Table 3.

Parameter estimates (medians and 95% posterior credible intervals) for the Matérn correlation model under different metrics

Parameter	Geodetic	Naive Euclidean	Chordal
Intercept	1.087 (0.789, 1.410)	1.031 (0.664, 1.447)	1.015 (0.707, 1.308)
Elevation	−0.430 (−0.533, −0.336)	−0.421 (−0.523, −0.322)	−0.422 (−0.515, −0.329)
${\sigma }^2$	0.171 (0.043, 1.539)	0.097 (0.033, 0.505)	0.093 (0.034, 0.435)
$\psi$	7.47 × 10−3 (4.79 × 10−3, 51.18 × 10−3)	4.26 × 10−3 (2.27 × 10−3, 41.42 × 10−3)	7.63 × 10−3 (4.85 × 10−3, 54.51 × 10−3)
$\nu$	0.770 (0.213, 1.413)	0.819 (0.227, 1.426)	0.742 (0.199, 1.402)
Range	273.7 (39.1, 426.7)	477.3 (48.2, 895.6)	268.7 (36.8, 422.8)
${\tau }^2$	0.008 (0.003, 0.019)	0.007 (0.003, 0.018)	0.008 (0.003, 0.017)
Parameter	Mercator	Sinusoidal	Centroid-based
Intercept	1.015 (0.332, 1.597)	1.014 (0.377, 1.603)	1.088 (0.735, 1.511)
Elevation	−0.426 (−0.527, −0.333)	−0.431 (−0.530, −0.330)	−0.427 (−0.527, −0.324)
${\sigma }^2$	0.111 (0.033, 0.363)	0.106 (0.031, 0.321)	0.102 (0.035, 0.684)
$\psi$	4.01 × 10−3 (1.98 × 10−3, 40.01 × 10−3)	7.61 × 10−3 (4.89 × 10−3, 55.08 × 10−3)	7.57 × 10−3 (4.74 × 10−3, 53.22 × 10−3)
$\nu$	0.843 (0.331, 1.533)	0.767 (0.225, 1.441)	0.791 (0.212, 1.421)
Range	506.9 (51.7, 1025.5)	270.3 (38.9, 418.0)	269.5 (37.4, 430.2)
${\tau }^2$	0.011 (0.004, 0.024)	0.009 (0.004, 0.024)	0.007 (0.003, 0.017)