Hello all,
I have a question about PCE based Sobol indices:
During calculation of PCE, I set my maximum interactions to be 2. I mean:
MetaOpts.TruncOptions.MaxInteraction = 2;
Does it mean that the maximum order of Sobol indices that I can calculate using this PCE is 2 as well?
I say this because when I calculate 3rd order Sobol indices they are all zero. So I think I cannot find third-order Sobol indices with a PCE that has 2nd order interaction.
In fact, with 2nd order PCE, I can only calculate first, second, and total order indices, and here total order Sobol index is just summation of first and second-order indices as it is the maximum order we can calculate.
Is this correct?
Any help is appreciated.
Indeed but setting the maximum interaction to 2, you get a polynomial function whose terms depend at most on two different variables. That is: there is no polynomials of three or more variables, and thus the 3rd order indices are zero for your PCE.
Unless you have an extremely high input dimension it is not necessary to truncate the interactions to 2.
BTW in 15 years of PCE I have never seen a single problem where third-order interactions would be non negligible! Is your problem so special?
Thanks for your response @bsudret. My problem is not very special, however, I was mostly asking about Sobol indices. You mentioned that 3rd order indices are zero for PCE. However, does it mean that the third-order (and higher-order) Sobol indices are zero as well?
Thanks in advance.