Robust quickest change detection in nonstationary processes

Exactly and asymptotically optimal algorithms are developed for robust detection of changes in nonstationary processes. In nonstationary processes, the distribution of the data after change varies with time. The decision maker does not have access to precise information on the post-change distribution. It is shown that if the post-change, nonstationary family has a distribution that is least favorable in a well-defined sense, then the algorithms designed using the least favorable laws are robust optimal. This is the first result in which an exactly robust-optimal solution is obtained in a nonstationary setting where the least favorable law is also allowed to be nonstationary. Examples of nonstationary processes encountered in public health monitoring and space and military applications are provided. Our robust algorithms are also applied to real and simulated data to show their effectiveness.