BRISC_prediction {BRISC}

Function for performing prediction with BRISC

Description

The function BRISC_prediction performs fast prediction on a set of new locations with univariate spatial regression models using Nearest Neighbor Gaussian Processes (NNGP) (Datta et al., 2016). BRISC_prediction uses the parameter estimates from BRISC_estimation for the prediction. Some code blocks are borrowed from the R package: spNNGP: Spatial Regression Models for Large Datasets using Nearest Neighbor Gaussian Processes
https://CRAN.R-project.org/package=spNNGP .

Usage

BRISC_prediction(BRISC_Out, coords.0, X.0 = NULL, n_omp = 1,
                 verbose = TRUE, tol = 12)

Arguments

BRISC_Out

an object of class BRISC_Out, obtained as an output of
BRISC_estimation.

coords.0

the spatial coordinates corresponding to prediction locations. Its structure should be same as that of coords in BRISC_estimation. Default value is a column of 1 to adjust for the mean (intercept).

X.0

the covariates for prediction locations. Its Structure should be identical (including intercept) with that of covariates provided for estimation purpose in BRISC_estimation.

n_omp

number of threads to be used, value can be more than 1 if source code is compiled with OpenMP support. Default is 1.

verbose

if TRUE, model specifications along with information regarding OpenMP support and progress of the algorithm is printed to the screen. Otherwise, nothing is printed to the screen. Default value is TRUE.

tol

the coordinates and the covariates corresponding to the prediction locations are rounded to this many places after the decimal. The default value is 12.

Value

A list comprising of the following:

prediction

predicted response corresponding to X.0 and coords.0.

prediction.ci

confidence intervals corresponding to the predictions.

prediction.time

time (in seconds) required to perform the prediction after preprocessing data in R, reported using proc.time().

Author(s)

Arkajyoti Saha [e-mail],
Abhirup Datta [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, 111:800-812.

Andrew Finley, Abhirup Datta and Sudipto Banerjee (2017). spNNGP: Spatial Regression Models for Large Datasets using Nearest Neighbor Gaussian Processes. R package version 0.1.1. https://CRAN.R-project.org/package=spNNGP

Examples

rmvn <- function(n, mu = 0, V = matrix(1)){
  p <- length(mu)
  if(any(is.na(match(dim(V),p))))
    stop("Dimension not right!")
  D <- chol(V)
  t(matrix(rnorm(n*p), ncol=p)%*%D + rep(mu,rep(n,p)))
}

set.seed(1)
n <- 500
coords <- cbind(runif(n,0,1), runif(n,0,1))

beta <- c(1,5)
x <- cbind(rnorm(n), rnorm(n))

sigma.sq = 1
phi = 1
tau.sq = 0.1

B <- as.matrix(beta)
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))

estimation_result <- BRISC_estimation(coords[1:400,], y[1:400], x[1:400,])
prediction_result <- BRISC_prediction(estimation_result,
                                      coords[401:500,], x[401:500,])