inla.matern.cov: Numerical evaluation of Matern and related covariance...

In inbo/INLA: Full Bayesian Analysis of Latent Gaussian Models using Integrated Nested Laplace Approximations

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 [e-mail]

inbo/INLA documentation built on Dec. 6, 2019, 9:51 a.m.