Simulation sensitivity analysis with Importance Sampling

I recently needed to compute the sensitivity indices of the probability of failure and I used the SimulationSensitivityAnalysis class. However I think this does not work properly if I perform a simulation with weighted experiment like ImportanceSamplingExperiment.
I provide a notebook in which I made a function that compute it but do you think this could be generalized directly in OT ? The tricky part may be that I want the indices with respect to the original distribution parameters and not in in the standard space.
For SubsetSampling, it is not direct but equations to compute it are provided in this paper, or also in Dubourg Thesis or Bourinet HDR.

In the notebook I also tried to get the indices using ParametrizedDistribution and this works fine.

Simulation_sensitivity_for_IS.ipynb (17.4 KB)