# nsCorr: Calculate a nonstationary Matern correlation matrix In BayesNSGP: Bayesian Analysis of Non-Stationary Gaussian Process Models

## 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

 `1` ```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

 ``` 1 2 3 4 5 6 7 8 9 10 11``` ```# 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)) ```

BayesNSGP documentation built on Jan. 9, 2022, 9:07 a.m.