spLMPredictJoint: Returns posterior predictive sample from spLM object

Description

The function spLMPredictJoint collects posterior predictive samples for a set of new locations given a spLM object from the spBayes package.

Usage

spLMPredictJoint(sp.obj, pred.coords, pred.covars, start = 1, 
    end = nrow(sp.obj$p.theta.samples), thin = 1, verbose = TRUE, n.report = 100, 
    noisy = FALSE, method = "eigen")

Arguments

sp.obj

An spLM object returned by the spLM function in the spBayes package.

pred.coords

An $np \times 2$ matrix of $np$ prediction location coordinates in $R^2$ (e.g., easting and northing). The first column is assumed to be easting coordinates and the second column northing coordinates.

pred.covars

An $n \times p$ matrix of covariates matrix associated with the new locations.

start

Specifies the first sample included in the composition sampling.

end

Specifies the last sample included in the composition. The default is to use all posterior samples in sp.obj.

thin

A sample thinning factor. The default of 1 considers all samples between start and end. For example, if thin = 10 then 1 in 10 samples are considered between start and

verbose

If TRUE, model specification and progress of the sampler is printed to the screen. Otherwise, nothing is printed to the screen.

n.report

The interval to report sampling progress.

noisy

If TRUE, then the posterior sample for the response is for the signal + error noise. The default, FALSE, assumes the user wants the error-free process.

method

Method used to decompose covariance matrix. Options are "chol", "eigen", and "svd" for the Cholesky, Eigen, and singular value decomposition approaches, respectively.

Value

The function returns a $np \times B$ matrix of posterior predictive samples, where B is the number of posterior samples. The class is jointPredicitveSample.

Details

This function samples from the joint posterior predictive distribution of a Bayesian spatial linear model. Specifically, it is intended to be similar to the spPredict function in the spBayes except that it samples from the joint distribution instead of the marginal distribution. However, it will only work for spLM objects and should have the same limitations as the spLM and spPredict functions. Note that the spRecover function is called internally to recover the posterior samples form the posterior distribution of the spatial model.

Examples

Run this code

# Set parameters
n <- 100
np <- 12
n.samples <- 10
burnin.start <- .5 * n.samples + 1
sigmasq <- 1
tausq <- 0.0
phi <- 1
cov.model <- "exponential"
n.report <- 5

# Generate coordinates
coords <- matrix(runif(2 * n), ncol = 2); 
pcoords <- as.matrix(expand.grid(seq(0, 1, len = 12), seq(0, 1, len = 12)))
  
# Construct design matrices
X <- as.matrix(cbind(1, coords))
Xp <- cbind(1, pcoords)

# Specify priors
starting <- list("phi" = phi, "sigma.sq"= sigmasq, "tau.sq" = tausq)
tuning <- list("phi"=0.1, "sigma.sq"=0.1, "tau.sq"=0.1)
priors.1 <- list("beta.Norm"=list(c(1, 2, 1), diag(100, 3)),
                     "phi.Unif"=c(0.00001, 10), "sigma.sq.IG"=c(1, 1))

# Generate data
B <- rnorm(3, c(1, 2, 1), sd = 10)
phi <- runif(1, 0, 10)
sigmasq <- 1/rgamma(1, 1, 1)
V <- simple.cov.sp(D = dist1(coords), cov.model, c(sigmasq, 1/phi), error.var = tausq, 
	smoothness = nu, finescale.var = 0)
y <- X %*% B + rmvnorm(1, rep(0, n), V) + rnorm(n, 0, sqrt(tausq))

# Create spLM object
library(spBayes)
m1 <- spBayes::spLM(y ~ X - 1, coords = coords, starting = starting,
	tuning = tuning, priors = priors.1, cov.model = cov.model,
	n.samples = n.samples, verbose = FALSE, n.report = n.report)

# Sample from joint posterior predictive distribution
y1 <- spLMPredictJoint(m1, pred.coords = pcoords, pred.covars = Xp, 
	start = burnin.start, verbose = FALSE, method = "chol")