I would like to kindly ask you a doubt about Sobol indices computed by Polynomial Chaos coefficients. Some time ago, considering a particular case of study, I tried to compute Sobol indices based on Polynomial Chaos coefficients. I used both OLS and LARS methodology and the ranking of the most important variables of the problem was coherent for both the two methods applied (I think this is a correct consequence when simulations are well-posed). Now, I am trying to analyze the Sobol indices for another phenomenon but the ranking of the most important initial variables is not preserved for this case when I apply OLS and LARS methods respectively. My questions are: is this situation only due to the quality of simulations? does the methodology (OLS and LARS for istance) influence the computation of Sobol Indices?
Thanks for this interesting question. The answer is simple: if OLS and LARS provide about the same accuracy of the surrogate models (in terms of LOO error or validation error), then the coefficients should be almost identical, and their combination should give the same Sobol’ indices.
You should check the reported “Leave-one-out error” and “Modified Leave-one-out error” when typing uq_print(myPCE). As soon as it is below 1%, you can safely use the Sobol indices.
In your case, I suspect that based on your (limited) data, the OLS solution is rather inaccurate.
In any case, the sparse PCEs almost always give a better accuracy than “full” PCEs obtained by OLS. You can try MetaOpts.Method = 'LARS' or MetaOpts.Method = 'SP': these are the most accurate sparse solvers in general.