Relationship between sensitivity indices defined by variance- and covariance-based methods

Sensitivity analysis is a challenge to perform with correlated variables, as often occur in practice. The variance-based methods for correlated variables use the same sensitivity indices defined for independent variables. The associate algorithms to determine the sensitivity indices are computationally demanding, and require explicit knowledge of the joint and conditional probability density function (pdf) of the input variables. As an alternative, a method referred to as structural and correlative sensitivity analysis (SCSA) based on a covariance decomposition has also been developed to fully quantify the deterministic and statistical contributions of independent and correlated variables, which can be applied in simulations as well as for laboratory/field data where the explicit forms of the function f(x) and the pdf are unknown. In this paper, we show that the sensitivity indices defined by the variance-based method may be re-expressed in terms of the SCSA sensitivity indices without further numerical computation, if the function f(x) and the pdf are known. If f(x) and the pdf are not known, the indices can still be accurately calculated from a single modest set of input-output data samples with SCSA.