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 UU denote the nn by mm matrix of the distances between the nn observed coordinates and mm pre-defined spatial knots. This function computes the following quantity

1ni=1nj=1mK(uij;ϕ,κ)2,\frac{1}{n}\sum_{i=1}^n \sum_{j=1}^m K(u_{ij}; \phi, \kappa)^2,

where K(.;ϕ,κ)K(.; \phi, \kappa) is the Matern kernel (see matern.kernel) and uiju_{ij} is the distance between the ii-th sampled location and the jj-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

See Also

matern.kernel, pdist.


[Package PrevMap version 1.5.4 Index]