Table 3.

Hyperparameter settings for Gaussian process regressors from Bayesian optimization, $r={\sum }_{j=1}^{19}\frac{{\left({\theta }_j-{\theta }_j^{\prime }\right)}^2}{{\sigma }_j^2}$ is weighted Euclidean distance between parameters θ and θ′.

Regressor	Type of Basis Function	Kernel Function
${\widehat{y}}_1$	Linear	$k\left(\theta ,{\theta }^{\prime }\right)={\sigma }_f^2\left(1+\sqrt{5}r+\frac{5}{3}{r}^2\right)\exp \left(-\sqrt{5}r\right),{\sigma }_f=0.2091$
${\widehat{y}}_2$	Constant	$k\left(\theta ,{\theta }^{\prime }\right)={\sigma }_f^2\left(1+\sqrt{5}r+\frac{5}{3}{r}^2\right)\exp \left(-\sqrt{5}r\right),{\sigma }_f=0.3101$
${\widehat{y}}_3$	Constant	$k\left(\theta ,{\theta }^{\prime }\right)={\sigma }_f^2{\left(1+\frac{r^2}{2\alpha }\right)}^{-\alpha },{\sigma }_f=0.4558,\alpha =0.063$