SRI International's real-time intrusion-detection expert system (IDES) contains a statistical subsystem that observes behavior on a monitored computer system and adaptively learns what is normal for individual users and groups of users. The statistical subsystem also monitors observed behavior and identifies behavior as a potential intrusion (or misuse by authorized users) if it deviates significantly from expected behavior. The multivariate methods used to profile normal behavior and identify deviations from expected behavior are explained in detail. The statistical test for abnormality contains a number of parameters that must be initialized and the substantive issues relating to setting those parameter values are discussed.