# hpd: Compute Highest Posterior Density Intervals In TeachingDemos: Demonstrations for Teaching and Learning

## 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

 ```1 2 3``` ```hpd(posterior.icdf, conf=0.95, tol=0.00000001,...) emp.hpd(x, conf=0.95) ```

## 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 confidence level desired. `tol` Scalar, the tolerance for `optimize`. `...` Additional arguments to `posterior.icdf`.

## 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 [email protected]

## See Also

`hdr` in the hdrcde package.

## Examples

 ```1 2 3 4``` ```hpd(qbeta, shape1=50, shape2=250) tmp <- rbeta(10000, 50, 250) emp.hpd(tmp) ```

TeachingDemos documentation built on May 29, 2017, 11:33 a.m.