Description Usage Arguments Value Functions Covariances on spheres
From a matrix of longitudes, latitudes, and times, and a vector covariance parameters of the form (variance, range_1, range_2, smoothness, nugget), return the square matrix of all pairwise covariances.
1 2 3 | matern_spheretime(covparms, lonlattime)
d_matern_spheretime(covparms, lonlattime)
|
covparms |
A vector with covariance parameters in the form (variance, range_1, range_2, smoothness, nugget), where range_1 is a spatial range (assuming sphere of radius 1), and range_2 is a temporal range. |
lonlattime |
A matrix with |
A matrix with n
rows and n
columns, with the i,j entry
containing the covariance between observations at lonlattime[i,]
and
lonlattime[j,]
.
d_matern_spheretime
: Derivatives with respect to parameters
The function first calculates the (x,y,z) 3D coordinates, and then inputs
the resulting locations into matern_spacetime
. This means that we construct
covariances on the sphere by embedding the sphere in a 3D space. There has been some
concern expressed in the literature that such embeddings may produce distortions.
The source and nature of such distortions has never been articulated,
and to date, no such distortions have been documented. Guinness and
Fuentes (2016) argue that 3D embeddings produce reasonable models for data on spheres.
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