SpatialTools: spLMPredictJoint – R documentation

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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 x 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 np x k 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 `end`.
`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.

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.

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.

Author(s)

Joshua French

Examples

# 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")

SpatialTools

Tools for Spatial Data Analysis

v1.0.4

GPL (>= 2)

Authors

Joshua French <joshua.french@ucdenver.edu>

Initial release