matern45_scaledim: Matern covariance function, smoothess = 3.5, different range...

In joeguinness/GpGp: Fast Gaussian Process Computation Using Vecchia's Approximation

Matern covariance function, smoothess = 3.5, different range parameter for each dimension

Description

From a matrix of locations and covariance parameters of the form (variance, range_1, ..., range_d, nugget), return the square matrix of all pairwise covariances.

Usage

matern45_scaledim(covparms, locs)

Arguments

covparms	A vector with covariance parameters in the form (variance, range_1, ..., range_d, nugget)
locs	A matrix with n rows and d columns. Each row of locs is a point in R^d.

Value

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

Parameterization

The covariance parameter vector is (variance, range_1, ..., range_d, nugget). The covariance function is parameterized as

M(x,y) = \sigma^2 ( \sum_{j=0}^4 c_j || D^{-1}(x - y) ||^j ) exp( - || D^{-1}(x - y) || )

where c_0 = 1, c_1 = 1, c_2 = 3/7, c_3 = 2/21, c_4 = 1/105. where D is a diagonal matrix with (range_1, ..., range_d) on the diagonals. The nugget value \sigma^2 \tau^2 is added to the diagonal of the covariance matrix. NOTE: the nugget is \sigma^2 \tau^2 , not \tau^2 .

joeguinness/GpGp documentation built on Feb. 22, 2024, 9:43 a.m.