ABSTRACT
The problem of changepoint detection in multiple data streams (sensors, populations or in multichannel systems) arises in numerous applications, including medical sphere, environmental monitoring, military defense, cyber security, and detection of malicious activity in social networks. This chapter considers a more general case where the change occurs in multiple data streams and more general multi-stream double-mixture-type change detection rules, assuming that the number and location of affected data streams are also unknown. It introduces two double-mixture detection rules. The first one mixes the Shiryaev-type statistic over the distributions of the unknown pattern and unknown post-change parameter; the second one is the double-mixture Shiryaev–Roberts statistic. The resulting statistics are compared to appropriate thresholds. The chapter also presents a general theory for very general stochastic models, providing sufficient conditions under which the suggested detection rules are first-order asymptotically optimal.
