where $\boldsymbol{x} = { x_1, x_2 }$ is the vector of input variables modeled as an independent uniform random variable in $[0, 1]^2$.
The model is used as a test function in the context of sensitivity analysis whose Sobol' sensitivity indices are available analytically.
[^1]: H. Moon, “Design and Analysis of Computer Experiments for Screening Input Variables,” Ohio State University, 2010. [Online]. Available: http://rave.ohiolink.edu/etdc/view?acc_num=osu1275422248 (see Eq. (5.46) in Section 5.1.4)
The three-dimensional test function from Moon (2010)[^1] is defined analytically as follows:
$$ \mathcal{M}(\boldsymbol{x}) = x_1 + x_2 + 3 x_1 x_3 $$
where $\boldsymbol{x} = { x_1, x_2 }$ is the vector of input variables modeled as an independent uniform random variable in $[0, 1]^2$.
The model is used as a test function in the context of sensitivity analysis whose Sobol' sensitivity indices are available analytically.
[^1]: H. Moon, “Design and Analysis of Computer Experiments for Screening Input Variables,” Ohio State University, 2010. [Online]. Available: http://rave.ohiolink.edu/etdc/view?acc_num=osu1275422248 (see Eq. (5.46) in Section 5.1.4)