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.

翻译：本文证明了，对于马尔可夫链的贝叶斯快速变化检测（QCD），一个精确最优的规则是对无变化后验概率进行阈值检验。我们还提出了一种计算高效的无变化后验概率标量滤波器，其计算复杂度与马尔可夫链的维数无关。我们证明了，当变化前后的马尔可夫链在相对熵率意义上过于接近时，无变化后验概率可能会表现出一种（不良的）弱实用超鞅现象。所提出的检测器在仿真研究中进行了验证。