  In topological data analysis, we want to discern topological and geometric
structure of data, and to understand whether or not certain features of data
are significant as opposed to simply random noise. While progress has been made
on statistical techniques for single-parameter persistence, the case of
two-parameter persistence, which is highly desirable for real-world
applications, has been less studied. This paper provides an accessible
introduction to two-parameter persistent homology and presents results about
matching distance between 2-D persistence modules obtained from families of
point clouds. Results include observations of how differences in geometric
structure of point clouds affect the matching distance between persistence
modules. We offer these results as a starting point for the investigation of
more complex data.
