Many Statistical methods involve summarizing a probability distributio
n by a region of the sample space covering a specified probability, On
e method of selecting such a region is to require it to contain points
of relatively high density. Highest density regions are particularly
useful for displaying multimodal distributions and, in such cases, may
consist of several disjoint subsets-one for each local mode. In this
paper, I propose a simple method for computing a highest density regio
n from any given (possibly multivariate) density f(x) that is bounded
and continuous in x. Several examples of the use of highest density re
gions in statistical graphics are also given. A new form of boxplot is
proposed based on highest density regions; versions in one and two di
mensions are given. Highest density regions in higher dimensions are a
lso discussed and plotted.