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

In andrewzm/INLA: Functions which allow to perform full Bayesian analysis of latent Gaussian models using Integrated Nested Laplace Approximaxion

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]

andrewzm/INLA documentation built on May 10, 2019, 11:12 a.m.