# Quickest Change Detection with Non-Stationary Post-Change Observations

arXiv: https://arxiv.org/abs/2110.01581 · HTML: https://mlsanity.com/paper/2110.01581/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Oct 2021.

## Built on by (most cited first, 4 of 4)

- [Reinforcement Learning Design for Quickest Change Detection](https://mlsanity.com/paper/2403.14109/) (2024)
- [Noise-contrastive Online Change Point Detection](https://mlsanity.com/paper/2206.10143/) (2022)
- [Reinforcement Learning for Optimal Stopping in POMDPs with Application to Quickest Change Detection](https://mlsanity.com/paper/2512.22347/) (2025)
- [High-Order Liquid Evidence Modeling for Continuous and Subtle GNSS Spoofing Detection in Autonomous Driving](https://mlsanity.com/paper/2609.26231/) (2026)

## Abstract (arXiv)

The problem of quickest detection of a change in the distribution of a sequence of independent observations is considered. The pre-change observations are assumed to be stationary with a known distribution, while the post-change observations are allowed to be non-stationary with some possible parametric uncertainty in their distribution. In particular, it is assumed that the cumulative Kullback-Leibler divergence between the post-change and the pre-change distributions grows in a certain manner with time after the change-point. For the case where the post-change distributions are known, a universal asymptotic lower bound on the delay is derived, as the false alarm rate goes to zero. Furthermore, a window-limited Cumulative Sum (CuSum) procedure is developed, and shown to achieve the lower bound asymptotically. For the case where the post-change distributions have parametric uncertainty, a window-limited (WL) generalized likelihood-ratio (GLR) CuSum procedure is developed and is shown to achieve the universal lower bound asymptotically. Extensions to the case with dependent observations are discussed. The analysis is validated through numerical results on synthetic data. The use of the WL-GLR-CuSum procedure in monitoring pandemics is also demonstrated.