Computing and graphing highest density regions

Many Statistical methods involve summarizing a probability distribution by a region of the sample space covering a specified probability, One 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 region from any given (possibly multivariate) density f(x) that is bounded and continuous in x. Several examples of the use of highest density regions in statistical graphics are also given. A new form of boxplot is proposed based on highest density regions; versions in one and two dimensions are given. Highest density regions in higher dimensions are also discussed and plotted.