Density based exploration of bivariate data

The difficulties of assessing details of the shape of a bivariate distribution, and of contrasting subgroups, from a raw scatterplot are discussed. The use of contours of a density estimate in highlighting features of distributional shape is illustrated on data on the development of aircraft technology. The estimated density height at each observation imposes an ordering on the data which can be used to select contours which contain specified proportions of the sample. This leads to a display which is reminiscent of a boxplot and which allows simple but effective comparison of different groups. Some simple properties of this technique are explored.Interesting features of a distribution such as arms and multimodality are found along the directions where the largest probability mass is located. These directions can be quantified through the modes of a density estimate based on the direction of each observation.