Add 10D Simple Test Function from Linkletter et al. (2006)

[damar-wicaksono]

The ten-dimensional simple function from Linkletter et al. (2006)¹ is a linear model defined as follows:

$$ \mathcal{M}(\boldsymbol{x}) = 0.2 x_1 + 0.2 x_2 + 0.2 x_3 + 0.2 x_4 + \epsilon $$

where $\boldsymbol{x} = { x_1, x_2, x_3, x_4 }$ is the vector of input variables modeled as an independent uniform random variable in $[0, 1]^4$. $\epsilon$ is a random error generated from $\mathcal{N}(\mu = 0.0, \sigma^2=0.05)$. Although the model is defined to be of ten-dimensional, only four input variables are active.

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 LinkLetter2006Simple.

The model is used as a test function in the context of sensitivity analysis.

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. ↩