PrevMap (version 1.5.3)

adjust.sigma2: Adjustment factor for the variance of the convolution of Gaussian noise

Description

This function computes the multiplicative constant used to adjust the value of sigma2 in the low-rank approximation of a Gaussian process.

Usage

adjust.sigma2(knots.dist, phi, kappa)

Arguments

knots.dist

a matrix of the distances between the observed coordinates and the spatial knots.

phi

scale parameter of the Matern covariance function.

kappa

shape parameter of the Matern covariance function.

Value

A value corresponding to the adjustment factor for sigma2.

Details

Let \(U\) denote the \(n\) by \(m\) matrix of the distances between the \(n\) observed coordinates and \(m\) pre-defined spatial knots. This function computes the following quantity $$\frac{1}{n}\sum_{i=1}^n \sum_{j=1}^m K(u_{ij}; \phi, \kappa)^2,$$ where \(K(.; \phi, \kappa)\) is the Matern kernel (see matern.kernel) and \(u_{ij}\) is the distance between the \(i\)-th sampled location and the \(j\)-th spatial knot.

See Also

matern.kernel, pdist.

Examples

# NOT RUN {
set.seed(1234)
# Observed coordinates
n <- 100
coords <- cbind(runif(n),runif(n))

# Spatial knots
knots <- expand.grid(seq(-0.2,1.2,length=5),seq(-0.2,1.2,length=5))

# Distance matrix
knots.dist <- as.matrix(pdist(coords,knots))

adjust.sigma2(knots.dist,0.1,2)

# }