  Persistent homology is a method for probing topological properties of point
clouds and functions. The method involves tracking the birth and death of
topological features (2000) as one varies a tuning parameter. Features with
short lifetimes are informally considered to be "topological noise," and those
with a long lifetime are considered to be "topological signal." In this paper,
we bring some statistical ideas to persistent homology. In particular, we
derive confidence sets that allow us to separate topological signal from
topological noise.
