Higher Order Sobol' Indices

Hello! I used a sobol analysis in a model 2d with 2 outputs variable. Compared with the total indices, the first order indices were not expressive. More precisely, i had variables with 0.2 first order indice and 0.8 total indice, for example.
This situation refers to the dependence between the variables? In this case, would be wrong assume independence variables? I appreciate some help with this theme.

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Hi @Thamires_Viana,

The difference between the first order Sobol index and the total index is due to interaction terms in your model. This is not the same as dependence. E.g., you could have two independent input RV X_1, X_2 and the model f(X_1, X_2) = X_1 X_2: here the first-order Sobol indices would be 0 for both variables, but the total Sobol indices for both would be 1.

See also @damarginal’s post in the thread Sensitivity Analysis in UQLab .

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Hello @nluethen! Thank you for your explanation. The conclusion on my problem is exactly what you said. There is important interaction terms but there is no relation with the dependences of the variables.

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