Statistical anomaly detection for streaming data under computational constraint

Ward, Kes and Eckley, Idris and Fearnhead, Paul (2025) Statistical anomaly detection for streaming data under computational constraint. PhD thesis, Lancaster University.

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Abstract

This thesis develops the Functional Online Cumulative Sum (FOCuS) anomaly detection method for detecting collective anomalies in streaming data under conditions of computational constraint. FOCuS performs a sequential likelihood ratio test for the presence of an anomaly in all intervals within a data stream, while only requiring a small constant cost per update. The FOCuS method is adapted from its original Gaussian form to work with Poisson-distributed count data, and extended to the wider one-parameter Exponential family model setting. Further extensions to FOCuS to find collective anomalies in multivariate streaming data are also examined. This thesis contains real applications with different kinds of computational constraints. These include handheld radiation monitoring devices with a limited battery life, and cube satellites detecting gamma ray bursts with limited processing power on board.