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arXiv · 2303.13778

Exactly Optimal Quickest Change Detection of Markov Chains

Jason J. Ford·Justin M. Kennedy·Caitlin Tompkins·Jasmin James·Aaron McFadyen
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Abstract

This paper establishes that an exactly optimal rule for Bayesian Quickest Change Detection (QCD) of Markov chains is a threshold test on the no change posterior. We also provide a computationally efficient scalar filter for the no change posterior whose effort is independent of the dimension of the chains. We establish that an (undesirable) weak practical super-martingale phenomenon can be exhibited by the no change posterior when the before and after chains are too close in a relative entropy rate sense. The proposed detector is examined in simulation studies.

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Jason J. Ford, Justin M. Kennedy, Caitlin Tompkins, Jasmin James, Aaron McFadyen. 2023-03-24. Exactly Optimal Quickest Change Detection of Markov Chains. https://arxiv.org/abs/2303.13778

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