BRISC_bootstrap {BRISC}R Documentation

Function for performing bootstrap with BRISC


The function BRISC_bootstrap performs bootstrap to provide confidence intervals for parameters of univariate spatial regression models using outputs of BRISC_estimation. The details of the bootstrap method can be found in BRISC (Saha & Datta, 2018). The optimization is performed with C library of limited-memory BFGS libLBFGS: a library of Limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS), (Naoaki Okazaki). For user convenience the soure codes of the package libLBFGS are provided in the package. Some code blocks are borrowed from the R package: spNNGP: Spatial Regression Models for Large Datasets using Nearest Neighbor Gaussian Processes .


BRISC_bootstrap(BRISC_Out, n_boot = 100, h = 1, n_omp = 1,
                init = "Initial", verbose = TRUE,
                nugget_status = 1)



an object of class BRISC_Out, obtained as an output of


number of bootstrap samples. Default value is 100.


number of core to be used in parallel computing setup for bootstrap samples. If h = 1, there is no parallelization. Default value is 1.


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


keyword that specifies initialization scheme to be used. Supported keywords are: "Initial" and "Estimate" for initialization of parameter values for bootstrap samples with initial values used in BRISC_estimate and estimated values of parameters in BRISC_estimate respectively.


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.


if nugget_status = 0, tau.sq is fixed to 0, if nugget_status = 1 tau.sq is estimated. Default value is 1.


A list comprising of the following:


estimates of spatial covariance parameters corresponding to bootstrap samples.


estimates of beta corresponding to bootstrap samples.


confidence intervals corresponding to the parameters.


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


Arkajyoti Saha,
Abhirup Datta


Saha, A., & Datta, A. (2018). BRISC: bootstrap for rapid inference on spatial covariances. Stat, e184, DOI: 10.1002/sta4.184.

Okazaki N. libLBFGS: a library of Limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS), .

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.


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

n <- 300
coords <- cbind(runif(n,0,1), runif(n,0,1))

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

sigma.sq = 1
phi = 5
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, y, x)
bootstrap_result <- BRISC_bootstrap(estimation_result, n_boot = 10)

[Package BRISC version 1.0.2 Index]