  The anomaly detection method presented by this paper has a special feature:
it does not only indicate whether an observation is anomalous or not but also
tells what exactly makes an anomalous observation unusual. Hence, it provides
support to localize the reason of the anomaly.
  The proposed approach is model-based; it relies on the multivariate
probability distribution associated with the observations. Since the rare
events are present in the tails of the probability distributions, we use copula
functions, that are able to model the fat-tailed distributions well. The
presented procedure scales well; it can cope with a large number of
high-dimensional samples. Furthermore, our procedure can cope with missing
values, too, which occur frequently in high-dimensional data sets.
  In the second part of the paper, we demonstrate the usability of the method
through a case study, where we analyze a large data set consisting of the
performance counters of a real mobile telecommunication network. Since such
networks are complex systems, the signs of sub-optimal operation can remain
hidden for a potentially long time. With the proposed procedure, many such
hidden issues can be isolated and indicated to the network operator.
