exponential_nonstat_var: Isotropic exponential covariance function, nonstationary...

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

Isotropic exponential covariance function, nonstationary variances

Description

From a matrix of locations and covariance parameters of the form (variance, range, nugget, <nonstat variance parameters>), return the square matrix of all pairwise covariances.

Usage

exponential_nonstat_var(covparms, Z)

d_exponential_nonstat_var(covparms, Z)

Arguments

covparms	A vector with covariance parameters in the form (variance, range, nugget, <nonstat variance parameters>). The number of nonstationary variance parameters should equal p.
Z	A matrix with n rows and 2 columns for spatial locations + p columns describing spatial basis functions. Each row of locs gives a point in R^2 (two dimensions only!) + the value of p spatial basis functions.

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,].

Functions

• d_exponential_nonstat_var(): Derivatives with respect to parameters

Parameterization

This covariance function multiplies the isotropic exponential covariance by a nonstationary variance function. The form of the covariance is

C(x,y) = exp( \phi(x) + \phi(y) ) M(x,y)

where M(x,y) is the isotropic exponential covariance, and

\phi(x) = c_1 \phi_1(x) + ... + c_p \phi_p(x)

where \phi_1,...,\phi_p are the spatial basis functions contained in the last p columns of Z, and c_1,...,c_p are the nonstationary variance parameters.

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