This function computes the multiplicative constant used to adjust the value of sigma2 in the low-rank approximation of a Gaussian process.
adjust.sigma2(knots.dist, phi, kappa)a matrix of the distances between the observed coordinates and the spatial knots.
scale parameter of the Matern covariance function.
shape parameter of the Matern covariance function.
A value corresponding to the adjustment factor for sigma2.
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.