R: Numerical evaluation of Matern and related covariance...

inla.matern.cov {INLA}

R Documentation

Numerical evaluation of Matern and related covariance functions.

Description

Calculates covariance and correlation functions for Matern models and related oscillating SPDE models, on R^d and on the sphere, S^2.

Usage

inla.matern.cov(
  nu,
  kappa,
  x,
  d = 1,
  corr = FALSE,
  norm.corr = FALSE,
  theta,
  epsilon = 1e-08
)

inla.matern.cov.s2(nu, kappa, x, norm.corr = FALSE, theta = 0)

Arguments

`nu`	The Matern smoothness parameter.
`kappa`	The spatial scale parameter.
`x`	Distance values.
`d`	Space dimension; the domain is R^d.
`corr`	If `TRUE`, calculate correlations, otherwise calculate covariances. Only used for pure Matern models (i.e. with theta=0).
`norm.corr`	If `TRUE`, normalise by the estimated variance, giving approximate correlations.
`theta`	Oscillation strength parameter.
`epsilon`	Tolerance for detecting points close to distance zero.

Details

On R^d, the models are defined by the spectral density given by

S(w) = 1 / ( (2π)^d * (kappa^4 + 2 kappa^2 * cos(pi * theta) * |w|^2 + |w|^4)^((nu + d/2)/2) )

On S^2, the models are defined by the spectral coefficients

S(k) = (2k+1) / (4 pi (kappa^4 + 2 kappa^2 cos(pi theta) k(k+1) + k^2(k+1)^2)^((ν + 1)/2) )

Author(s)

Finn Lindgren finn.lindgren@gmail.com

[Package INLA version 21.06.11 Index]