where $\boldsymbol{x} = { x_1, x_2 }$ is the vector of input variables modeled as an independent uniform random variable in $[0, 1]^2$. $\epsilon$ is a random error generated from $\mathcal{N}(\mu = 0.0, \sigma^2=0.05)$.
In the paper, the response is standardized (with mean 0 and standard deviation 1.0), but we will skip this in the implementation of the function in UQTestFuns. The candidate name for this function is LinkLetter2006Sine.
The model is used as a test function in the context of sensitivity analysis. Although the model is in principle separable the impact of $x_1$ and $x_2$ on the output is (very) different.
[^1]: C. Linkletter, D. Bingham, N. Hengartner, D. Higdon, and K. Q. Ye, “Variable Selection for Gaussian Process Models in Computer Experiments,” Technometrics, vol. 48, no. 4, pp. 478–490, Nov. 2006, doi: 10.1198/004017006000000228.
The two-dimensional test function from Linkletter et al. (2006)[^1] is a model involving sine terms:
$$ \mathcal{M}(\boldsymbol{x}) = \sin{(x_1)} + \sin{(5 x_2)} + \epsilon $$
where $\boldsymbol{x} = { x_1, x_2 }$ is the vector of input variables modeled as an independent uniform random variable in $[0, 1]^2$. $\epsilon$ is a random error generated from $\mathcal{N}(\mu = 0.0, \sigma^2=0.05)$.
In the paper, the response is standardized (with mean 0 and standard deviation 1.0), but we will skip this in the implementation of the function in UQTestFuns. The candidate name for this function is
LinkLetter2006Sine.The model is used as a test function in the context of sensitivity analysis. Although the model is in principle separable the impact of $x_1$ and $x_2$ on the output is (very) different.
[^1]: C. Linkletter, D. Bingham, N. Hengartner, D. Higdon, and K. Q. Ye, “Variable Selection for Gaussian Process Models in Computer Experiments,” Technometrics, vol. 48, no. 4, pp. 478–490, Nov. 2006, doi: 10.1198/004017006000000228.