This work considers the problem of detecting signals from multiple sequentially observed data streams, where only one stream can be observed at every time instant. The goal is to detect signals as quickly as possible while controlling the global probabilities of false alarm and missed detection. In this active sampling setup, it is impossible to minimize the expected detection time simultaneously for every signal, so we formulate a novel set of performance criteria that aim to minimize the expectations of the order statistics of the detection times. A novel procedure is proposed, which incorporates an exploration mechanism to a "follow-the-leader" procedure, and is shown to optimize all the criteria asymptotically as the global error probabilities go to zero. Its finite-sample performance is compared with existing and oracle procedures in simulation studies.

翻译：本文研究了在多个顺序观测的数据流中检测信号的问题，其中每个时间点只能观测一个数据流。目标是在控制全局虚警概率和漏检概率的同时，尽可能快速地检测信号。在这种主动采样设置下，无法同时最小化每个信号的期望检测时间，因此我们制定了一组新颖的性能准则，旨在最小化检测时间顺序统计量的期望值。我们提出了一种新方法，该方法将探索机制融入"跟随领导者"策略，并在全局误差概率趋于零时渐近优化所有准则。通过仿真研究，将其有限样本性能与现有方法及最优基准方法进行了比较。