Minimax Robust Quickest Change Detection

—The popular criteria of optimality for quickest change detection procedures are the Lorden criterion, the Pollak criterion, and the Bayesian criterion. In this paper, a robust version of these quickest change detection problems is considered when the pre-change and post-change distributions are not known exactly but belong to known uncertainty classes of distributions. For uncertainty classes that satisfy a specific condition, it is shown that one can identify least favorable distributions (LFDs) from the uncertainty classes, such that the detection rule designed for the LFDs is optimal for the robust problem in a minimax sense. The condition is similar to that required for the identification of LFDs for the robust hypothesis testing problem originally studied by Huber. An upper bound on the delay incurred by the robust test is also obtained in the asymptotic setting under the Lorden criterion of optimality. This bound quantifies the delay penalty incurred to guarantee robustness...

• Type: Journal
• Year: 2011
• Where: TIT
• Authors: Jayakrishnan Unnikrishnan, Venugopal V. Veeravalli, Sean P. Meyn
• Keywords: Change Detection, Education, Quickest Change Detection, TIT 2011, Uncertainty Classes