  Global sensitivity analysis is the main quantitative technique for
identifying the most influential input variables in a numerical simulation
model. In particular when the inputs are independent, Sobol' sensitivity
indices attribute a portion of the output of interest variance to each input
and all possible interactions in the model, thanks to a functional ANOVA
decomposition. On the other hand, moment-independent sensitivity indices focus
on the impact of input variables on the whole output distribution instead of
the variance only, thus providing complementary insight on the inputs / output
relationship. Unfortunately they do not enjoy the nice decomposition property
of Sobol' indices and are consequently harder to analyze. In this paper, we
introduce two moment-independent indices based on kernel-embeddings of
probability distributions and show that the RKHS framework used for their
definition makes it possible to exhibit a kernel-based ANOVA decomposition.
This is the first time such a desirable property is proved for sensitivity
indices apart from Sobol' ones. When the inputs are dependent, we also use
these new sensitivity indices as building blocks to design kernel-embedding
Shapley effects which generalize the traditional variance-based ones used in
sensitivity analysis. Several estimation procedures are discussed and
illustrated on test cases with various output types such as categorical
variables and probability distributions. All these examples show their
potential for enhancing traditional sensitivity analysis with a kernel point of
view.
