Quickest change point identification across a sensor array

The problem of quickly detecting a statistical change and identifying the change source is considered. In the problem studied, there are multiple sensors. A change can first occur at any one of these sensors and propagate to other sensors. One is required to detect the presence of such change with a minimal delay and furthermore identify the sensor that first observes the change. Three performance metrics, namely detection delay, false alarm probability and false identification probability, are of interest. The optimal stopping rule, determining when one should stop sampling and claim a change has occurred, and the optimal terminal decision rule, determining which sensor first observes the change, that minimize a weighted sum of these three performance metrics are characterized. We obtain the optimal solution by first converting the problem at the hand to a Markovian stopping time problem and then solving the problem using tools from the optimal stopping theory.