Quickest Change-Point Detection over Multiple Data Streams via Sequential Observations

The problem of quickly detecting the occurrence of an unusual event that happens on one of multiple independent data streams is considered. In the considered problem, all data streams at the initial are under normal state and are generated by probability distribution P-0. At some unknown time, an unusual event happens and the distribution of one data stream is modified to P-1 while the distributions of the rest remain unchange. The observer can only observe one data stream at one time. With his sequential observations, the observer wants to design an online stopping rule and a data stream switching rule to minimize the detection delay, namely the time difference between the occurrence of the unusual event and the time of raising an alarm, while keeping the false alarm rate under control. We model the problem under non-Bayesian quickest detection framework, and propose a detection procedure based on the CUSUM statistic. We show that this proposed detection procedure is asymptotically optimal.