hpd: Compute Highest Posterior Density Intervals

In TeachingDemos: Demonstrations for Teaching and Learning

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

posterior.icdf	Function, the inverse cdf of the posterior distribution (usually a function whose name starts with 'q').
x	A vector of realizations from the posterior distribution.
conf	Scalar, the credible level desired.
tol	Scalar, the tolerance for optimize.
...	Additional arguments to posterior.icdf.
lower	Optional lower bound on support of x.
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 hpd function is used when you have a function representing the inverse cdf (the common case with conjugate families). The 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.

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.

Author(s)

Greg Snow [e-mail]

See Also

hdr in the hdrcde package.

Examples

hpd(qbeta, shape1=50, shape2=250)

tmp <- rbeta(10000, 50, 250)
emp.hpd(tmp)

TeachingDemos documentation built on May 29, 2024, 5:59 a.m.