Quickest Mean-Change Detection via Confidence Sequence and Backward Sample Averages

This study addresses the critical challenge of quickest mean-change detection (QMCD), which involves promptly detecting changes in the mean of a sequence of independent observations, particularly under the challenging condition where both pre-change and post-change distributions are unknown. A novel detector is proposed to tackle the QMCD problem. It recursively computes the backward sample average and checks whether the result escapes the forward confidence sequence, hence the name BAckward Recursive AVerage escapes Outside Confidence Sequence (BRAVO-CS). Rigorous analysis demonstrates that the proposed BRAVO-CS detector achieves an average detection delay that scales inversely with the magnitude of the mean shift-significantly better than the inverse quadratic scaling of current state-of-the-art approaches when the change is subtle. Furthermore, BRAVO-CS incurs linear time complexity, in stark contrast to the quadratic time complexity of state-of-the-art methods. Extensive simulations further confirm its robustness and efficiency across diverse scenarios, establishing BRAVO-CS as a compelling solution for real-time systems requiring rapid and reliable mean change detection.