This paper considers the quickest detection problem for hidden Markov models (HMMs) in a Bayesian setting. We construct an augmented HMM representation of the problem that allows the application of a dynamic programming approach to prove that Shiryaev's rule is an (exact) optimal solution. This augmented representation highlights the problem's fundamental information structure and suggests possible relaxations to more exotic change event priors not appearing in the literature. Finally, this augmented representation also allows us to present an efficient computational method for implementing the optimal solution.

翻译：本文研究贝叶斯框架下隐马尔可夫模型（HMMs）的快速检测问题。通过构建问题的增广HMM表示，我们得以应用动态规划方法证明Shiryaev规则是（精确）最优解。该增广表示揭示了问题的基本信息结构，并为文献中尚未出现的更复杂变化事件先验提供了可能的松弛方案。最后，该增广表示还使我们能够提出一种实现最优解的高效计算方法。