Title: Modeling of Persistent Homology,
Abstract: Topological Data Analysis (TDA) is a novel statistical technique,
particularly powerful for the analysis of large and high dimensional data sets.
Much of TDA is based on the tool of persistent homology, represented visually
via persistence diagrams. In an earlier paper we proposed a parametric
representation for the probability distributions of persistence diagrams, and
based on it provided a method for their replication. Since the typical
situation for big data is that only one persistence diagram is available, these
replications allow for conventional statistical inference, which, by its very
nature, requires some form of replication. In the current paper we continue
this analysis, and further develop its practical statistical methodology, by
investigating a wider class of examples than treated previously.