I understand that first order and total effect Sobol' indices demonstrate the relative importance of the input parameters on the output of a given model. My question is, do the specific values of each index provide any quantifiable information about the outcome of a model or can they only be used to compare the relative importance of each parameter?

For example, say one calculated first and total indices of an input parameter to be 0.1 and 0.6, respectively, using Monte-Carlo sampling. That means that 10% of the outcome variance is due to that individual parameter. Now let's say that my input variable has a value of 2, I run the given model and receive an output. If I were to change my input variable by 20% for example, would I be able to conclude anything about the outcome based off of the value of the Sobol' indices?

Thank you in advanced!

I understand that first order and total effect Sobol' indices demonstrate the relative importance of the input parameters on the output of a given model. My question is, do the specific values of each index provide any quantifiable information about the outcome of a model or can they only be used to compare the relative importance of each parameter?

For example, say one calculated first and total indices of an input parameter to be 0.1 and 0.6, respectively, using Monte-Carlo sampling. That means that 10% of the outcome variance is due to that individual parameter. Now let's say that my input variable has a value of 2, I run the given model and receive an output. If I were to change my input variable by 20% for example, would I be able to conclude anything about the outcome based off of the value of the Sobol' indices?