  An important task in visualization is the extraction and highlighting of
dominant features in data to support users in their analysis process.
Topological methods are a well-known means of identifying such features in
deterministic fields. However, many real-world phenomena studied today are the
result of a chaotic system that cannot be fully described by a single
simulation. Instead, the variability of such systems is usually captured with
ensemble simulations that produce a variety of possible outcomes of the
simulated process. The topological analysis of such ensemble data sets and
uncertain data, in general, is less well studied. In this work, we present an
approach for the computation and visual representation of confidence intervals
for the occurrence probabilities of critical points in ensemble data sets. We
demonstrate the added value of our approach over existing methods for critical
point prediction in uncertain data on a synthetic data set and show its
applicability to a data set from climate research.
