Computing the Highest Density Region using Voronoi and Delaunay techniques

Highest density regions have a great use as prediction regions. There are some methods to compute a highest density region, but they need information about the probability density function or are only suited for certain cases. In this paper we show a new method to approximate the highest density region using Voronoi and Delaunay techniques. First we use these techniques to create a graph, after which we compute the highest density region using two different graph algorithms: one that is faster and one that is more accurate. Compared to the symmetric prediction region, these algorithms perform very well and also for non-convex contour shaped densities both algorithms work as expected.