nsCrosscorr {BayesNSGP}

Calculate a nonstationary Matern cross-correlation matrix

Description

nsCrosscorr calculates a nonstationary cross-correlation matrix between two fixed sets of locations (a prediction set with M locations, and the observed set with N 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

nsCrosscorr(
  Xdist1_sq,
  Xdist2_sq,
  Xdist12,
  Sigma11,
  Sigma22,
  Sigma12,
  PSigma11,
  PSigma22,
  PSigma12,
  nu,
  d
)

Arguments

Xdist1_sq

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

Xdist2_sq

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

Xdist12

M x N matrix; contains values of pairwise signed cross/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 observed location.

Sigma22

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

Sigma12

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

PSigma11

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

PSigma22

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

PSigma12

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

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 domain.

Value

A M x N cross-correlation matrix for two fixed sets 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)
Pcoords <- cbind(runif(200),runif(200))
PSigma11 <- rep(1, 200) # Identity anisotropy process
PSigma22 <- rep(1, 200)
PSigma12 <- rep(0, 200)
nu <- 2
# Calculate distances
Xdist_list <- nsCrossdist(coords, Pcoords)
# Calculate the correlation matrix
XcorMat <- nsCrosscorr(Xdist_list$dist1_sq, Xdist_list$dist2_sq, Xdist_list$dist12,
   Sigma11, Sigma22, Sigma12, PSigma11, PSigma22, PSigma12, nu, ncol(coords))