Moment independent sensitivity analysis with correlations

The moment independent importance measure is a popular global sensitivity analysis technique, and aims at evaluating contributions of the inputs to the whole output distribution. In this work, moment independent sensitivity analysis is performed for models with correlated inputs, by decomposing the importance measure into the uncorrelated part and correlated part. The correlated input variables are first orthogonalized, then the moment independent sensitivity analysis of the newly generated independent variables is performed. Discussions indicate that the moment independent importance measures, so obtained, can be interpreted as the full, correlated and uncorrelated contributions of the original inputs to the whole output distribution. Procedure of the proposed approach has been generalized. By the decomposition, the information provided by the moment independent importance analysis is enriched, which has been demonstrated by the application to several examples.