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I would like to know if a python package exists that estimates specific Sobol indices, namely those that are higher than 2nd order. The Wikipedia article for variance-based sensitivity analysis is quite good for understanding the Sobol method / indices.

For example, given a model with 10 parameters, what are the Sijk and Smnop third and fourth order indices respectively?

I am keenly aware that the number of model evaluations needed to calculate all higher order indices is 2d - 1; however, I am only interested in less than ten specific indices.

If no python package exists, please recommend some other software.

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