Estimation of target and conditional HSIC using goal-oriented sampling

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When the threshold used by conditional and target HSIC analyses is high, few samples exceed it, which makes it difficult to estimate the sensitivity indices. I’ve already had some numerical issues with OpenTURNS.

As pointed out by Marrel and Chabridon (2021) who introduced these indices (see [1]):

“if the objective is only to perform a target sensitivity analysis (TSA) or conditional sensitivity analysis (CSA) of the model and if the choice of sampling is possible, it is obvious that goal-oriented sampling methods such as importance sampling would be of great interest. Indeed, by adding simulations in the critical area, these methods would significantly improve the estimation of TSA and CSA indices”.

That way, we could use FORM-based importance sampling to estimate. This option should be discouraged if the user wishes to estimate global sensitivity analysis.

Are there any plans to implement this in OpenTURNS?

Furthermore, are there any plans to add other reliability-oriented sensitivity analysis techniques, e.g., FORM-IS-based Sobol’ analysis?

  1. Amandine Marrel, Vincent Chabridon. Statistical developments for target and conditional sensitivity analy sis: application on safety studies for nuclear reactor. Reliability Engineering and System Safety, 2021, 214, pp.107711. ⟨10.1016/j.ress.2021.107711⟩. ⟨hal-02541142v2 ↩︎

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Hi Matthias!

Are there any plans to implement this in OpenTURNS?

I do not know of any plan to implement this in the near future. How can the TSA and CSA indices take into account the instrumental distribution in this method?

You suggest adding new FORM-IS-based Sobol’ indices: can you share pointers on this topic?

Regards,
Michaël
PS
This might be interesting for @m-balesdent or @l-brevault, as some developments on adaptive sampling for reliability are on their way.

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Hi Michael,

Concerning the estimation of Sobol’ indices with importance sampling, there is a recent paper from Boucharif, Morio and Rochet (2026). One of the first contributions to this topic was Ziu et al. (2012). You can find other reduction variance techniques for the estimation of Sobol’ indices in the literature, particularly for rare events. My proposal (using IS-FORM) is closed to these references, perhaps already adressed somewhere. In OpenTURNS, I think this would imply to sample the model from the IS-FORM distribution in the standard space and estimate the indices from the samples and the user distribution.

Concerning target and conditional HSIC, I do not know if some recent research works adress the perspective proposed by Chabridon and Marrel. I think the extension of HSIC from MC to IS should be easy as these indices are expresses in terms of expectations. In practice, for high threshold and small data, such a reduction variance technique is required to get a few samples crossing the threshold. Otherwise, the use of these HSIC variants leads to very bad results, or even numerical issues (I experienced this situation with OpenTURNS).

Best regards,

Matthias