ABSTRACT
There are many disciplines in which data arises on object spaces which are ma-
nifolds. Among these are anthropology, astronomy, bioinformatics, computer
vision, geology, image analysis, medical imaging, meteorology, and statistics.
Over the next several chapters, this monograph will present the general the-
ory and methodology underlying a nonparametric statistical analysis of data
arising on manifolds. However, each application and type of data will have its
own specific problems that need to be taken into consideration in the analysis,
which will be addressed in later portions of this book. First, though, we wish
to provide a number of examples of data lying on manifolds. In addition to
showing applications in which such data arise, these example can help provide
context in subsequent chapters focusing on theory.
