exponential_sphere_warp {GpGp}

Deformed exponential covariance function on sphere

Description

From a matrix of longitudes and latitudes and a vector covariance parameters of the form (variance, range, nugget, <5 warping parameters>), return the square matrix of all pairwise covariances.

Usage

exponential_sphere_warp(covparms, lonlat)

d_exponential_sphere_warp(covparms, lonlat)

Arguments

covparms

A vector with covariance parameters in the form (variance, range, nugget, <5 warping parameters>). 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_exponential_sphere_warp(): Derivatives with respect to parameters

Warpings

The function first calculates the (x,y,z) 3D coordinates, and then "warps" the locations to (x,y,z) + \Phi(x,y,z), where \Phi is a warping function composed of gradients of spherical harmonic functions of degree 2. See Guinness (2019, "Gaussian Process Learning via Fisher Scoring of Vecchia's Approximation") for details. The warped locations are input into exponential_isotropic.