Practical Aspects of False Alarm Control for Change Point Detection: Beyond Average Run Length
- 17 Downloads
A popular method for detecting changes in the probability distribution of a sequence of observations is CUSUM, which proceeds by sequentially evaluating a log-likelihood ratio test statistic and comparing it to a predefined threshold; a change point is detected as soon as the threshold is exceeded. It is desirable to choose the threshold such that the number of false alarms is kept to a specified level. Traditionally, the number of false alarms is measured by the average run length – the expected stopping time until the first false alarm. However, this is does not in general allow one to control the number of false alarms at every particular time instance. Thus, in this paper two stronger false alarm criteria are considered, for which approximation methods are investigated to facilitate the selection of a threshold.
KeywordsChange point detection False alarm control Threshold selection
Mathematics Subject Classification (2010)62L10
Julia Kuhn is supported by Australian Research Council (ARC) grant DP130100156. Michel Mandjes’ research is partly funded by the NWO Gravitation Project NETWORKS grant 024002003.
- Basseville M, Nikiforov I (1993) Detection of Abrupt Changes:Theory and Application. Prentice Hall, Englewood CliffsGoogle Scholar
- Bucklew J (1985) Large Deviation Techniques in Decision, Simulation and Estimation. Wiley, New YorkGoogle Scholar
- Ellens W, Kuhn J, Mandjes M, żuraniewski P (2013) Changepoint detection for dependent Gaussian sequences. Work report, arXiv:1307.0938
- Kuhn J (2017) Monitoring and Control of Stochastic Systems. PhD thesis, University of Amsterdam & The University of Queensland, Australia. Retrievable from http://dare.uva.nl/search?identifier=7ea1bd7d-c372-47ad-8582-e9bcd0fbacce Google Scholar
- Kuhn J, Mandjes M, Taimre T (2015) Mean shift detection for state space models. Proceedings of the 21st International Congress on Modelling and Simulation (MODSIM2015)Google Scholar
- Tartakovsky AG, Nikiforov I, Basseville M (2014) Sequential Analysis: Hypothesis Testing and Changepoint Detection. Monographs on Statistics & Applied Probability, vol 136. Chapman & Hall/CRC, Boca RatonGoogle Scholar
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.