https://hal-upec-upem.archives-ouvertes.fr/hal-02918215Arnst, MaartenMaartenArnstUniversité de LiègeSoize, ChristianChristianSoizeMSME - Laboratoire Modélisation et Simulation Multi-Echelle - UPEC UP12 - Université Paris-Est Créteil Val-de-Marne - Paris 12 - CNRS - Centre National de la Recherche Scientifique - Université Gustave EiffelBulthuis, KevinKevinBulthuisUniversité de LiègeComputation of Sobol indices in global sensitivity analysis from small data sets by probabilistic learning on manifoldsHAL CCSD2021global sensitivity analysisSobol indexprobabilistic learning on manifoldssmall data[STAT.ML] Statistics [stat]/Machine Learning [stat.ML][MATH.MATH-PR] Mathematics [math]/Probability [math.PR][MATH.MATH-ST] Mathematics [math]/Statistics [math.ST]Soize, Christian2020-08-20 11:02:062022-06-26 02:52:432020-08-20 16:17:52enJournal articleshttps://hal-upec-upem.archives-ouvertes.fr/hal-02918215/document10.1615/Int.J.UncertaintyQuantification.2020032674application/pdf1Global sensitivity analysis provides insight into how sources of uncertainty contribute to uncertainty in predictions of computational models. Global sensitivity indices, also called variance-based sensitivity indices and Sobol indices, are most often computed with Monte Carlo methods. However, when the computational model is computationally expensive and only a small number of samples can be generated, that is, in so-called small-data settings, usual Monte Carlo estimates may lack sufficient accuracy. As a means of improving accuracy in such small-data settings, we explore the use of probabilistic learning. The objective of the probabilistic learning is to learn from the available samples a probabilistic model that can be used to generate additional samples, from which Monte Carlo estimates of the global sensitivity indices are then deduced. We demonstrate the interest of such a probabilistic learning method by applying it in an illustration concerned with forecasting the contribution of the Antarctic ice sheet to sea-level rise.