Statistics on spheres

the long version

Watson's book is a milestone in the literature on spherical distributions. For the specialist it brings together many results and points to paths for new research directions. For the statistician who is new to the subject, it is an excellent introduction to much of what is important in the field. One of the exciting things about the area of orientation statistics is that there are still many areas where we scarcely have an inkling of what to do. Appropriate models would find immediate application in geophysics. In fact, given practically any problem area in "flat" statistics—robustness, clustering, modelling, influential observations, to name a few—there is a corresponding problem for spheres. Progress is being made, but there is much to be done. And, of course, when statistics on the sphere are as familiar as N(0, 1), there are worlds of more complicated curved manifolds to conquer.