Kucherenko total indices equal to one

Dear UQLab Team,

Thanks for the amazing code. I am learning to use UQLab for sensitivity study. I have an existing dataset from 1000 simulations. Each data has 14 independent inputs and one output. I chose the Kucherenko indices because this method supports existing sample data, and doesn’t require PCE which had a large LOO error for my dataset, e.g., 0.26. It turned out that the Kucherentko first indices of each of the 14 input parameter seemed reasonable, e.g., 0.1, 0.3… But the total indices of all the 14 input parameters are exactly one. Are the results interpretable or just useless?

Thanks in advance.

Dear Li_Wei

thanks for your question. If your inputs are independent, there is a priori no reason to use Kucherenko indices. Standard Sobol’ indices would work. I’m surprised that a sparse PCE with 1,000 simulations in 14 (independent) dimensions does not provide a leave-one-out error smaller than 5%, which would be enough for accurate Sobol’ indices.
Did you use “subspace pursuit” as a sparse solver, and appropriate truncation schemes, e.g.:

MetaOpts.Method = 'SP'; 
MetaOpts.Degree = 2:7;
MetaOpts.TruncOptions.qNorm = [0.5 0.7 0.9];

Otherwise, if you can trust your Kucherenko indices, and if their sum is equal to one, it seems that there is no interaction between input variables. In that case, you could use the standard rank regression coefficients as an alternative.

Best regards

Dear Prof. Dr. Bruno Sudret,
Thank you so much for answering my question. The inputs are treated as independent ( “Copula” was not specified in the run script). Following your advice, the LOO error can be reduced to ~5%. I also obtained the Borgonovo indices, the sum of which is 1.7, So I will go head with Sobol’s indices.

Best regards,