spBayes (version 0.2-4)

mvCovInvLogDet: Utility function for constructing multivariate predictive process covariance matrices

Description

Utility function for constructing multivariate predictive process covariance matrices

Usage

mvCovInvLogDet(coords, knots, cov.model, V,
                  Psi, theta, modified.pp=TRUE, SWM=TRUE, ...)

Arguments

coords

a $n \times 2$ matrix of the observation coordinates in $R^2$ (e.g., easting and northing).

knots

a $m \times 2$ matrix of knot coordinates.

V

spatial cross-covariance matrix.

Psi

residual cross-covariance matrix.

theta

if cov.model is matern then theta is a vector of the multivariate spatial decays followed by the associated smoothness parameters; otherwise, theta is the spatial decays vector.

modified.pp

a logical value indicating if the modified predictive process should be used.

cov.model

a quoted key word that specifies the covariance function used to model the spatial dependence structure among the observations. Supported covariance model key words are: "exponential", "matern", "spherical"

SWM

a logical value indicating if the Sherman-Woodbury-Morrison equation should be used for computing the inverse (this is ignored if modified.pp is FALSE).

...

currently no additional arguments.

Value

• Returns the covariance matrix, log-determinant, and inverse.

Examples

set.seed(1)

n <- 100 ##number of coords
m <- 25  ##number of knots
q <- 5   ##number of response variables

coords <- cbind(runif(n),runif(n))
knots <- cbind(runif(m), runif(m))

theta <- c(rep(6,q),rep(0.5,q)) #phi and nu

A <- matrix(0,q,q)
A[lower.tri(A,TRUE)] <- rnorm(q*(q-1)/2+q)

V <- A%*%t(A)

P <- matrix(0,q,q)
P[lower.tri(A,TRUE)] <- rnorm(q*(q-1)/2+q)

Psi <- P%*%t(P)

tol <- 1.0e-8


##
##non bias-adjusted predictive process
##
c1 <- mvCovInvLogDet(coords=coords, knots=knots, cov.model="exponential",
                   V=V, Psi=Psi, theta=theta,
                   modified.pp=FALSE, SWM=FALSE)

if(max(abs(chol2inv(chol(c1$C)) - c1$C.inv)) > tol) stop("test-1 failed")
if(max(abs(2*sum(log(diag(chol(c1$C)))) - c1$log.det)) > tol)
stop("test-1 failed")


c2 <- mvCovInvLogDet(coords=coords, knots=knots, cov.model="matern",
                   V=V, Psi=Psi, theta=theta,
                   modified.pp=FALSE, SWM=FALSE)

if(max(abs(chol2inv(chol(c2$C)) - c2$C.inv)) > tol) stop("test-2 failed")
if(max(abs(2*sum(log(diag(chol(c2$C)))) - c2$log.det)) > tol)
stop("test-2 failed")

##
##bias-adjusted predictive process
##
c3 <- mvCovInvLogDet(coords=coords, knots=knots, cov.model="exponential",
                   V=V, Psi=Psi, theta=theta,
                   modified.pp=TRUE, SWM=FALSE)

if(max(abs(chol2inv(chol(c3$C)) - c3$C.inv)) > tol) stop("test-3 failed")
if(max(abs(2*sum(log(diag(chol(c3$C)))) - c3$log.det)) > tol)
stop("test-3 failed")


c4 <- mvCovInvLogDet(coords=coords, knots=knots, cov.model="matern",
                   V=V, Psi=Psi, theta=theta,
                   modified.pp=TRUE, SWM=FALSE)

if(max(abs(chol2inv(chol(c4$C)) - c4$C.inv)) > tol) stop("test-4 failed")
if(max(abs(2*sum(log(diag(chol(c4$C)))) - c4$log.det)) > tol)
stop("test-4 failed")

##
##non bias-adjusted predictive process using SWM
##
c5 <- mvCovInvLogDet(coords=coords, knots=knots, cov.model="exponential",
                   V=V, Psi=Psi, theta=theta,
                   modified.pp=FALSE, SWM=TRUE)

if(max(abs(chol2inv(chol(c5$C)) - c5$C.inv)) > tol) stop("test-5 failed")
if(max(abs(2*sum(log(diag(chol(c5$C)))) - c5$log.det)) > tol)
stop("test-5 failed")

c6 <- mvCovInvLogDet(coords=coords, knots=knots, cov.model="matern",
                   V=V, Psi=Psi, theta=theta,
                   modified.pp=FALSE, SWM=TRUE)

if(max(abs(chol2inv(chol(c6$C)) - c6$C.inv)) > tol) stop("test-6 failed")
if(max(abs(2*sum(log(diag(chol(c6$C)))) - c6$log.det)) > tol)
stop("test-6 failed")

##
##bias-adjusted predictive process using SWM
##
c7 <- mvCovInvLogDet(coords=coords, knots=knots, cov.model="exponential",
                   V=V, Psi=Psi, theta=theta,
                   modified.pp=TRUE, SWM=TRUE)

if(max(abs(chol2inv(chol(c7$C)) - c7$C.inv)) > tol) stop("test-7 failed")
if(max(abs(2*sum(log(diag(chol(c7$C)))) - c7$log.det)) > tol)
stop("test-7 failed")

c8 <- mvCovInvLogDet(coords=coords, knots=knots, cov.model="matern",
                   V=V, Psi=Psi, theta=theta,
                   modified.pp=TRUE, SWM=TRUE)

if(max(abs(chol2inv(chol(c8$C)) - c8$C.inv)) > tol) stop("test-8 failed")
if(max(abs(2*sum(log(diag(chol(c8$C)))) - c8$log.det)) > tol)
stop("test-8 failed")