  Global sensitivity analysis aims at measuring the relative importance of
different variables or groups of variables for the variability of a quantity of
interest. Among several sensitivity indices, so-called Shapley effects have
recently gained popularity mainly because the Shapley effects for all the
individual variables are summed up to the overall variance, which gives a
better interpretability than the classical sensitivity indices called main
effects and total effects. In this paper, assuming that all the input variables
are independent, we introduce a quite simple Monte Carlo algorithm to estimate
the Shapley effects for all the individual variables simultaneously, which
drastically simplifies the existing algorithms proposed in the literature. We
present a short Matlab implementation of our algorithm and show some numerical
results. A possible extension to the case where the input variables are
dependent is also discussed.
