matern.kernel: Matern kernel

In PrevMap: Geostatistical Modelling of Spatially Referenced Prevalence Data

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 rho = 2*sqrt(kappa)*phi.
kappa	value of the shape parameter.

Details

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.

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-mail]

Peter J. Diggle [e-mail]

PrevMap documentation built on Oct. 7, 2021, 5:07 p.m.