发表机构
Rensselaer Polytechnic Institute; Cruise LLC（伦斯勒理工学院; Cruise有限责任公司）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文将概率最大化变化检测框架推广至允许在ξ个观测窗口内检测、应对多段非重叠瞬态变化的场景，提出生存加权平均成功准则，给出有限记忆最优停止规则。
AI 中文摘要
本文研究概率最大化序贯变化检测，该方法以在变化发生后于时长为ξ的容许区间内停止的概率衡量性能，而非采用期望检测延迟。早期工作在贝叶斯框架下引入该视角，后续针对成功检测必须在变化后首个观测时刻完成（即ξ=1）的情况，在Lorden型和Pollak型极小极大准则下对其进行了形式化。本文从两个方向推广该框架：一是允许决策者在变化后的ξ∈ℕ个观测时刻构成的规定窗口内停止；二是允许被监测过程经历多个未知发生时刻与持续时长的非重叠瞬态变化时段，成功检测指在任一此类时段对应的容许窗口内停止。虚警通过平均运行长度约束进行控制。为开展精确有限样本分析，本文提出生存加权平均成功准则，其表示在检测器在变化发生时处于激活状态的条件下，成功检测随机遇到的变化机会的概率。研究确定该准则可精确表示为停止时刻处的截断Shiryaev-Roberts（TSR）统计量除以平均运行长度的期望，且该准则刻画了其精确最优停止规则。最优过程具有有限记忆，聚合最近窗口内所有可能变化发生时刻对应的似然比证据，并将所得TSR统计量与最优停止公式得到的状态依赖延续边界进行比较。
英文摘要
This paper investigates probability-maximizing sequential change detection, a formulation in which performance is measured by the probability of stopping within an admissible interval of duration $ξ$ after a change rather than by the expected detection delay. Earlier work introduced this viewpoint in a Bayesian setting and subsequently formalized it under Lorden- and Pollak-type minimax criteria for the case in which successful detection must occur on the \textbf{first} post-change observation, i.e., $ξ=1$. This paper generalizes this framework in two directions. First, the decision maker is allowed to stop within a prescribed window of $ξ\in\mathbb{N}$ post-change observations. Second, the monitored process is allowed to experience multiple, non-overlapping transient change episodes with unknown onset times and durations, so that success consists of stopping within the admissible window associated with any one of these episodes. False alarms are controlled through an average run-length constraint. For exact finite-sample analysis, the paper introduces a survival-weighted average success criterion, which represents the probability of successfully detecting a randomly encountered change opportunity conditional on the detector being active at its onset. It is established that this criterion admits an exact representation as the expected \textbf{truncated} Shiryaev--Roberts (TSR) statistic at the stopping time normalized by the average run length, and it characterizes its exactly optimal stopping rule. The optimal procedure has finite memory and aggregates the likelihood-ratio evidence corresponding to all possible change onsets within the most recent window and compares the resulting TSR statistic with a \textbf{state-dependent} continuation boundary obtained from an optimal-stopping formulation.
Comments54 pages, 14 figures
