Table 3
Marginal log-likelihood of the Gaussian process emulator 
in Equation (8) for the two principal component outputs 
, 
, with four choices of the covariance function
| Covariance function |  |  |
|---|---|---|
| Squared exponential | 13.434 | 71.017 |
| Matérn 1 | –58.845 | 17.475 |
| Matérn 3 | –20.119 | 46.549 |
| Matérn 5 | –1.486 | 61.232 |
| Covariance function | | |
|---|---|---|
| Squared exponential | 13.434 | 71.017 |
| Matérn 1 | –58.845 | 17.475 |
| Matérn 3 | –20.119 | 46.549 |
| Matérn 5 | –1.486 | 61.232 |
All covariance functions use automatic relevance determination. The Matérn covariance functions have regularity parameters 1, 3, and 5 respectively.