Sobol' indices with acceptance-rejection sampling

Python usage
1

Hi everyone,

I’d like to compute Sobol’ indices in a setting where not all input samples are valid, due to feasibility or constraint criteria. I see two possible scenarios and would appreciate your advice on whether either is supported in OpenTURNS:

  1. Acceptance–rejection filtering applied beforehand:
    I already have a set of valid input–output pairs (Xi,Yi), where they​ were sampled and filtered according to some acceptance criterion. Can I directly use these filtered pairs to estimate Sobol’ indices, even though the sampling is no longer from the original input distribution?
  2. Acceptance rule as part of the model:
    Alternatively, is it possible to find in OpenTURNS a function that has as input:
  • the input distribution
  • the model
  • a custom rejection rule (e.g., only accept inputs that satisfy some condition)
    and have the estimation account for this while still computing valid Sobol’ indices for the conditional model?

Thanks in advance!

Lorenzo

2

The easiest solution would be to use your filtered samples with
RankSobolSensitivityAlgorithm, but as you are using acceptance your input samples are no longer iid so the resulting Sobol’ indices will be more or less invalid depending on the acceptance ratio.

3

Thanks for the answer, indeed that was also a test that I’ve done and the results are not satisfactory / not correct from a theoretical viewpoint.