where $\boldsymbol{x} = { x_1, \ldots, x_8 }$ is the vector of input variables modeled as an independent uniform random variable in $[0, 1]^8$. $\epsilon$ 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 eight 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 LinkLetter2006Decreasing.
The model was used as a test function in the context of sensitivity analysis.
[^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 ten-dimensional linear function with decreasing coefficients from Linkletter et al. (2006)[^1] (see Eq. (6)) is defined as follows:
$$ \mathcal{M}(\boldsymbol{x}) = 0.2 x_1 + \frac{0.2}{2} x_2 + \frac{0.2}{4} x_3 + \frac{0.2}{8} x_4 + + \frac{0.2}{16} x_5 + \frac{0.2}{32} x_6 + \frac{0.2}{64} x_7 + \frac{0.2}{128} x_8 + \epsilon $$
where $\boldsymbol{x} = { x_1, \ldots, x_8 }$ is the vector of input variables modeled as an independent uniform random variable in $[0, 1]^8$. $\epsilon$ 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 eight 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
LinkLetter2006Decreasing.The model was used as a test function in the context of sensitivity analysis.
[^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.