  In urgent decision making applications, ensemble simulations are an important
way to determine different outcome scenarios based on currently available data.
In this paper, we will analyze the output of ensemble simulations by
considering so-called persistence diagrams, which are reduced representations
of the original data, motivated by the extraction of topological features.
Based on a recently published progressive algorithm for the clustering of
persistence diagrams, we determine the optimal number of clusters, and
therefore the number of significantly different outcome scenarios, by the
minimization of established statistical score functions. Furthermore, we
present a proof-of-concept prototype implementation of the statistical
selection of the number of clusters and provide the results of an experimental
study, where this implementation has been applied to real-world ensemble data
sets.
