matern_spacetime_categorical: Space-Time Matern covariance function with random effects for...

Description Usage Arguments Value Functions Parameterization

View source: R/RcppExports.R

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

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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) = (σ^2,α_1,α_2,ν,c^2,τ^2), and the covariance function is parameterized as

d = ( || x - y ||^2/α_1 + |s-t|^2/α_2^2 )^{1/2}

M(x,y) = σ^2 2^{1-ν}/Γ(ν) (d)^ν K_ν(d)

(x,s) and (y,t) are the space-time locations of a pair of observations. The nugget value σ^2 τ^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 σ^2 τ^2 , not τ^2 .


GpGp documentation built on June 10, 2021, 1:07 a.m.