Table 1.

Simulation study results. Values reported as the mean (standard error) over the S = 25 data sets. The three models fit to each data set are the stationary model (“Stationary”), covariate dependent covariance model (“CDC”), and the non-stationary kernel convolution model (“Kernel Con.”).

(a) MSE for the training observations
True M	x model	Cov model	Stationary	CDC	Kernel Con.
1	Linear	Expo	0.102 (0.001)	0.102 (0.001)	0.100 (0.001)
1	Linear	Matérn	0.118 (0.005)	0.107 (0.003)	0.149 (0.006)
2	Linear	Expo	0.501 (0.010)	0.106 (0.002)	0.124 (0.002)
2	Linear	Matérn	0.172 (0.007)	0.087 (0.001)	0.091 (0.001)
2	Periodic	Expo	0.698 (0.018)	0.106 (0.002)	0.682 (0.014)
2	Periodic	Matérn	0.101 (0.001)	0.087 (0.001)	0.105 (0.003)

(b) MSE for the testing observations
True M	x model	Cov model	Stationary	CDC	Kernel Con.
1	Linear	Expo	0.495 (0.007)	0.494 (0.007)	0.506 (0.008)
1	Linear	Matérn	0.638 (0.007)	0.638 (0.007)	0.642 (0.008)
2	Linear	Expo	0.753 (0.013)	0.721 (0.013)	0.765 (0.013)
2	Linear	Matérn	0.437 (0.012)	0.424 (0.013)	0.433 (0.012)
2	Periodic	Expo	0.835 (0.012)	0.738 (0.011)	0.835 (0.013)
2	Periodic	Matérn	0.620 (0.015)	0.469 (0.015)	0.727 (0.023)

(c) Coverage probabilities of 90% intervals for the testing observations
True M	x model	Cov model	Stationary	CDC	Kernel Con.
1	Linear	Expo	0.89 (0.01)	0.89 (0.01)	0.91 (0.01)
1	Linear	Matérn	0.89 (0.01)	0.90 (0.01)	0.88 (0.01)
2	Linear	Expo	0.68 (0.01)	0.88 (0.01)	0.86 (0.01)
2	Linear	Matérn	0.83 (0.01)	0.92 (0.01)	0.85 (0.01)
2	Periodic	Expo	0.51 (0.02)	0.89 (0.01)	0.52 (0.02)
2	Periodic	Matérn	0.91 (0.01)	0.91 (0.01)	0.78 (0.01)