hdi: Highest Density Interval
In mikemeredith/MMmisc: Stuff that Mike wants to have available

Description Usage Arguments Details Value Author(s) References Examples

Calculate the highest density interval (HDI) for a given probability mass, see Details. The function is generic, with methods for a range of input objects.

hdi(object, credMass = 0.95, ...)

## Default S3 method:
hdi(object, credMass = 0.95, ...)

## S3 method for class 'function'
hdi(object, credMass = 0.95, tol, ...)

## S3 method for class 'matrix'
hdi(object, credMass = 0.95, ...)

## S3 method for class 'data.frame'
hdi(object, credMass = 0.95, ...)

## S3 method for class 'mcmc.list'
hdi(object, credMass = 0.95, ...)

## S3 method for class 'bugs'
hdi(object, credMass = 0.95, ...)

## S3 method for class 'rjags'
hdi(object, credMass = 0.95, ...)

`object`	an object specifying the target distribution; see Details.
`credMass`	a scalar [0, 1] specifying the mass within the credible interval.
`tol`	the desired accuracy; see `optimize`; default is 1e-8.
`...`	named parameters to be passed to other methods; see Examples.

The HDI is the interval which contains the required mass such that all points within the interval have a higher probability density than points outside the interval. When applied to a posterior probability density, it is often known as the Highest Posterior Density (HPD).

In contrast, a symmetric density interval defined by (eg.) the 2.5% and 97.5% quantiles may include values with lower probability than those excluded.

For a unimodal distribution, the HDI is also the narrowest interval containing the specified mass, and the hdi function actually returns the narrowest interval. This does not always work properly for multimodel densities, where the HDI may be discontinuous (the horizontal black line in the Figure below). The single interval returned by hdi (the blue line) may incorrectly include values between the modes with low probability density.

The default method expects a vector representing draws from the target distribution, such as is produced by an MCMC process. Missing values are silently ignored; if the vector has no non-missing values, NAs are returned.

The matrix and data frame methods expect an object with vectors of the above type for each parameter in columns. The result is a matrix with parameters in columns and rows with the upper and lower limits of the HDI.

The mcmc.list method expects an object of type mcmc.list as defined in package coda.

None of the above use interpolation: the values returned correspond to specific values in the data object. Results thus depend on the random draws, and will be unstable if few values are provided. For a 95% HDI, 10,000 independent draws are recommended; a smaller number will be adequate for a 80% HDI, many more for a 99% HDI.

The function method requires the name for the inverse cumulative density function (ICDF) of the distribution; standard R functions for this have a q- prefix, eg. qbeta. Arguments required by the ICDF must the specified by their (abbreviated) names; see the examples.

a vector of length 2 or a 2-row matrix with the lower and upper limits of the HDI, with an attribute "credMass".

Mike Meredith. Code for hdi.function based on hpd by Greg Snow, corrected by John Kruschke.

Kruschke, J. K. 2011. Doing Bayesian data analysis: a tutorial with R and BUGS. Elsevier, Amsterdam.

# for a vector:
tst <- rgamma(1e5, 2.5, 2)
hdi(tst)
hdi(tst, credMass=0.8)
# For comparison, the symmetrical 80% CrI:
quantile(tst, c(0.1,0.9))

# Now a data frame:
tst <- data.frame(mu = rnorm(1e4, 4, 1), sigma = rlnorm(1e4))
hdi(tst, 0.8)
apply(tst, 2, quantile, c(0.1,0.9))

# For a function:
hdi(qgamma, 0.8, shape=2.5, rate=2)
# and the symmetrical 80% CrI:
qgamma(c(0.1, 0.9), 2.5, 2)