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Asymptotically Optimal Quickest Change Detection in Multistream Data—Part 1: General Stochastic Models

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  • Alexander G. Tartakovsky

    (Moscow Institute of Physics and Technology
    AGT StatConsult)

Abstract

Assume that there are multiple data streams (channels, sensors) and in each stream the process of interest produces generally dependent and non-identically distributed observations. When the process is in a normal mode (in-control), the (pre-change) distribution is known, but when the process becomes abnormal there is a parametric uncertainty, i.e., the post-change (out-of-control) distribution is known only partially up to a parameter. Both the change point and the post-change parameter are unknown. Moreover, the change affects an unknown subset of streams, so that the number of affected streams and their location are unknown in advance. A good changepoint detection procedure should detect the change as soon as possible after its occurrence while controlling for a risk of false alarms. We consider a Bayesian setup with a given prior distribution of the change point and propose two sequential mixture-based change detection rules, one mixes a Shiryaev-type statistic over both the unknown subset of affected streams and the unknown post-change parameter and another mixes a Shiryaev–Roberts-type statistic. These rules generalize the mixture detection procedures studied by Tartakovsky (IEEE Trans Inf Theory 65(3):1413–1429, 2019) in a single-stream case. We provide sufficient conditions under which the proposed multistream change detection procedures are first-order asymptotically optimal with respect to moments of the delay to detection as the probability of false alarm approaches zero.

Suggested Citation

  • Alexander G. Tartakovsky, 2019. "Asymptotically Optimal Quickest Change Detection in Multistream Data—Part 1: General Stochastic Models," Methodology and Computing in Applied Probability, Springer, vol. 21(4), pages 1303-1336, December.
    • Handle: RePEc:spr:metcap:v:21:y:2019:i:4:d:10.1007_s11009-019-09735-3
    DOI: 10.1007/s11009-019-09735-3
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    References listed on IDEAS

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    1. Y. Mei, 2010. "Efficient scalable schemes for monitoring a large number of data streams," Biometrika, Biometrika Trust, vol. 97(2), pages 419-433.
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