Is there a method for Global Sensitivity Analysis that does not require special sampling methods? I want to perform a global sensitivity analysis using randomly sampled data that already exists (or can be generated with only N randomized model runs). The impetus for this is to be able to use the same data for uncertainty quantification (which requires randomized sampling rather than special slices) as well as the sensitivity analysis. I can guarantee the input variables are independent and square-integratable over the unit hypercube, but the underlying model is a nonlinear one with discontinuities and so a "metamodeling" approach that requires spline fitting or the like is not appropriate. Obviously, this rules out a linear ANOVA or the like. Ultimately I want to end up with the Total Order sobol sensitivity index for my input/output variable pairs.
I have read [1], and it seems that at its time of publishing Section 5.4 says that there is not a method that fits the bill. Saltelli's method of calculating sensitivity indices requires special sampling, the Fourier/FAST-based methods require special sampling and don't give the total order effects, and the response-surface approximation methods both are not appropriate as discussed above and are not able to give total order effects either.
The VARS [2] approach is the only truly new approach that's been developed since 2008 that I've been able to find, and it also requires a special sampling method. The recent [3] doesn't list anything that fits my bill either. Is there anything I'm missing? I'm really just a curious layman here so there may be a swath of the field that I'm not aware of.
[1] Saltelli, Andrea, et al. Global sensitivity analysis: the primer. John Wiley & Sons, 2008.
[2] Razavi, Saman, and Hoshin V. Gupta. "A new framework for comprehensive, robust, and efficient global sensitivity analysis: 1. Theory." Water Resources Research 52.1 (2016): 423-439.
[3] Puy, Arnald, et al. "A comprehensive comparison of total-order estimators for global sensitivity analysis." International Journal for Uncertainty Quantification (2020).

It looks like the closest thing right now is: Sheikholeslami, Razi, and Saman Razavi. "A fresh look at variography: measuring dependence and possible sensitivities across geophysical systems from any given data." Geophysical Research Letters 47.20 (2020): e2020GL089829.
Looking at the supplementary material it looks like this is sensitive to the choice of correlation function chosen. A linear correlation function like they use in the paper should suffice for an estimate of the total order sensitivity via IVARS100, however you don't get the scale-dependent benefits of the VARS approach.
