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

Description Usage Arguments Details Author(s)

Description

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

Usage

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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


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