Table 1.

Univariate synthetic data analysis parameter estimates and computing time in minutes for NNGP and full GP models. Parameter posterior summary 50 (2.5, 97.5) percentiles.

		NNGP (𝒮 ≠ 𝒯)		NNGP (𝒮 = 𝒯)
	True	m = 10, k = 2000	m = 20, k = 2000	m = 10	m = 20
β0	1	0.99 (0.71, 1.48)	1.02 (0.73, 1.49)	1.00 (0.62, 1.31)	1.03 (0.65, 1.34)
β1	5	5.00 (4.98, 5.03)	5.01 (4.98, 5.03)	5.01 (4.99, 5.03)	5.01 (4.99, 5.03)
σ2	1	1.09 (0.89, 1.49)	1.04 (0.85, 1.40)	0.96 (0.78, 1.23)	0.94 (0.77, 1.20)
τ2	0.1	0.07 (0.04, 0.10)	0.07 (0.04, 0.10)	0.10 (0.08, 0.13)	0.10 (0.08, 0.13)
φ	12	11.81 (8.18, 15.02)	12.21 (8.83, 15.62)	12.93 (9.70, 16.77)	13.36 (9.99, 17.15)
pD	—	1491.08	1478.61	1243.32	1249.57
DIC	—	1856.85	1901.57	2390.65	2377.51
G	—	33.67	35.68	77.84	76.40
P	—	253.03	259.13	340.40	337.88
D	—	286.70	294.82	418.24	414.28
RMSPE	—	1.22	1.22	1.2	1.2
95% CI cover %	—	97.2	97.2	97.6	97.6
95% CI width	—	2.19	2.18	2.13	2.12
Time	—	14.2	47.08	9.98	33.5
	True	Predictive process 64 knots	Full Gaussian process
β0	1	1.30 (0.54, 2.03)	1.03 (0.69, 1.34)
β1	5	5.03 (4.99, 5.06)	5.01 (4.99, 5.03)
σ2	1	1.29 (0.96, 2.00)	0.94 (0.76, 1.23)
τ2	0.1	0.08 (0.04, 0.13)	0.10 (0.08, 0.12)
φ	12	5.61 (3.48, 8.09)	13.52 (9.92, 17.50)
pD	—	1258.27	1260.68
DIC	—	13677.97	2364.80
G	—	1075.63	74.80
P	—	200.39	333.27
D	—	1276.03	408.08
RMSPE	—	1.68	1.2
95% CI cover %	—	95.6	97.6
95% CI width	—	2.97	2.12
Time	—	43.36	560.31