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

See Also

matern.kernel, pdist.


[Package PrevMap version 1.5.4 Index]