In this paper, we formulate and solve a two-stage Bayesian sequential change diagnosis (SCD) problem. Different from the one-stage sequential change diagnosis problem considered in the existing work, after a change has been detected, we can continue to collect low-cost samples so that the post-change distribution can be identified more accurately. The goal of a two-stage SCD rule is to minimize the total cost including delay, false alarm probability, and misdiagnosis probability. To solve the two-stage SCD problem, we first convert the problem into a two-ordered optimal stopping time problem. Using tools from optimal multiple stopping time theory, we obtain the optimal SCD rule. Moreover, to address the high computational complexity issue of the optimal SCD rule, we further propose a computationally efficient threshold-based two-stage SCD rule. By analyzing the asymptotic behaviors of the delay, false alarm, and misdiagnosis costs, we show that the proposed threshold SCD rule is asymptotically optimal as the per-unit delay costs go to zero.

中文翻译：

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两阶段贝叶斯序列变化诊断


在本文中，我们制定并解决了两阶段贝叶斯顺序变化诊断（SCD）问题。与现有工作中考虑的一阶段顺序变更诊断问题不同，在检测到变更后，我们可以继续收集低成本样本，以便更准确地识别变更后的分布。两阶段 SCD 规则的目标是最小化总成本，包括延迟、误报概率和误诊概率。为了解决两阶段SCD问题，我们首先将问题转换为二阶最优停止时间问题。使用最优多次停止时间理论的工具，我们获得了最优 SCD 规则。此外，为了解决最优SCD规则的高计算复杂性问题，我们进一步提出了一种计算高效的基于阈值的两阶段SCD规则。通过分析延迟、误报和误诊成本的渐近行为，我们表明，当单位延迟成本趋于零时，所提出的阈值 SCD 规则是渐近最优的。