matern_spheretime_warp {GpGp}

Deformed Matern covariance function on sphere

Description

From a matrix of longitudes, latitudes, times, and a vector covariance parameters of the form (variance, range_1, range_2, smoothness, nugget, <5 warping parameters>), return the square matrix of all pairwise covariances.

Usage

matern_spheretime_warp(covparms, lonlattime)

d_matern_spheretime_warp(covparms, lonlattime)

Arguments

covparms

A vector with covariance parameters in the form (variance, range_1, range_2, smoothness, nugget, <5 warping parameters>). range_1 is a spatial range parameter that assumes that the sphere has radius 1 (units are radians). range_2 is a temporal range parameter.

lonlattime

A matrix with n rows and three columns: longitudes in (-180,180), latitudes in (-90,90), and times. Each row of lonlattime describes a point on the sphere x time.

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_spheretime_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 matern_spacetime. The function does not do temporal warping.