A False Discovery Rate Oriented Approach to Parallel Sequential Change Detection Problems

Abstract

The problem of sequentially detecting changes in parallel data streams is formulated and investigated. Each data stream may have its own change point at which the underlying probability distribution of its data changes, and the decision maker needs to declare, sequentially, which data streams have passed their change points. With a large number of parallel data streams, the error metric is the false discovery rate (FDR), which is the expected ratio of the number of falsely declared data streams to the total number of declared data streams. A data stream is falsely declared if the detected change point is ahead of its actual change point. Decision procedures that are guaranteed to control the FDR level are developed, and it is also shown that the average decision delays (ADDs) of these decision procedures do not grow with the number of data streams. Numerical simulations and case studies are conducted to corroborate the analytical results, and to illustrate the utility of the decision procedures.