Hi,
I have a general question about ANCOVA and Kucherenko methods. As I understood after a read through that these two methods are dedicated for dependent input random variables. However, both of these methods are applicable regardless of the dependence since we can get the output of uncorrelated input variables and show the independent contributions.

So, if I apply these methods for a computational model that does not have any dependence or correlations for the inputs, does that mean that the sensitivity indices results are similar from the Sobolâ€™ sensitivity indices method since I read that the ANCOVA is a way to generalize the formulation of Sobolâ€™ indices for dependent input case?

Basically, can I actually do a comparison between the results from Sobolâ€™, ANCOVA and Kucherenko methods?

Thanks for asking here. Yes, your general understanding is correct: ANCOVA and Kucherenko indices are designed for dependent input variables, but they are generally applicable to any input structures. Nevertheless, these two types of indices are not equivalent for dependent inputs: the definition of ANCOVA relies on the functional decomposition, while the Kucherenko indices are defined directly by conditional expectation/variance. Moreover, for ANCOVA indices, only those of the first-order are well-defined (and implemented in UQLab), and the definition of higher-order and total ANCOVA indices remains open (as clearly pointed out in the sensitivity manual).

If the input variables are independent, the two types of indices by definition are identical to Sobolâ€™ indices. However, numerical results are generally different:

Since the calculation of ANCOVA indices depends on PCE, their values correspond to the Sobolâ€™ indices of the PCE. If you use PCE to evaluate the Sobolâ€™ indices of the computational model, then the values of these two indices coincide in theory. However, UQLab uses Monte Carlo simulations to calculate the ANCOVA indices while it makes use of the independence and the properties of PCE to compute the Sobolâ€™ indices by post-processing the coefficients without sampling.

For Kucherenko indices, UQLab provides two sampling-based methods which are different from the estimator based on Monte Carlo simulation designed for Sobolâ€™ indices. More precisely, UQLab uses the so-called pick-and-freeze algorithm to efficiently evaluate the Sobolâ€™ indices.

In summary, if your input variables are independent, ANCOVA and Kucherenko indices coincide with the definition of Sobolâ€™ indices. However, I would recommend using Sobolâ€™ indices in this case for the sake of efficiency and accuracy.