Asymptotic Analysis for the Variance-Based Global Sensitivity Indices

We discuss the estimation of the uncertainty and sensitivity parameters for a model response under the assumption that the input variables are normally distributed and block-wise correlated with the covariance matrix, which is small in some norm. These conditions may arise when considering the impact of the group-wise neutron cross-sections' uncertainties on the uncertainty of some reactor parameters such as the neutron multiplication factor. The variance-based global sensitivity analysis, considered in our work, involves the calculation of multidimensional integrals. When the input uncertainties are small, the values of these integrals can be estimated using an asymptotic analysis method called the Laplace approximation. The asymptotic formulas for the output variance and for the global sensitivity indices have been obtained using the Laplace approximation method. It is demonstrated that the asymptotic formula for uncertainty propagation matches the uncertainty propagation formula being used in the local sensitivity analysis. The applicability of the obtained asymptotic approximations was successfully demonstrated on a test problem with realistic cross-section and covariance matrix values.