Hi,

I was trying to calculate the analytical total sensitivity index for Sobol G-function using the default values for a ([0, 1, 4.5, 9, 99, 99, 99, 99]). These values appear to come from Sobol et al (2007; DOI: 10.1016/j.ress.2006.07.001). But the results from SALib do not match the analytical values given in the paper.

I can get matching results with Sobol et al. using the formula from Saltelli et al., (2010; https://doi.org/10.1016/j.cpc.2009.09.018) but this formula appears different to the one used in SALib for the Sobol G-function, see Table below.

I am unable to find which method SALib is using to calculate the analytic values.

Here is the code I used:

a = [0, 1, 4.5, 9, 99, 99, 99, 99]
vd = np.array([1/3/ (i +1)**2 for i in a])
vtd = np.zeros(vd.shape[0])
total_vtd = np.prod([i + 1 for i in vd])
for i in range(vtd.shape[0]):
    vtd[i] = vd[i] * total_vtd / (vd[i] + 1) / _total_variance(a)

_total_variance() is the same one as found in SALib

Best wishes,
Qian