MaternCorr: Matern correlation function.

Description

A family of correlation function describing realizations of Gaussian spatial processes with different smoothnesses (i.e. either smooth or rugged surfaces). Also includes a scaling and a 'nugget' parameter.

Usage

"MaternCorr"(d, rho = 1, smoothness, nu = smoothness, Nugget = 0L)

Arguments

A distance, typically an Euclidean distance

rho

A scaling factor for distance. The 'range' considered in some formulations is the reciprocal of this scaling factor

smoothness

The smoothness parameter, >0. $\nu=0.5$ corresponds to the exponential correlation function, and the limit function when $\mu$ goes to $\infty$ is the squared exponential function (as in a Gaussian).

Same as smoothness

Nugget

(Following the jargon of Kriging) a parameter describing a discontinuous decrease in correlation at zero distance. Correlation will always be 1 at $d=0$, and from which it immediately drops to (1-Nugget)

Value

Details

The correlation at distance $d>0$ is $$(1-\textrm{Nugget}) \frac{(\rho d)^\nu K_\nu(\rho d)}{2^{(\nu - 1)} \Gamma(\nu)}$$ where $K_\nu$ is the besselK function of order $\nu$.

References

Stein, M.L. (1999) Statistical Interpolation of Spatial Data: Some Theory for Kriging. Springer, New York.

Examples

Run this code

## The Matérn function can be used in Euclidean spaces of any dimension:
set.seed(123)
randpts <- matrix(rnorm(20),nrow=5)
distMatrix <- as.matrix(proxy::dist(randpts))
MaternCorr(distMatrix,nu=2)

Run the code above in your browser using DataCamp Workspace