cWhittleMatern {INLAspacetime} | R Documentation |
Computes the Whittle-Matern correlation function.
Description
This computes the correlation function as derived in Matern model, see Matern (1960) eq. (2.4.7). For nu=1, see Whittle (1954) eq. (68). For the limiting case of nu=0, see Besag (1981) eq. (14-15).
Usage
cWhittleMatern(x, range, nu, kappa = sqrt(8 * nu)/range)
Arguments
x |
distance. |
range |
practical range (our prefered parametrization) given as range = sqrt(8 * nu) / kappa, where kappa is the scale parameter in the specialized references. |
nu |
process smoothness parameter. |
kappa |
scale parameter, commonly considered in the specialized literature. |
Value
the correlation.
Details
Whittle, P. (1954) On Stationary Processes in the Plane. Biometrika, Vol. 41, No. 3/4, pp. 434-449. http://www.jstor.org/stable/2332724
Matern, B. (1960) Spatial Variation: Stochastic models and their application to some problems in forest surveys and other sampling investigations. PhD Thesis.
Besag, J. (1981) On a System of Two-Dimensional Recurrence Equations. JRSS-B, Vol. 43 No. 3, pp. 302-309. https://www.jstor.org/stable/2984940
Examples
plot(function(x) cWhittleMatern(x, 1, 5),
bty = "n", las = 1,
xlab = "Distance", ylab = "Correlation"
)
plot(function(x) cWhittleMatern(x, 1, 1), add = TRUE, lty = 2)
plot(function(x) cWhittleMatern(x, 1, 0.5), add = TRUE, lty = 3)
abline(h = 0.139, lty = 3, col = gray(0.5, 0.5))