Sum of Sobol indices in the case of orthogonal inputs

[moesphere]

In the case of orthogonal inputs, the sum over all Sobol indices should be equal to 1. Currently, this is not the case.
MWE, where the second-order Sobol indices already exceed 1 considerably:

using GlobalSensitivity, QuasiMonteCarlo

function ishi(X)
    A= 7
    B= 0.1
    sin(X[1]) + A*sin(X[2])^2+ B*X[3]^4 *sin(X[1])
end

n = 600000
lb = -ones(4)*π
ub = ones(4)*π
sampler = SobolSample()
A,B = QuasiMonteCarlo.generate_design_matrices(n,lb,ub,sampler)

res1 = gsa(ishi,Sobol(order=[0,1,2]),A,B)

For a more thorough discussion, see this thread on julia discourse.

[Vaibhavdixit02]

I am not sure what the issue is, as I mentioned in the discourse thread and even you said the same thing https://discourse.julialang.org/t/how-to-interpret-2nd-order-sobol-global-sensitivity-analysis-result/47804/14, if you sum over all the possible orders' indices then only you are guaranteed to get to 1, otherwise it would be "close" to 1, and that is true for the results you get. Please let me know if I am misunderstanding what issue you are seeing?

[moesphere]

If you run the MWE from above the Sobol indices are:

The second order indices, if res1.S2 are the second order indices, are very much too large. The sum of all of the first and second order indices should not exceed 1.

[moesphere]

If you run the same example with the GlobalSensitivityAnalysis package, you end up with the following indices:

And they seem to be correct. Note that the sum over all indices does not exceed 1.

[moesphere]

Bottomline is that the calculation of the first-order Sobol indices seems to be correct, but not the calculation of the higher-order indices.

[Vaibhavdixit02]

Oh I get it now, sorry, I didn't notice GlobalSensitivityAnalysis, I thought they were results from this package. 😅

Yes this looks incorrect, most probably from some changes we had earlier to the implementation. I'll take a look, thanks for reporting!

[moesphere]

Adding the MWE as a test might be a good idea.

[Vaibhavdixit02]

Thanks for this important issue @moesphere. It is fixed now in the latest release, please try it out.