Optimal detection in multi-stream data

Consider a large number of detectors each generating a data stream. The task here is to detect online distribution changes in a small fraction of the data streams. Previous approaches to this problem include the use of mixture likelihood ratios and sum of CUSUMs. We provide here extensions and modifications of these approaches that lead to optimal detection. More specifically we show that minimum detection delay is achieved subject to the usual average run length constraint. The basic idea is to compute for each observation a detectability score that is based on the likelihood ratio between no change, and a distribution change at the limits of detectability.