Description Usage Arguments Details Value Author(s)
This function computes values of the Matern kernel for given distances and parameters.
1 | matern.kernel(u, rho, kappa)
|
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. |
The Matern kernel is defined as:
K(u; φ, κ) = \frac{Γ(κ + 1)^{1/2}κ^{(κ+1)/4}u^{(κ-1)/2}}{π^{1/2}Γ((κ+1)/2)Γ(κ)^{1/2}(2κ^{1/2}φ)^{(κ+1)/2}}\mathcal{K}_{κ}(u/φ), u > 0,
where φ and κ are the scale and shape parameters, respectively, and \mathcal{K}_{κ}(.) is the modified Bessel function of the third kind of order κ. The family is valid for φ > 0 and κ > 0.
A vector matrix or array, according to the argument u, with the values of the Matern kernel function for the given distances.
Emanuele Giorgi e.giorgi@lancaster.ac.uk
Peter J. Diggle p.diggle@lancaster.ac.uk
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