Sound, robust methods identify the most suitable, parsimonious set of tests to use with respect to prioritized, sequential anomaly detection in a collected batch of sample data. While the focus is on detecting anomalies in network traffic flows and classifying network traffic flows into application types, the methods are also applicable to other anomaly detection and classification application settings, including detecting email spam, (e.g. credit card) fraud detection, detecting imposters, unusual event detection (for example, in images and video), host-based computer intrusion detection, detection of equipment or complex system failures, as well as of anomalous measurements in scientific experiments.