A new framework of variance based global sensitivity analysis for models with correlated inputs

In the past few decades, variance based global sensitivity analysis for models with only uncorrelated inputs has been well developed. It aims at investigating the impact of variations in uncorrelated inputs on the variation of a model output and ranking the importance of the inputs. However, for models with correlated inputs, only a few researches have been done and the existing theory of variance based global sensitivity is not so consummate. In this article, a new framework of variance based global sensitivity analysis is presented, which is suitable for models with both uncorrelated and correlated inputs. With this new framework, the variance based global sensitivity analysis for models with correlated variables can be conducted conveniently and the variance contributions of a correlated variable to the variance of model output can be identified and interpreted distinctly.