| matern.kernel {PrevMap} | R Documentation |
Matern kernel
Description
This function computes values of the Matern kernel for given distances and parameters.
Usage
matern.kernel(u, rho, kappa)
Arguments
u |
a vector, matrix or array with values of the distances between pairs of data locations. |
rho |
value of the (re-parametrized) scale parameter; this corresponds to the re-parametrization |
kappa |
value of the shape parameter. |
Details
The Matern kernel is defined as:
K(u; \phi, \kappa) = \frac{\Gamma(\kappa + 1)^{1/2}\kappa^{(\kappa+1)/4}u^{(\kappa-1)/2}}{\pi^{1/2}\Gamma((\kappa+1)/2)\Gamma(\kappa)^{1/2}(2\kappa^{1/2}\phi)^{(\kappa+1)/2}}\mathcal{K}_{\kappa}(u/\phi), u > 0,
where \phi and \kappa are the scale and shape parameters, respectively, and \mathcal{K}_{\kappa}(.) is the modified Bessel function of the third kind of order \kappa. The family is valid for \phi > 0 and \kappa > 0.
Value
A vector matrix or array, according to the argument u, with the values of the Matern kernel function for the given distances.
Author(s)
Emanuele Giorgi e.giorgi@lancaster.ac.uk
Peter J. Diggle p.diggle@lancaster.ac.uk