Open Access
December 2017 Optimal sequential detection in multi-stream data
Hock Peng Chan
Ann. Statist. 45(6): 2736-2763 (December 2017). DOI: 10.1214/17-AOS1546


Consider a large number of detectors each generating a data stream. The task is to detect online, distribution changes in a small fraction of the data streams. Previous approaches to this problem include the use of mixture likelihood ratios and sum of CUSUMs. We provide here extensions and modifications of these approaches that are optimal in detecting normal mean shifts. We show how the (optimal) detection delay depends on the fraction of data streams undergoing distribution changes as the number of detectors goes to infinity. There are three detection domains. In the first domain for moderately large fractions, immediate detection is possible. In the second domain for smaller fractions, the detection delay grows logarithmically with the number of detectors, with an asymptotic constant extending those in sparse normal mixture detection. In the third domain for even smaller fractions, the detection delay lies in the framework of the classical detection delay formula of Lorden. We show that the optimal detection delay is achieved by the sum of detectability score transformations of either the partial scores or CUSUM scores of the data streams.


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Hock Peng Chan. "Optimal sequential detection in multi-stream data." Ann. Statist. 45 (6) 2736 - 2763, December 2017.


Received: 1 June 2015; Revised: 1 July 2016; Published: December 2017
First available in Project Euclid: 15 December 2017

zbMATH: 06838149
MathSciNet: MR3737908
Digital Object Identifier: 10.1214/17-AOS1546

Primary: 62G10 , 62L10

Keywords: average run length , CUSUM , detectability score , detection delay , mixture likelihood ratio , sparse detection , stopping rule

Rights: Copyright © 2017 Institute of Mathematical Statistics

Vol.45 • No. 6 • December 2017
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