predict.NNGP {spNNGP}

Function for prediction at new locations using NNGP models.

Description

The function predict collects posterior predictive samples for a set of new locations given an object of class NNGP.

Usage

## S3 method for class 'NNGP'
predict(object, X.0, coords.0, sub.sample,
        n.omp.threads = 1, verbose=TRUE, n.report=100, ...)

Arguments

object

an object of class NNGP.

X.0

the design matrix for prediction locations. An intercept should be provided in the first column if one is specified in sp.obj model.

coords.0

the spatial coordinates corresponding to X.0.

sub.sample

an optional list that specifies the samples to included in the composition sampling a non-Conjugate model. Valid tags are start, end, and thin. Given the value associated with the tags, the sample subset is selected using seq(as.integer(start), as.integer(end), by=as.integer(thin)). The default values are start=floor(0.5*n.samples), end=n.samples and thin=1.

n.omp.threads

a positive integer indicating the number of threads to use for SMP parallel processing. The package must be compiled for OpenMP support. For most Intel-based machines, we recommend setting n.omp.threads up to the number of hyperthreaded cores. Note, n.omp.threads > 1 might not work on some systems.

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.

...

currently no additional arguments.

Value

An object of class predict.NNGP which is a list comprising:

p.y.0

a matrix that holds the response variable posterior predictive samples where rows are locations corresponding to coords.0 and columns are samples.

p.w.0

a matrix that holds the random effect posterior predictive samples where rows are locations corresponding to coords.0 and columns are samples. This is only returned if the input class has method = "latent".

run.time

execution time reported using proc.time().

Author(s)

Andrew O. Finley [e-mail],
Abhirup Datta [e-mail],
Sudipto Banerjee [e-mail]

References

Datta, A., S. Banerjee, A.O. Finley, and A.E. Gelfand. (2016) Hierarchical Nearest-Neighbor Gaussian process models for large geostatistical datasets. Journal of the American Statistical Association, doi: 10.1080/01621459.2015.1044091.

Finley, A.O., A. Datta, B.D. Cook, D.C. Morton, H.E. Andersen, and S. Banerjee. (2019) Efficient algorithms for Bayesian Nearest Neighbor Gaussian Processes. Jurnal of Computational and Graphical Statistics, doi: 10.1080/10618600.2018.1537924.

Examples

rmvn <- function(n, mu=0, V = matrix(1)){
  p <- length(mu)
  if(any(is.na(match(dim(V),p))))
    stop("Dimension problem!")
  D <- chol(V)
  t(matrix(rnorm(n*p), ncol=p)%*%D + rep(mu,rep(n,p)))
}

##Make some data
set.seed(1)
n <- 100
coords <- cbind(runif(n,0,1), runif(n,0,1))

x <- cbind(1, rnorm(n))

B <- as.matrix(c(1,5))

sigma.sq <- 5
tau.sq <- 1
phi <- 3/0.5

D <- as.matrix(dist(coords))
R <- exp(-phi*D)
w <- rmvn(1, rep(0,n), sigma.sq*R)
y <- rnorm(n, x%*%B + w, sqrt(tau.sq))

ho <- sample(1:n, 50)

y.ho <- y[ho]
x.ho <- x[ho,,drop=FALSE]
w.ho <- w[ho]
coords.ho <- coords[ho,]

y <- y[-ho]
x <- x[-ho,,drop=FALSE]
w <- w[-ho,,drop=FALSE]
coords <- coords[-ho,]

##Fit a Response, Latent, and Conjugate NNGP model
n.samples <- 500

starting <- list("phi"=phi, "sigma.sq"=5, "tau.sq"=1)

tuning <- list("phi"=0.5, "sigma.sq"=0.5, "tau.sq"=0.5)

priors <- list("phi.Unif"=c(3/1, 3/0.01), "sigma.sq.IG"=c(2, 5), "tau.sq.IG"=c(2, 1))

cov.model <- "exponential"

n.report <- 500

##Latent
m.s <- spNNGP(y~x-1, coords=coords, starting=starting, method="latent", n.neighbors=10,
              tuning=tuning, priors=priors, cov.model=cov.model,
              n.samples=n.samples, n.omp.threads=1, n.report=n.report)

p.s <- predict(m.s, X.0 = x.ho, coords.0 = coords.ho, n.omp.threads=1)

plot(apply(p.s$p.w.0, 1, mean), w.ho)
plot(apply(p.s$p.y.0, 1, mean), y.ho)

##Response
m.r <- spNNGP(y~x-1, coords=coords, starting=starting, method="response", n.neighbors=10,
              tuning=tuning, priors=priors, cov.model=cov.model,
              n.samples=n.samples, n.omp.threads=1, n.report=n.report)

p.r <- predict(m.r, X.0 = x.ho, coords.0 = coords.ho, n.omp.threads=1)

points(apply(p.r$p.y.0, 1, mean), y.ho, pch=19, col="blue")

##Conjugate
theta.alpha <- c(phi, tau.sq/sigma.sq)
names(theta.alpha) <- c("phi", "alpha")

m.c <- spConjNNGP(y~x-1, coords=coords, n.neighbors=10,
                  theta.alpha=theta.alpha, sigma.sq.IG=c(2, sigma.sq),
                  cov.model=cov.model, n.omp.threads=1)

p.c <- predict(m.c, X.0 = x.ho, coords.0 = coords.ho, n.omp.threads=1)

points(p.c$y.0.hat, y.ho, pch=19, col="orange")