THE MAP TEST FOR MULTIMODALITY

We introduce a test for detecting multimodality in distributions based on minimal constrained spanning trees. We define a Minimal Ascending Path Spanning Tree (MAPST) on a set of points as a spanning tree that has the minimal possible sum of lengths of links with the constraint t hat starting from any link, the lengths of the finks are non-increasin g towards a root node. We define similarly MAPSTs with more than one r oot. We present some algorithms for finding such trees. Based on these trees, we devise a test for multimodality, called the MAP Test (for M inimal Ascending Path). Using simulations, we estimate percentage poin ts of the MAP statistic and assess the power of the test. Finally, we illustrate the use of MAPSTs for determining the number of modes in a distribution of positions of galaxies on photographic plates from a ri ch galaxy cluster.