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\name{hpd}
\alias{hpd}
\alias{emp.hpd}
\title{Compute Highest Posterior Density Intervals}
\description{
Compute the Highest Posterior Density Interval (HPD) from an inverse
density function (hpd) or a vector of realizations of the distribution
(emp.hpd).
}
\usage{
hpd(posterior.icdf, conf=0.95, tol=0.00000001,...)
emp.hpd(x, conf=0.95, lower, upper)
}
\arguments{
\item{posterior.icdf}{ Function, the inverse cdf of the posterior
distribution (usually a function whose name starts with 'q').}
\item{x}{ A vector of realizations from the posterior distribution.}
\item{conf}{ Scalar, the credible level desired. }
\item{tol}{ Scalar, the tolerance for \code{optimize}.}
\item{\dots}{Additional arguments to \code{posterior.icdf}.}
\item{lower}{Optional lower bound on support of x.}
\item{upper}{Optional upper bound on support of x.}
}
\details{
These functions compute the highest posterior density intervals
(sometimes called minimum length confidence intervals) for a Bayesian
posterior distribution. The \code{hpd} function is used when you have
a function representing the inverse cdf (the common case with
conjugate families). The \code{emp.hpd} function is used when you
have realizations of the posterior (when you have results from an MCMC
run).
}
\value{
A vector of length 2 with the lower and upper limits of the interval.
}
\author{ Greg Snow \email{538280@gmail.com}}
\note{These functions assume that the posterior distribution is
unimodal, they compute only 1 interval, not the set of intervals that
are appropriate for multimodal distributions.}
\seealso{\code{hdr} in the hdrcde package.}
\examples{
hpd(qbeta, shape1=50, shape2=250)
tmp <- rbeta(10000, 50, 250)
emp.hpd(tmp)
}
\keyword{univar}
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