matern_anisotropic3D_alt: Geometrically anisotropic Matern covariance function (three...
In GpGp: Fast Gaussian Process Computation Using Vecchia's Approximation

Description Usage Arguments Value Parameterization

From a matrix of locations and covariance parameters of the form (variance, B11, B12, B13, B22, B23, B33, smoothness, nugget), return the square matrix of all pairwise covariances.

1	matern_anisotropic3D_alt(covparms, locs)

`covparms`	A vector with covariance parameters in the form (variance, B11, B12, B13, B22, B23, B33, smoothness, nugget)
`locs`	A matrix with `n` rows and `3` columns. Each row of locs is a point in R^3.

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

The covariance parameter vector is (variance, B11, B12, B13, B22, B23, B33, smoothness, nugget) where B11, B12, B13, B22, B23, B33, transform the three coordinates as

u_1 = B11[ x_1 + B12 x_2 + (B13 + B12 B23) x_3]

u_2 = B22[ x_2 + B23 x_3]

u_3 = B33[ x_3 ]

NOTE: the u_1 transformation is different from previous versions of this function. NOTE: now (B13,B23) can be interpreted as a drift vector in space over time. Assuming x is transformed to u and y transformed to v, the covariances are

M(x,y) = σ^2 2^{1-ν}/Γ(ν) (|| u - v || )^ν K_ν(|| u - v ||)

The nugget value σ^2 τ^2 is added to the diagonal of the covariance matrix. NOTE: the nugget is σ^2 τ^2 , not τ^2 .

GpGp documentation built on June 10, 2021, 1:07 a.m.