Compound Sequential Change Point Detection in Multiple Data Streams
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We consider sequential change point detection in multiple data streams, where each stream has its own change point. Once a change point is detected for a data stream, this stream is deactivated permanently. The goal is to maximize the normal operation of the pre-change streams, while controlling the proportion of post-change streams among the active streams at all time points. This problem has wide applications in science, social science, and engineering. Taking a Bayesian formulation, we develop a compound sequential decision theory framework for this problem. Under this framework, an oracle procedure is proposed that is optimal among all sequential procedures which control the expected proportion of post-change streams at each time point. We also investigate the asymptotic behavior of the proposed method when the number of data streams grows large. Several non-standard technical tools involving partially ordered spaces and monotone coupling of stochastic processes are developed for proving the optimality result. Numerical examples are provided to illustrate the use and performance of the proposed method.
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