det.rnd {detpack}

Bootstrapping from Distribution Element Trees

Description

Smooth bootstrapping or generation of (un)conditional random vectors based on an existing distribution element tree (DET).

Usage

det.rnd(n, det, xc = vector("numeric", length = 0), dc = vector("numeric",
  length = 0), cores = Inf)

Arguments

n

number of samples to generate.

det

distribution element tree object resulting from det.construct.

xc

vector with conditioning values of probability-space components listed in dc. If empty (default), unconditional samples are generated.

dc

integer vector with indices of conditioning components corresponding to xc. If empty (default), unconditional samples are generated.

cores

for large n, cores > 1 allows for parallel bootstrapping using the indicated number of cores. The default is cores = Inf, which allocates half of the available cores (see detectCores). cores = 1 corresponds to serial bootstrapping.

Value

A matrix containing n random vectors (columns) with d components or dimensions (rows) is returned. d is equal to the dimensionality of the underlying det object.

Examples

## 2d example
require(stats); require(graphics)
# data from uniform distribution on a wedge
x <- matrix(runif(2e4), ncol = 2); x <- x[x[,2]<x[,1],]
x2c <- 0.75 # conditioning component
# data and conditioning line
split.screen(c(2, 1)); screen(1)
plot(x, type = "p", pch = ".", asp = 1)
lines(c(0,1), x2c*c(1,1), col = "red")
# DET construction and bootstrapping
det <- det.construct(t(x), mode = 1, lb = 0, ub = 0) # const. de's, no pre-white
y <- det.rnd(1e3, det, xc = x2c, dc = 2, cores = 2) # conditional bootstrap'g
# compare generated data (black) with exact cond. distribution (red)
screen(2); det1(y[1,], mode = 1)
lines(c(0,x2c,x2c,1,1),c(0,0,1/(1-x2c),1/(1-x2c),0), col = "red")

## example 2d unconditional
require(stats); require(graphics)
x <- matrix(runif(2e4), ncol = 2); x <- x[x[,2]<x[,1],] # uniform wedge
det <- det.construct(t(x), mode = 1, lb = 0, ub = 0) # no pre-white
y <- t(det.rnd(nrow(x), det, cores = 2)) # smooth bootstrapping
split.screen(c(2, 1))
screen(1); plot(x, type = "p", pch = ".", asp = 1, main = "original")
screen(2); plot(y, type = "p", pch = ".", asp = 1, main = "bootstrapped")

## example 3d
require(stats); require(graphics)
# mean and covariance of Gaussian, data generation
mu <- c(1,3,2); C <- matrix(c(25,7.5,1.75,7.5,7,1.35,1.75,1.35,0.43), nrow = 3)
A <- eigen(C); B <- diag(A$values); A <- A$vectors
x <- matrix(rnorm(3e4), nrow = 3)
x <- A %*% (sqrt(B) %*% x) + mu %*% t(rep(1,ncol(x)))
lbl <- "x1 | x2 = 7 & x3 = 2.5"
pairs(t(x), labels = c("x1","x2","x3"), pch = ".", main = lbl)
# bootstrapping conditional on x2 and x3
det <- det.construct(x, lb = 0, ub = 0)
xc <- c(2.5,7); d <- c(3,2) # conditional on x2 = 7 & x3 = 2.5
y <- det.rnd(1e4, det, xc, d, cores = 1)
det1(y[1,], mode = 1, main = lbl)
# compare with exact conditional density
Cm1 <- solve(C); var1 <- det(C)/det(C[2:3,2:3]) # conditional variance
mu1 <- mu[1] + var1*((mu[2]-xc[d==2])*Cm1[1,2]+(mu[3]-xc[d==3])*Cm1[1,3]) # cond. mean
x1 <- mu1 + seq(-50,50)/50 * 5*sqrt(var1) # x1-axis grid points
lines(x1, dnorm(x1,mu1,sqrt(var1)), col = "red")