THE BUMPY ROAD TO THE MODE FOREST

The mode tree of Minnotte and Scott provides a valuable method of inve stigating features such as modes and bumps in a unknown density. By ex amining kernel density estimates for a range of bandwidths, we can lea rn a lot about the structure of a data set. Unfortunately, the basic m ode toe can be strongly affected by small changes in the data, and giv es no way to differentiate between important modes and those caused, f or example, by outliers. The mode forest overcomes these difficulties by looking simultaneously at a large collection of mode trees, all bas ed on some variation of the original data, by means such as resampling or jittering. The resulting graphic tool is both visually appealing a nd informative.