The increasing complexity of cellular radio networks yields new demands concerning network security. Especially the task of detecting, repulsing and preventing abuse both by in- and outsiders becomes more and more difficult. This paper deals with a relatively new technique that appears to be suitable for solving these issues, i.e. anomaly detection based on profiling mobile users. Mobility pattern generation and behavior prediction are discussed in depth, before a new model of anomaly detection that is based on the Bayes decision rule is introduced. Applying this model to mobile user profiles proves the feasibility of our approach. Finally, a special emphasis is put on discussing privacy aspects of anomaly detection.