matern_spacetime_categorical {GpGp}R Documentation

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

Parameterization

The covariance parameter vector is (variance, range, smoothness, category, nugget) = (σ2,α1,α2,ν,c2,τ2)(\sigma^2,\alpha_1,\alpha_2,\nu,c^2,\tau^2), and the covariance function is parameterized as

d=(xy2/α1+st2/α22)1/2 d = ( || x - y ||^2/\alpha_1 + |s-t|^2/\alpha_2^2 )^{1/2}

M(x,y)=σ221ν/Γ(ν)(d)νKν(d) 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 σ2τ2 \sigma^2 \tau^2 is added to the diagonal of the covariance matrix. The category variance c2c^2 is added if two observation from same category NOTE: the nugget is σ2τ2 \sigma^2 \tau^2 , not τ2 \tau^2 .


[Package GpGp version 0.5.0 Index]