nsCorr {BayesNSGP}

Calculate a nonstationary Matern correlation matrix

Description

nsCorr calculates a nonstationary correlation matrix for a fixed set of locations, based on vectors of the unique anisotropy parameters for each station. Since the correlation function uses a spatially-varying Mahalanobis distance, this function requires coordinate- specific distance matrices (see below). The function is coded as a nimbleFunction (see the nimble package) but can also be used as a regular R function.

Usage

nsCorr(dist1_sq, dist2_sq, dist12, Sigma11, Sigma22, Sigma12, nu, d)

Arguments

dist1_sq

N x N matrix; contains values of pairwise squared distances in the x-coordinate.

dist2_sq

N x N matrix; contains values of pairwise squared distances in the y-coordinate.

dist12

N x N matrix; contains values of pairwise signed cross- distances between the x- and y-coordinates. The sign of each element is important; see nsDist function for the details of this calculation. in the x-coordinate.

Sigma11

Vector of length N; contains the 1-1 element of the anisotropy process for each station.

Sigma22

Vector of length N; contains the 2-2 element of the anisotropy process for each station.

Sigma12

Vector of length N; contains the 1-2 element of the anisotropy process for each station.

nu

Scalar; Matern smoothness parameter. nu = 0.5 corresponds to the Exponential correlation; nu = Inf corresponds to the Gaussian correlation function.

d

Scalar; dimension of the spatial coordinates.

Value

A correlation matrix for a fixed set of stations and fixed parameter values.

Examples

# Generate some coordinates and parameters
coords <- cbind(runif(100),runif(100))
Sigma11 <- rep(1, 100) # Identity anisotropy process
Sigma22 <- rep(1, 100)
Sigma12 <- rep(0, 100)
nu <- 2
# Calculate distances
dist_list <- nsDist(coords)
# Calculate the correlation matrix
corMat <- nsCorr(dist_list$dist1_sq, dist_list$dist2_sq, dist_list$dist12,
                 Sigma11, Sigma22, Sigma12, nu, ncol(coords))