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

Alexander G. Tartakovsky ()
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Alexander G. Tartakovsky: Moscow Institute of Physics and Technology

Methodology and Computing in Applied Probability, 2019, vol. 21, issue 4, 1303-1336

Abstract: 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.

Keywords: Asymptotic optimality; Changepoint detection; General non-i.i.d. models; Hidden Markov models; Moments of the delay to detection; r-Complete convergence; Statistical process control; Surveillance; MSC 62L10; MSC 62L15; MSC 60G40; MSC 62C10; MSC 62C20 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s11009-019-09735-3

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