  We introduce \emph{topological density estimation} (TDE), in which the
multimodal structure of a probability density function is topologically
inferred and subsequently used to perform bandwidth selection for kernel
density estimation. We show that TDE has performance and runtime advantages
over competing methods of kernel density estimation for highly multimodal
probability density functions. We also show that TDE yields useful auxiliary
information, that it can determine its own suitability for use, and we explain
its performance.
