On one-dimensional weighted Poincaré inequalities for Global Sensitivity Analysis

par David Heredia (Institut de Mathématiques de Toulouse)

mardi 2 déc. 2025, 11:15 → 12:15 Europe/Paris

Salle K. Johnson (1R3, 1er étage)

Recently, one-dimensional Poincaré inequalities have been applied in Global Sensitivity Analysis (GSA) to provide upper bounds and chaos-type approximations of Sobol indices. As a new contribution, we have developed the use of one-dimensional weighted Poincaré inequalities. The introduction of weights adds an extra degree of freedom to improve the accuracy of both the upper bounds and the approximations. In particular, we propose a method for constructing weights that ensures the existence of an orthonormal system of eigenfunctions, as well as data-driven weights specifically adapted to the model. Finally, we illustrate the benefits of using weights in GSA through an application to a real-world flooding model.