cov_gen {hetGP}

Correlation function of selected type, supporting both isotropic and product forms

Description

Correlation function of selected type, supporting both isotropic and product forms

Usage

cov_gen(X1, X2 = NULL, theta, type = c("Gaussian", "Matern5_2", "Matern3_2"))

Arguments

X1

matrix of design locations, one point per row

X2

matrix of design locations if correlation is calculated between X1 and X2 (otherwise calculated between X1 and itself)

theta

vector of lengthscale parameters (either of size one if isotropic or of size d if anisotropic)

type

one of "Gaussian", "Matern5_2", "Matern3_2"

Details

Definition of univariate correlation function and hyperparameters:

• "Gaussian": c(x, y) = exp(-(x-y)^2/theta)

• "Matern5_2": c(x, y) = (1+sqrt(5)/theta * abs(x-y) + 5/(3*theta^2)(x-y)^2) * exp(-sqrt(5)*abs(x-y)/theta)

• "Matern3_2": c(x, y) = (1+sqrt(3)/theta * abs(x-y)) * exp(-sqrt(3)*abs(x-y)/theta)

Multivariate correlations are product of univariate ones.