Quantif. 14 (2024) 69–98. [Google Scholar]
  59. G.-K. Delipei, J. Garnier, J. Le Pallec and B. Normand, Uncertainty analysis methodology for multi-physics coupled rod ejection accident, in International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering (M & C 2019) (2019). [Google Scholar]
  60. N. Marie, S. Li, A. Marrel, M. Marques, S. Bajard, A. Tosello, J. Perez, B. Grosjean, A. Gerschenfeld, M. Anderhuber et al., VVUQ of a thermal-hydraulic multi-scale tool on unprotected loss of flow accident in SFR reactor. EPJ N Nucl. Sci. Technol. 7 (2021) 3. [Google Scholar]
  61. A. Rollón de Pinedo, M. Couplet, B. Iooss, N. Marie, A. Marrel, E. Merle and R. Sueur, Functional outlier detection by means of h-mode depth and dynamic time warping. Appl. Sci. 11 (2021) 11475. [Google Scholar]
  62. T. Wang, X. Dai and Y. Liu,. Learning with Hilbert-Schmidt independence criterion: A review and new perspectives. Knowl. Based Syst. 234 (2021) 107567. [Google Scholar]
  63. T. Wang, Z. Hu and H. Liu, A unified view of feature selection based on Hilbert-Schmidt independence criterion. Chemometrics Intell. Lab. Syst. 236 (2023) 104807. [Google Scholar]
  64. T. Wang, J. Lu and G. Zhang, Two-stage fuzzy multiple kernel learning based on Hilbert-Schmidt independence criterion. IEEE Trans. Fuzzy Syst. 26 (2018) 3703–3714. [Google Scholar]
  65. A. Gretton, O. Bousquet, A. Smola and B. Scholkopf, Measuring statistical dependence with Hilbert-Schmidt norms, in International Conference on Algorithmic Learning Theory. Springer (2005) 63–77. [Google Scholar]
  66. S. Bernaud, I. Ramiere, G. Latu and B. Michel, PLEIADES: A numerical framework dedicated to the multiphysics and multiscale nuclear fuel behavior simulation. Ann. Nucl. Energy 205 (2024) 110577. [Google Scholar]
  67. B. Iooss and A. Marrel, Advanced methodology for uncertainty propagation in computer experiments with large number of inputs. Nucl. Technol. 205 (2019) 1588–1606. [Google Scholar]
  68. C. Sriperumbudur, K. Fukumizu and G. Lanckriet, On the relation between universality, characteristic kernels and RKHS embedding of measures, in Proceedings of the 13th International Conference on Artificial Intelligence and Statistics. JMLR Workshop and Conference Proceedings (2010) 773–780. [Google Scholar]
  69. J. Ziegel, D. Ginsbourger and L. Dumbgen, Characteristic kernels on Hilbert spaces, Banach spaces, and on sets of measures. Bernoulli 30 (2024) 1441–1457. [Google Scholar]
  70. O. Baldóe, G. Damblin, A. Marrel, A. Bouloróe and L. Giraldi, Nonparametric Bayesian approach for quantifying the conditional uncertainty of input parameters in chained numerical models (2023). https://arxiv.org/pdf/2307.01111. [Google Scholar]
  71. N. Fellmann, C. Blanchet-Scalliet, C. Helbert, A. Spagnol and D. Sinoquet, Kernel-based sensitivity analysis for (excursion) sets. Technometrics 66 (2024) 575–587. [Google Scholar]
  72. L. Song, A. Smola, A. Gretton, J. Bedo and K. Borgwardt, Feature selection via dependence maximization. J. Mach. Learn. Res. 13 (2012) 1393–1434. [Google Scholar]
  73. B.K. Sriperumbudur, A. Gretton, K. Fukumizu, B. Scholkopf and G.R. Lanckriet, Hilbert space embeddings and metrics on probability measures. J. Mach. Learn. Res. 11 (2010) 1517–1561. [Google Scholar]
  74. Z. Szabóo and B.K. Sriperumbudur, Characteristic and universal tensor product kernels. J. Mach. Learn. Res. 18 (2017) 1–29. [Google Scholar]
  75. R. Serfling, Approximation Theorems of Mathematical Statistics. John Wiley & Sons (1980). [Google Scholar]
  76. K. Zhang, J. Peters, D. Janzing and B. Schöolkopf, Kernel-based conditional independence test and application in causal Discovery, in Proceedings of the Twenty-Seventh Conference on Uncertainty in Artificial Intelligence (2011) 804–813. [Google Scholar]
  77. F. Kazi-Aoual, S. Hitier, R. Sabatier and J.-D. Lebreton, Refined approximations to permutation tests for multivariate inference. Computat. Statist. Data Anal. 20 (1995) 643–656. [Google Scholar]
  78. M. Yamada, W. Jitkrittum, L. Sigal, E.P. Xing and M. Sugiyama, High-dimensional feature selection by feature-wise kernelized lasso. Neural Computat. 26 (2014) 185–207. [Google Scholar]
  79. M. Kanagawa, P. Hennig, D. Sejdinovic and B.K. Sriperumbudur, Gaussian processes and kernel methods: a review on connections and Equivalences (2018). https://arxiv.org/pdf/1807.02582. [Google Scholar]
  80. A. Gretton and L. Gyorfi, Consistent nonparametric tests of independence. J. Mach. Learn. Res. 11 (2010) 1391–1423. [Google Scholar]

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