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The problem of quickest detection of a change in the distribution of asequence of independent observations is considered. The pre-change observationsare assumed to be stationary with a known distribution, while the post-changeobservations are allowed to be non-stationary with some possible parametricuncertainty in their distribution. In particular, it is assumed that thecumulative Kullback-Leibler divergence between the post-change and thepre-change distributions grows in a certain manner with time after thechange-point. For the case where the post-change distributions are known, auniversal asymptotic lower bound on the delay is derived, as the false alarmrate 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, awindow-limited (WL) generalized likelihood-ratio (GLR) CuSum procedure isdeveloped and is shown to achieve the universal lower bound asymptotically.Extensions to the case with dependent observations are discussed. The analysisis validated through numerical results on synthetic data. The use of theWL-GLR-CuSum procedure in monitoring pandemics is also demonstrated.

Quickest Change Detection with Non-Stationary Post-Change Observations