The Annals of Statistics

Sequential multi-sensor change-point detection

Yao Xie and David Siegmund

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We develop a mixture procedure to monitor parallel streams of data for a change-point that affects only a subset of them, without assuming a spatial structure relating the data streams to one another. Observations are assumed initially to be independent standard normal random variables. After a change-point the observations in a subset of the streams of data have nonzero mean values. The subset and the post-change means are unknown. The procedure we study uses stream specific generalized likelihood ratio statistics, which are combined to form an overall detection statistic in a mixture model that hypothesizes an assumed fraction $p_{0}$ of affected data streams. An analytic expression is obtained for the average run length (ARL) when there is no change and is shown by simulations to be very accurate. Similarly, an approximation for the expected detection delay (EDD) after a change-point is also obtained. Numerical examples are given to compare the suggested procedure to other procedures for unstructured problems and in one case where the problem is assumed to have a well-defined geometric structure. Finally we discuss sensitivity of the procedure to the assumed value of $p_{0}$ and suggest a generalization.

Article information

Ann. Statist., Volume 41, Number 2 (2013), 670-692.

First available in Project Euclid: 26 April 2013

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Primary: 62L10: Sequential analysis

Change-point detection multi-sensor


Xie, Yao; Siegmund, David. Sequential multi-sensor change-point detection. Ann. Statist. 41 (2013), no. 2, 670--692. doi:10.1214/13-AOS1094.

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  • [1] Aldous, D. (1989). Probability Approximations Via the Poisson Clumping Heuristic. Applied Mathematical Sciences 77. Springer, New York.
  • [2] Chen, M., Gonzalez, S., Vasilakos, A., Cao, H. and Leung, V. C. M. (2010). Body area networks: A survey. Mobile Netw. Appl. 16 171–193.
  • [3] Lai, T. L. (1995). Sequential changepoint detection in quality control and dynamical systems. J. Roy. Statist. Soc. Ser. B 57 613–658.
  • [4] Lévy-Leduc, C. and Roueff, F. (2009). Detection and localization of change-points in high-dimensional network traffic data. Ann. Appl. Stat. 3 637–662.
  • [5] Lorden, G. (1971). Procedures for reacting to a change in distribution. Ann. Math. Statist. 42 1897–1908.
  • [6] Mei, Y. (2010). Efficient scalable schemes for monitoring a large number of data streams. Biometrika 97 419–433.
  • [7] Page, E. S. (1954). Continuous inspection schemes. Biometrika 41 100–115.
  • [8] Page, E. S. (1955). A test for a change in a parameter occurring at an unknown point. Biometrika 42 523–527.
  • [9] Petrov, A., Rozovskii, B. L. and Tartakovsky, A. G. (2003). Efficient Nonlinear Filtering Methods for Detection of Dim Targets by Passive Systems, Vol. IV. Artech House, Boston, MA.
  • [10] Pollak, M. and Siegmund, D. (1975). Approximations to the expected sample size of certain sequential tests. Ann. Statist. 3 1267–1282.
  • [11] Rabinowitz, D. (1994). Detecting clusters in disease incidence. In Change-point Problems (South Hadley, MA, 1992). Institute of Mathematical Statistics Lecture Notes—Monograph Series 23 255–275. IMS, Hayward, CA.
  • [12] Shafie, K., Sigal, B., Siegmund, D. and Worsley, K. J. (2003). Rotation space random fields with an application to fMRI data. Ann. Statist. 31 1732–1771.
  • [13] Siegmund, D. (1985). Sequential Analysis: Tests and Confidence Intervals. Springer, New York.
  • [14] Siegmund, D. and Venkatraman, E. S. (1995). Using the generalized likelihood ratio statistic for sequential detection of a change-point. Ann. Statist. 23 255–271.
  • [15] Siegmund, D. and Yakir, B. (2007). The Statistics of Gene Mapping. Springer, New York.
  • [16] Siegmund, D. and Yakir, B. (2008). Detecting the emergence of a signal in a noisy image. Stat. Interface 1 3–12.
  • [17] Siegmund, D., Yakir, B. and Zhang, N. R. (2011). Detecting simultaneous variant intervals in aligned sequences. Ann. Appl. Stat. 5 645–668.
  • [18] Širjaev, A. N. (1963). Optimal methods in quickest detection problems. Theory Probab. Appl. 8 22–46.
  • [19] Tartakovsky, A. G. and Veeravalli, V. V. (2008). Asymptotically optimal quickest change detection in distributed sensor systems. Sequential Anal. 27 441–475.
  • [20] Xie, Y. (2011). Statistical signal detection with multi-sensor and sparsity. Ph.D. thesis, Stanford Univ.