matern45_isotropic: Isotropic Matern covariance function, smoothness = 4.5

In GpGp: Fast Gaussian Process Computation Using Vecchia's Approximation

Description

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

Usage

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,].

Parameterization

The covariance parameter vector is (variance, range, nugget) = (σ^2,α,τ^2), and the covariance function is parameterized as

M(x,y) = σ^2 ( ∑_{j=0}^4 c_j || x - y ||^j/ α^j ) exp( - || x - y ||/ α )

where c_0 = 1, c_1 = 1, c_2 = 3/7, c_3 = 2/21, c_4 = 1/105. The nugget value σ^2 τ^2 is added to the diagonal of the covariance matrix. NOTE: the nugget is σ^2 τ^2 , not τ^2 .

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