Sobol Indices

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Dear all:

I am new to UQ lab for the sensitivity analysis. Could anyone explain me why a negative Sobol index could appear when I use UQ lab? From my understanding it is defined by the ratio of variance Vi by the total variance V. And since the variance is defined to be always positive I can’t understand why the Sobol index would be negative.

Thanks for your help in advance.

Best regards
Adrian

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Hi @Adrian,

Welcome to UQWorld! :slight_smile: A negative Sobol index can appear when you compute the Sobol indices by Monte Carlo and don’t use enough samples (see also the first few posts by @damarginal in this thread). You could also check the equations on page 15 of the Sensitivity analysis manual.

Have you considered using PCE to compute the Sobol indices? This is typically much more efficient than using MC.

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Thanks for your answer. Yes with PCE the results make more sense. I will give the post of @damarginal a closer look.