  We introduce a new model for planar point point processes, with the aim of
capturing the structure of point interaction and spread in persistence
diagrams. Persistence diagrams themselves are a key tool of TDA (topological
data analysis), crucial for the delineation and estimation of global
topological structure in large data sets. To a large extent, the statistical
analysis of persistence diagrams has been hindered by difficulties in providing
replications, a problem that was addressed in an earlier paper, which
introduced a procedure called RST (replicating statistical topology). Here we
significantly improve on the power of RST via the introduction of a more
realistic class of models for the persistence diagrams. In addition, we
introduce to TDA the idea of bagplotting, a powerful technique from
non-parametric statistics well adapted for differentiating between
topologically significant points, and noise, in persistence diagrams.
  Outside the setting of TDA, our model provides a setting for fashioning point
processes, in any dimension, in which both local interactions between the
points, along with global restraints on the general point cloud, are important
and perhaps competing.
