This paper describes an approach to handle multivariate training data which contain outliers. The aim is to analyze the training patterns and to detect anomalous patterns. Therefore we explicitly model the existence of outliers in the training data using a widespread outlier distribution. Indicator variables assign each pattern to either the outlier distribution or the distribution of normal patterns. Thus we can estimate the data distribution using the EM-algorithm or Data Augmentation. We present the general approach as well as a concrete realization where we use Gaussian mixture models to describe the patterns’ distribution. Experimental results show the applicability of this approach for practical studies.