Variance-based sensitivity indices for models with dependent inputs

Thierry A. Mara (1) , Stefano Tarantola (2)

1 PIMENT - Physique et Ingénierie Mathématique pour l'Énergie, l'environnemeNt et le bâtimenT
2 Institute for the Protection and Security of the Citizen

Computational models are intensively used in engineering for risk analysis or prediction of future outcomes. Uncertainty and sensitivity analyses are of great help in these purposes. Although several methods exist to perform variance-based sensitivity analysis of model output with independent inputs only a few are proposed in the literature in the case of dependent inputs. This is explained by the fact that the theoretical framework for the independent case is set and an univocal set of variance-based sensitivity indices is defined. In the present work, we propose a set of variance-based sensitivity indices to perform sensitivity analysis of models with dependent inputs. These measures allow us to distinguish between the mutual dependent contribution and the independent contribution of an input to the model response vari-ance. Their definition relies on a specific orthogonalisation of the inputs and ANOVA-representations of the model output. In the applications, we show the interest of the new sensitivity indices for model simplification setting.

Mots clés: dependent inputs; variance-based sensitivity indices; dependent contributions; independent contributions; ANOVA-HDMR

Domaines: Applications [stat.AP]

Thierry A. Mara, Stefano Tarantola. Variance-based sensitivity indices for models with dependent inputs. Reliability Engineering and System Safety, 2012, 107, pp.115 - 121. ⟨10.1016/j.ress.2011.08.008⟩. ⟨hal-01093038⟩