Averaging Sobol Indices and Spearman Correlation Coefficients

All About UQ UQ Discussion Forum
1

I’m working on a project where I’m evaluating multiple combinations of input variables using a PCE model. My aim is to identify which combinations result in significant changes in the system’s output, specifically those that exceed the allowable boundary of the Quantity of Interest (QoI).

For the combinations that result in these changes, I calculate the Spearman Correlation Coefficient and the Total Sobol Indices. To simplify the analysis, I am considering averaging these metrics.

Here are my questions:

  1. Is it theoretically valid to average the Spearman Correlation Coefficients and Total Sobol Indices across different input combinations that lead to system changes?
  2. What precautions should I take to ensure that the averaged values are meaningful and representative of the system’s behavior?
  3. Are there any specific methods or best practices for averaging these metrics in such a constrained and specific setting?

Thanks in advance!