Add the Two-Dimensional Test Function from Linkletter et al. (2006)

[damar-wicaksono]

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.

Footnotes

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. ↩