Résumé
Variance-based sensitivity analysis and multivariate sensitivity analysis aim to apportion the variability of model output(s) into input factors and their interactions. Total sensitivity index (TSI) gives for each input its overall contribution, including the effects of its interactions with all the other inputs, in the variability of the model output(s). We investigate a numerical approximation of TSIs mainly based upon quadrature rules and quasi-Monte Carlo. The estimation of a TSI relies on the estimation of a total effect function (TEF), which allows for computing the TSI values by taking its variance. First, the paper derives the specific formula for the computation of the TEF, including the theoretical properties of the approximation, and second, it gives an overview of its application in many situations. Our approach gives the exact estimation of TSIs for a class of exact quadrature rules (especially for polynomial functions) and an interesting approximation for other functions. Numerical tests show the faster convergence rate of our approach and their usefulness in practice.