Understanding the confidence interval of Sobol indices

Bootstrap is Bootstrapping (statistics) - Wikipedia

Similarly, how does changing the confidence level change anything

That changes only the level (pretty well explained in Confidence interval - Wikipedia just in case you are not familiar) and not the number of samples, nboot changes the number of samples

. To clarify my understanding sobol.ST_Conf_Int will return a matrix where each row is a confidence number and each column is a variable passed

EDIT: Sorry I misread this before.

No, the way the results are reported for first and total order indices’ CI is

 param1 param2 param3 .. ... ...

u1
u2

with each cell being the error for that parameter (the columns)'s sensitivity index for the observed variable (row). So that’s why you have a 4*12 matrix for 4 observed variables and 12 parameters. To get the CIs for the indices you’d do S1[I,j] - S1_Conf_Int[I,j] and S1[I,j] + S1_Conf_Int[I,j] (or through broadcasting)