Parseval inequalities and lower bounds for variance-based sensitivity indices (Q2286373)

The authors discuss the role played by the functional basis bounds for global sensitivity analysis, and the suggest using generalized polynomial chaos expansions in Hilbert spaces to obtain lower, making use of Parseval's inequality. This provides a tool for variable screening. They choose a special Hilbert space basis obtained by diagonalizing the Poincaré differential operators. The authors discuss the relation to the principal component expansion: The two expansions coincide in case of the normal or the gamma distribution. It is shown how to choose the orthonormal functions in the generalized chaos expansion in order to avoid weightings in the derivative-based sensitivity analysis. Several examples are discussed, and the authors consider two applications: A model for the cost of floods and a predator-prey model. For these models, the authors give numerical results, where bootstrap is used to obtain confidence intervals.