matern35_isotropic {GpGp}

Isotropic Matern covariance function, smoothness = 3.5

Description

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

Usage

matern35_isotropic(covparms, locs)

d_matern35_isotropic(covparms, locs)

d_matern45_isotropic(covparms, locs)

Arguments

covparms

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

locs

A matrix with n rows and d columns. Each row of locs is 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_matern35_isotropic(): Derivatives of isotropic matern covariance function with smoothness 3.5

• d_matern45_isotropic(): Derivatives of isotropic matern covariance function with smoothness 3.5

Parameterization

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

M(x,y) = \sigma^2 ( \sum_{j=0}^3 c_j || x - y ||^j/ \alpha^j ) exp( - || x - y ||/ \alpha )

where c_0 = 1, c_1 = 1, c_2 = 2/5, c_3 = 1/15. 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 .