Matern52.Kernel {rkriging}

Matern(5/2) Kernel

Description

This function specifies the Matern kernel with smoothness parameter \nu=5/2.

Usage

Matern52.Kernel(lengthscale)

Arguments

lengthscale

a vector for the positive length scale parameters

Details

The Matern(5/2) kernel is given by

k(r)=(1+\sqrt{5}r+5r^2/3)\exp(-\sqrt{5}r),

where

r(x,x^{\prime})=\sqrt{\sum_{i=1}^{p}\left(\frac{x_{i}-x_{i}^{\prime}}{l_{i}}\right)^2}

is the euclidean distance between x and x^{\prime} weighted by the length scale parameters l_{i}'s.

Value

A Matern(5/2) Kernel Class Object.

Author(s)

Chaofan Huang and V. Roshan Joseph

References

Duvenaud, D. (2014). The kernel cookbook: Advice on covariance functions.

Rasmussen, C. E. & Williams, C. K. (2006). Gaussian Processes for Machine Learning. The MIT Press.

See Also

Matern.Kernel, Get.Kernel, Evaluate.Kernel.

Examples

n <- 5
p <- 3
X <- matrix(rnorm(n*p), ncol=p)
lengthscale <- c(1:p)

# approach 1
kernel <- Matern52.Kernel(lengthscale)
Evaluate.Kernel(kernel, X)

# approach 2
kernel <- Get.Kernel(lengthscale, type="Matern52")
Evaluate.Kernel(kernel, X)