##' Create FAB intervals, given the spending function
##'
##'
##' @title Create FAB intervals, given the spending function
##' @param theta
##' @param w
##' @param sigma
##' @param alpha
##' @param yMin
##' @param yMax
##' @param yNum
##' @param verbose
##' @return
##' @author Spencer Woody
##'
##' @export
FAB <- function(theta, w, sigma, alpha = 0.10, yMin = -5, yMax = 5,
yNum = 5000, verbose = TRUE) {
require(dplyr)
require(rootSolve)
require(splines)
require(ggplot2)
require(latex2exp)
numTheta <- length(theta)
# Create vectors for upper and lower acceptance regions
Al <- rep(NA, numTheta)
Au <- rep(NA, numTheta)
if (verbose) cat("\nCreating acceptance regions...\n")
# Fill create acceptance regions
prog <- progress_estimated(numTheta)
for (i in 1:numTheta) {
# Tail regions
wl <- alpha * w[i]
wu <- 1 - alpha + wl
# saFAB acceptance regions
Al[i] <- qnorm(wl, theta[i], sigma)
Au[i] <- qnorm(wu, theta[i], sigma)
# Print progress update
if (verbose) prog$tick()$print()
}
if (verbose) cat("\n")
# Make data.frame for acceptance regions
Adf <- data.frame(
theta = rep(theta, 2),
A = c(Al, Au),
ul = c(rep("lower", numTheta), rep("upper", numTheta))
)
# Create spline functions for acceptance regions
AlFun <- splinefun(theta, Al)
AuFun <- splinefun(theta, Au)
# Create confidence intervals along a sequence of y values
yGrid <- seq(yMin, yMax, length.out = yNum)
Cdf <- data.frame(
y = yGrid,
intervals = I(vector("list", length(yGrid))),
numIntervals = NA,
intervalLength = NA
)
if (verbose) cat("\nCreating confidence intervals...\n")
prog <- progress_estimated(yNum)
for (i in 1:length(yGrid)) {
# Temporary auxillary functions
Lfun <- function(x) {
AlFun(x) - yGrid[i]
}
Ufun <- function(x) {
AuFun(x) - yGrid[i]
}
# Roots of auxillary functions
rootsL <- uniroot.all(Lfun, range(theta))
rootsU <- uniroot.all(Ufun, range(theta))
# Intervals come from roots of auxillary functions
Cdf$intervals[[i]] <- c(rootsU, rootsL)
# Number of disjoint intervals
Cdf$numIntervals[i] <- length(Cdf$intervals[[i]]) / 2
# Length of intervals
Cdf$intervalLength[i] <- totalLength(Cdf$intervals[[i]])
# Print progress bar
if (verbose) prog$tick()$print()
}
if (verbose) cat("\n")
# Output the confidence interval dataframe for plotting
# Confidence interval dataframe for plotting
CdfPlotting <- data.frame(
y = rep(NA, sum(Cdf$numIntervals)),
lower = NA,
upper = NA
)
rowCount <- 1
for (j in 1:nrow(Cdf)) {
numIntervalsJ <- Cdf$numIntervals[j]
Rows <- (rowCount):(rowCount + numIntervalsJ - 1)
CdfPlotting$y[Rows] <- rep(Cdf$y[j], numIntervalsJ)
CdfPlotting$lower[Rows] <- Cdf$intervals[[j]][seq(1, numIntervalsJ * 2, by = 2)]
CdfPlotting$upper[Rows] <- Cdf$intervals[[j]][seq(2, numIntervalsJ * 2, by = 2)]
rowCount <- rowCount + numIntervalsJ
}
CdfPlot <- ggplot(CdfPlotting) +
geom_linerange(aes(y, ymin = lower, ymax = upper), alpha = 0.25) +
labs(x = "y", y = TeX("$\\theta \\in C(y)$"))
# Output
return(list(
Adf = Adf,
Cdf = Cdf,
CdfPlotting = CdfPlotting,
CdfPlot = CdfPlot
))
}
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