accrej: Acceptance-Rejection Algorithm Visualization

Description

This function animates the process of generating variates via acceptance-rejection for a specified density function (pdf) bounded by a specified majorizing function.

Usage

accrej(
  n = 20,
  pdf = function(x) dbeta(x, 3, 2),
  majorizingFcn = NULL,
  majorizingFcnType = NULL,
  support = c(0, 1),
  seed = NA,
  maxTrials = Inf,
  plot = TRUE,
  showTitle = TRUE,
  plotDelay = plot * -1
)

Arguments

number of variates to generate.

pdf

desired probability density function from which random variates are to be drawn

majorizingFcn

majorizing function. Default value is NULL, corresponding to a constant majorizing function that is 1.01 times the maximum value of the pdf. May alternatively be provided as a user-specified function, or as a data frame requiring additional notation as either piecewise-constant or piecewise-linear. See examples.

majorizingFcnType

used to indicate whether a majorizing function that is provided via data frame is to be interpreted as either piecewise-constant ("pwc") or piecewise-linear ("pwl"). If the majorizing function is either the default or a user-specified function (closure), the value of this parameter is ignored.

support

the lower and upper bounds of the support of the probability distribution of interest, specified as a two-element vector.

seed

initial seed for the uniform variates used during generation.

maxTrials

maximum number of accept-reject trials; infinite by default

plot

if TRUE, visual display will be produced. If FALSE, generated variates will be returned without visual display.

showTitle

if TRUE, display title in the main plot.

plotDelay

wait time, in seconds, between plots; -1 (default) for interactive mode, where the user is queried for input to progress.

Value

Returns the n generated variates accepted.

Details

There are three modes for visualizing the acceptance-rejection algorithm for generating random variates from a particular probability distribution:

interactive advance (plotDelay = -1), where pressing the 'ENTER' key advances to the next step (an accepted random variate) in the algorithm, typing 'j #' jumps ahead # steps, typing 'q' quits immediately, and typing 'e' proceeds to the end;
automatic advance (plotDelay > 0); or
final visualization only (plotDelay = 0).

As an alternative to visualizing, variates can be generated

Examples

Run this code

# NOT RUN {
accrej(n = 20, seed = 8675309, plotDelay = 0)
# }
# NOT RUN {
accrej(n = 10, seed = 8675309, plotDelay = 0.1)
accrej(n = 10, seed = 8675309, plotDelay = -1)

# Piecewise-constant majorizing function
m <- function(x) {
  if      (x < 0.3)  1.0 
  else if (x < 0.85) 2.5
  else               1.5
}
accrej(n = 100, seed = 8675309, majorizingFcn = m, plotDelay = 0)

# Piecewise-constant majorizing function as data frame
m <- data.frame(
  x = c(0.0, 0.3, 0.85, 1.0),
  y = c(1.0, 1.0, 2.5,  1.5))
accrej(n = 100, seed = 8675309, majorizingFcn = m, 
       majorizingFcnType = "pwc", plotDelay = 0)

# Piecewise-linear majorizing function as data frame
m <- data.frame(
   x = c(0.0, 0.1, 0.3, 0.5, 0.7, 1.0), 
   y = c(0.0, 0.5, 1.1, 2.2, 1.9, 1.0))
accrej(n = 100, seed = 8675309, majorizingFcn = m, 
       majorizingFcnType = "pwl", plotDelay = 0)

# invalid majorizing function; should give warning
accrej(n = 20, majorizingFcn = function(x) dbeta(x, 1, 3), plotDelay = 0)
# }
# NOT RUN {
# Piecewise-linear majorizing function with power-distribution density function
m <- data.frame(x = c(0, 1, 2), y = c(0, 0.375, 1.5))
samples <- accrej(n = 100, pdf = function(x) (3 / 8) * x ^ 2, support = c(0,2),
                  majorizingFcn = m, majorizingFcnType = "pwl", plotDelay = 0)

# }