A setup with multiple, independent, sequentially monitored data streams is considered. For each of them, two composite hypotheses are postulated, with the interpretation that the stream is anomalous if the corresponding alternative hypothesis holds. It is of interest to detect as quickly as possible whether there is at least one anomalous stream, and also to identify upon stopping the subset of anomalous streams. To address this joint sequential detection and isolation problem, we propose a sequential multiple testing framework where the probabilities of four kinds of error are controlled below distinct, user-specified levels. Two of them refer to the detection task, and the other two to the isolation task. A testing policy is proposed and it is shown to achieve the minimum possible expected sample size, under each point of the parameter space, to a first order asymptotic approximation as the four target error probabilities go to 0. The general theory is illustrated in the case that the data streams generate iid observations that belong to a multiparameter exponential family.

This paper considers the problem of sequentially detecting a change in the joint distribution of multiple data sources under a sampling constraint. Specifically, the channels or sources generate observations that are independent over time, but not necessarily across channels. The joint distribution of an unknown subset of sources changes at an unknown time instant. Moreover, there is a hard constraint that only a fixed number of sources can be sampled at each time instant, but the sources can be selected dynamically based on the already collected data. The goal is to sequentially observe the sources according to the constraint, and stop sampling as quickly as possible after the change while controlling the false alarm rate below a user-specified level. Thus, a policy for this problem consists of a joint sampling and change-detection rule. A non-randomized policy is studied, and an upper bound is established on its worst-case conditional expected detection delay with respect to both the change point and the observations from the affected sources before the change. In certain cases, this rule achieves first-order asymptotic optimality as the false alarm rate tends to zero, simultaneously under every possible post-change distribution and among all schemes that satisfy the same sampling and false alarm constraints. These general results are subsequently applied to the problems of (i) detecting a change in the marginal distributions of (not necessarily independent) information sources, and (ii) detecting a change in the covariance structure of Gaussian information sources.

The problem of sequentially detecting a change in the correlation structure of multiple Gaussian information sources is considered when it is possible to sample only two of them at each time instance. It is assumed that all sources are initially independent and that at least two of them become positively correlated after the change. The problem is to stop sampling as quickly as possible after the change, while controlling the false alarm rate and without assuming any prior information on the number of sources that become correlated. A joint sampling and change-detection rule is proposed and is shown to achieve the smallest possible worst-case conditional expected detection delay among all processes that satisfy the same constraints, to a first order approximation as the false alarm rate goes to 0, for any possible number of post-change correlated sources.

The problem of detecting and isolating a correlated pair among multiple Gaussian information sources is considered. It is assumed that there is at most one pair of correlated sources and that observations from all sources are acquired sequentially. The goal is to stop sampling as quickly as possible, declare upon stopping whether there is a correlated pair or not, and if yes, to identify it. Specifically, it is required to control explicitly the probabilities of three kinds of error: false alarm, missed detection, wrong identification. We propose a procedure that not only controls these error metrics, but also achieves the smallest possible average sample size, to a first-order approximation, as the target error rates go to 0. Finally, a simulation study is presented in which the proposed rule is compared with an alternative sequential testing procedure that controls the same error metrics.