matern_sphere {GpGp}

Isotropic Matern covariance function on sphere

Description

From a matrix of longitudes and latitudes and a vector covariance parameters of the form (variance, range, smoothness, nugget), return the square matrix of all pairwise covariances.

Usage

matern_sphere(covparms, lonlat)

d_matern_sphere(covparms, lonlat)

Arguments

covparms

A vector with covariance parameters in the form (variance, range, smoothness, nugget). Range parameter assumes that the sphere has radius 1 (units are radians).

lonlat

A matrix with n rows and one column with longitudes in (-180,180) and one column of latitudes in (-90,90). Each row of lonlat describes a point on the sphere.

Value

A matrix with n rows and n columns, with the i,j entry containing the covariance between observations at lonlat[i,] and lonlat[j,].

Functions

• d_matern_sphere(): Derivatives with respect to parameters

Matern on Sphere Domain

The function first calculates the (x,y,z) 3D coordinates, and then inputs the resulting locations into matern_isotropic. 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.