Estimation of global sensitivity indices for models with dependent variables

A novel approach for estimation variance based sensitivity indices for models with dependent variables is presented. Both the first order and total sensitivity indices are derived as generalizations of Sobol’ sensitivity indices. Formulas and Monte Carlo numerical estimates similar to Sobol’ formulas are derived. A copula based approach is proposed for sampling from arbitrary multivariate probability distributions. A good agreement between analytical and numerical values of the first order and total indices for considered test cases is obtained. The behaviour of sensitivity indices depends on the relative predominance of interactions and correlations. The method is shown to be efficient and general.