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 26.08.22 Index]