  We consider the estimation of sensitivity indices based on divergence
measures such as Hellinger distance. For sensitivity analysis of complex
models, these divergence-based indices can be estimated by Monte-Carlo sampling
(MCS) in combination with kernel density estimation (KDE). In a direct
approach, the complex model must be evaluated at every input point generated by
MCS, resulting in samples in the input-output space that can be used for
density estimation. However, if the computational cost of the complex model
strongly limits the number of model evaluations, this direct method gives large
errors. We propose to use Gaussian process (GP) surrogates to increase the
number of samples in the combined input-output space. By enlarging this sample
set, the KDE becomes more accurate, leading to improved estimates. To compare
the GP surrogates, we use a surrogate constructed by samples obtained with
stochastic collocation, combined with Lagrange interpolation. Furthermore, we
propose a new estimation method for these sensitivity indices based on minimum
spanning trees. Finally, we also propose a new type of sensitivity indices
based on divergence measures, namely direct sensitivity indices. These are
useful when the input data is dependent.
