Joint Sequential Detection and Isolation for Dependent Data Streams
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The problem of joint sequential detection and isolation is considered in the context of multiple, not necessarily independent, data streams. A multiple testing framework is proposed, where each hypothesis corresponds to a different subset of data streams, the sample size is a stopping time of the observations, and the probabilities of four kinds of error are controlled below distinct, user-specified levels. Two of these errors reflect the detection component of the formulation, whereas the other two the isolation component. The optimal expected sample size is characterized to a first-order asymptotic approximation as the error probabilities go to 0. Different asymptotic regimes, expressing different prioritizations of the detection and isolation tasks, are considered. A novel, versatile family of testing procedures is proposed, in which two distinct, in general, statistics are computed for each hypothesis, one addressing the detection task and the other the isolation task. Tests in this family, of various computational complexities, are shown to be asymptotically optimal under different setups. The general theory is applied to the detection and isolation of anomalous, not necessarily independent, data streams, as well as to the detection and isolation of an unknown dependence structure.
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