| adjust.sigma2 {PrevMap} | R Documentation |
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. |
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.
Value
A value corresponding to the adjustment factor for sigma2.
Author(s)
Emanuele Giorgi e.giorgi@lancaster.ac.uk
Peter J. Diggle p.diggle@lancaster.ac.uk