Anomaly detection is of increasing importance in the data rich world of today. It can be applied to a broad range of challenges ranging from fault detection to fraud prevention and cyber-security. Many of these application require algorithms which are very scalable, as well as accurate, due to large data volumes and/or limited computational resources.

This thesis contributes three novel approaches to the field of anomaly detection.
The first contribution, Collective And Point Anomalies (CAPA) detects and distinguishes between both collective and point anomalies in linear time. The second contribution, MultiVariate Collective And Point Anomalies (MVCAPA) extends CAPA to the multivariate setting. The third contribution is a novel particle based kalman filter which detects and distinguished between additive outliers and innovative outliers.