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, freq.max = NULL)

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.

freq.max

The maximum allowed harmonic order. Current default 40, to be changed to a dynamic choice based on error bounds.

Details

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

S(w) = \frac{1}{(2\pi)^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) = \frac{2k+1}{4\pi (\kappa^4 + 2 \kappa^2 \cos(\pi \theta) k(k+1) + k^2(k+1)^2)^{(\nu + 1)/2}}

Author(s)

Finn Lindgren finn.lindgren@gmail.com

[Package INLA version 25.10.19 Index]