I’ve read a lot about the Sobol method for sensitivity analysis, and I’ll admit I don’t have a firm grasp of the mathematics, so I’d like to pose what might be a trivial question here. If I analyze the linear model

Y=X1+X2+X3+X4

where Xi∼N(0,1) and are independent.

Then the Sobol first-order and total order indices are naturally 0.25 for each independent variable or factor. If the linear model is modified to the following:

Y=X1+2*X2+X3+X4

the first-order and total order indices are about 0.14 for X1, X3, and X4, and 0.58 for X2. I don’t understand these results. I would expect the values for X1, X3, and X4 to be 0.2 and the value for X2 to be 0.4. I wonder if anyone can provide a good explanation for the results.