matern_isotropic {GpGp}

Isotropic Matern covariance function

Description

From a matrix of locations and covariance parameters of the form (variance, range, smoothness, nugget), return the square matrix of all pairwise covariances.

Usage

matern_isotropic(covparms, locs)

d_matern_isotropic(covparms, locs)

Arguments

covparms

A vector with covariance parameters in the form (variance, range, smoothness, nugget)

locs

A matrix with n rows and d columns. Each row of locs gives a point in R^d.

Value

A matrix with n rows and n columns, with the i,j entry containing the covariance between observations at locs[i,] and locs[j,].

Functions

• d_matern_isotropic(): Derivatives of isotropic Matern covariance

Parameterization

The covariance parameter vector is (variance, range, smoothness, nugget) = (\sigma^2,\alpha,\nu,\tau^2), and the covariance function is parameterized as

M(x,y) = \sigma^2 2^{1-\nu}/\Gamma(\nu) (|| x - y ||/\alpha )^\nu K_\nu(|| x - y ||/\alpha )

The nugget value \sigma^2 \tau^2 is added to the diagonal of the covariance matrix. NOTE: the nugget is \sigma^2 \tau^2 , not \tau^2 .