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

In barryrowlingson/PrevMap: Geostatistical Modelling of Spatially Referenced Prevalence Data

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.

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}∑_{i=1}^n ∑_{j=1}^m K(u_{ij}; φ, κ)^2,

where K(.; φ, κ) 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.

Value

A value corresponding to the adjustment factor for sigma2.

Author(s)

Emanuele Giorgi [e-mail]

Peter J. Diggle [e-mail]

See Also

matern.kernel, pdist.

Examples

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)

barryrowlingson/PrevMap documentation built on May 11, 2019, 6:24 p.m.