Stochastic sensitivity analysis: determination of the best approximation of Sobol' sensitivity indices

For the identification of the most influential input variables in a simulation model, global sensitivity analyses can be applied. For deterministic simulation models, i.e. models that yield the same outputs when being evaluated twice with the same set of inputs, sensitivity analyses are widely known. However, some simulation models are non-deterministic (i.e. stochastic) and include uncontrollable variables (also called seed or stochastic inputs). For stochastic models, each model evaluation leads to at least slightly different results. As a consequence, total sensitivity indices - measuring the influence of an input including all its interactions - cannot be calculated exactly, since uncontrollable variables cannot be fixed. So far, approximations are either based on an averaging approach or quasi total indices are used. Depending on the model and the considered input, any of the two approaches can yield better results. That is why, here, a method to determine the preferable approach is proposed.