matern_spacetime_categorical {GpGp}

Space-Time Matern covariance function with random effects for categories

Description

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

Usage

matern_spacetime_categorical(covparms, locs)

d_matern_spacetime_categorical(covparms, locs)

Arguments

covparms

A vector with covariance parameters in the form (variance, spatial range, temporal range, smoothness, category, 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_spacetime_categorical(): Derivatives of isotropic Matern covariance

Parameterization

The covariance parameter vector is (variance, range, smoothness, category, nugget) = (\sigma^2,\alpha_1,\alpha_2,\nu,c^2,\tau^2), and the covariance function is parameterized as

d = ( || x - y ||^2/\alpha_1 + |s-t|^2/\alpha_2^2 )^{1/2}

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

(x,s) and (y,t) are the space-time locations of a pair of observations. The nugget value \sigma^2 \tau^2 is added to the diagonal of the covariance matrix. The category variance c^2 is added if two observation from same category NOTE: the nugget is \sigma^2 \tau^2 , not \tau^2 .