% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/ars.R
\name{ars}
\alias{ars}
\title{Adaptive Rejection Sampling
\code{ars}}
\usage{
ars(f, N = 1000, bounds = c(-Inf, Inf), ...)
}
\arguments{
\item{f}{function to sample from (must fit log-concave properties)}

\item{N}{number of observations outputted}

\item{bounds}{vector of length 2 containing the lower and upper bounds for the distribution function f}

\item{...}{additional arguments to pass to f (e.g. mean, sd, shape, etc.)}
}
\value{
Returns vector of samples, length N, from the distribution f(x)
}
\description{
Adaptive rejection sampling (ARS) is a sampling algorithm for log-concave univariate functions. One could use Rejection Sampling, but ARS is less computationally expensive through assumption of log-concavity and the unique function of updating the envelope and squeeze functions.
}
\examples{
library(ars)

# Example 1: Sample 1500 values from a gamma distribution (Gammma(2,5))
N <- 1500
samples <- ars(dgamma, N, bounds=c(0,Inf), shape = 2, rate = 5)

# plot a histogram and curve of actual to check for similarity
hist(samples, prob= TRUE, breaks = 50)
curve(dgamma(x, shape = 2, rate = 5),
    col="darkblue", lwd=2, add=TRUE, yaxt="n")


# Example 2: Sample 1000 values from a beta distribution (Beta(2,6))
f <- dbeta
samples <- ars(f, bounds=c(0,1), shape1 = 2, shape2 = 6)

# plot a histogram and curve of actual to check for similarity
hist(samples, prob= TRUE)
curve(dbeta(x, shape1 = 2, shape2 = 6),
    col="darkblue", lwd=2, add=TRUE, yaxt="n")

}
\references{
Gilks, W. R., & Wild, P. (1992). Adaptive Rejection Sampling for Gibbs Sampling.
\emph{Journal of the Royal Statistical Society. Series C (Applied Statistics)}, 41(2), 337–348.

Markou, S. (Dec 2022). \emph{Adaptive rejection sampling.} Random walks.
https://random-walks.org/content/misc/ars/ars.html

Wickham, H. (2015). \emph{R packages.} O'Reilly Media.
https://r-pkgs.org/testing-basics.html
}
\author{
Kristoffer Hernandez, Leon Weingartner, Nikita Mehandru
}