Computation of sobol indices in global sensitivity analysis from small data sets by probabilistic learning on manifolds

• Published in: International Journal for Uncertainty Quantification
• Main Authors: Arnst, Maarten, Soize, Christian, Bulthuis, Kevin
• Format: Article in Journal/Newspaper
• Language: English
• Published: Begell House Inc. 2021
• Subjects: Global sensitivity analysis; Probabilistic learning on manifolds; Small data; Sobol index; Statistics and Probability; Modeling and Simulation; Discrete Mathematics and Combinatorics; Control and Optimization; Engineering; computing & technology; Ingénierie; informatique & technologie; Antarc*; Antarctic; Ice Sheet
• Online Access: https://orbi.uliege.be/handle/2268/295234; https://doi.org/10.1615/Int.J.UncertaintyQuantification.2020032674

peer reviewed Global 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.