Developments and applications of Shapley effects to reliability-oriented sensitivity analysis with correlated inputs. (September 2021) - Il Idrissi, Marouane; Chabridon, Vincent; Iooss, Bertrand
Abstract: Reliability-oriented sensitivity analysis methods have been developed for understanding the influence of model inputs relative to events which characterize the failure of a system (e.g., a threshold exceedance of the model output). In this field, the target sensitivity analysis focuses primarily on capturing the influence of the inputs on the occurrence of such a critical event. This paper proposes new target sensitivity indices, based on the Shapley values and called "target Shapley effects", allowing for interpretable sensitivity measures under dependent inputs. Two algorithms (one based on Monte Carlo sampling, and a given-data algorithm based on a nearest-neighbors procedure) are proposed for the estimation of these target Shapley effects based on the ℓ 2 norm. Additionally, the behavior of these target Shapley effects are theoretically and empirically studied through various toy-cases. Finally, the application of these new indices in two real-world use-cases (a river flood model and a COVID-19 epidemiological model) is discussed. Highlights: Reliability-oriented sensitivity analysis for correlated inputs is addressed. New indices for target sensitivity analysis are proposed: the target Shapley effects. Two estimation methods are discussed (Monte Carlo and given-data). The usefulness of the new indices is showcased on two toy-cases and a flood model. A final application is proposed on a COVID-19 epidemiological model.