| matern_scaledim {GpGp} | R Documentation |
Matern covariance function, different range parameter for each dimension
Description
From a matrix of locations and covariance parameters of the form (variance, range_1, ..., range_d, smoothness, nugget), return the square matrix of all pairwise covariances.
Usage
matern_scaledim(covparms, locs)
d_matern_scaledim(covparms, locs)
Arguments
covparms |
A vector with covariance parameters in the form (variance, range_1, ..., range_d, smoothness, nugget) |
locs |
A matrix with |
Value
A matrix with n rows and n columns, with the i,j entry
containing the covariance between observations at locs[i,] and
locs[j,].
Functions
-
d_matern_scaledim(): Derivatives with respect to parameters
Parameterization
The covariance parameter vector is (variance, range_1, ..., range_d, smoothness, nugget). The covariance function is parameterized as
M(x,y) = \sigma^2 2^{1-\nu}/\Gamma(\nu) (|| D^{-1}(x - y) || )^\nu K_\nu(|| D^{-1}(x - y) || )
where D is a diagonal matrix with (range_1, ..., range_d) on the diagonals.
The nugget value \sigma^2 \tau^2 is added to the diagonal of the covariance matrix.
NOTE: the nugget is \sigma^2 \tau^2 , not \tau^2 .