Outlier detection is a fundamental issue in data mining, specifically in fraud detections network intrusion detection, network monitoring, etc. SmartSifter, which we abbreviate as SS, is an outlier detection engine adrressing this problem from the viewpoint of statistical learning theory. This paper provides a theoretical basis for SS and empirically demonstrates its effectiveness. SS detects outliers in an online process through the on-line unsupervised learning of a probabilistic model (using a finite mixture model) of the information source. Each time a datum is input SS employs an on-line discounting learning algorithm to learn the probabilistic model. A score is given to the datum based on the learned model, with a high score indicating a high possibility of being a statistical outlier. The novel features of SS are: 1) it is adaptive to non-stationary sources of data; 2) a score has a clear statistical/information-theoretic meaning; 3) it is computationally inexpensive; and 4) it can handle both categorical and continuous variables. An experimental application to network intrusion detection shows that SS was able to identify data with high scores that corresponded to attacks, with low computational costs. Further experimental application has identified a number of meaningful rare cases in actual health insurance pathology data from Australia's Health Insurance Commission.