  This paper considers the detection of change points in parallel data streams,
a problem widely encountered when analyzing large-scale real-time streaming
data. Each stream may have its own change point, at which its data has a
distributional change. With sequentially observed data, a decision maker needs
to declare whether changes have already occurred to the streams at each time
point.Once a stream is declared to have changed, it is deactivated permanently
so that its future data will no longer be collected. This is a compound
decision problem in the sense that the decision maker may want to optimize
certain compound performance metrics that concern all the streams as a whole.
Thus, the decisions are not independent for different streams. Our contribution
is three-fold. First, we propose a general framework for compound performance
metrics that includes the ones considered in the existing works as special
cases and introduces new ones that connect closely with the performance metrics
for single-stream sequential change detection and large-scale hypothesis
testing. Second, data-driven decision procedures are developed under this
framework. Finally, optimality results are established for the proposed
decision procedures. The proposed methods and theory are evaluated by
simulation studies and a case study.
