Global sensitivity analysis is the main quantitative technique for identifying the most influential input variables in a numerical model.
In particular when the inputs are independent, Sobol’ sensitivity indices attribute a portion of the output 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 inputs on the whole output distribution instead of the variance only, thus providing complementary insight on the inputs/output  relationship. But they do not enjoy the nice decomposition property of  Sobol’ indices and are consequently harder to analyze.
In this talk, we introduce two moment-independent indices based on kernel-embeddings of probability distributions and show that the RKHS framework 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. With dependent inputs, we also use these new sensitivity indices as building blocks to design kernel-embedding Shapley effects which generalize the traditional ones.
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 sensitivity analysis with a kernel viewpoint.