通过噪声观测跟踪停时
Tracking Stopping Times Through Noisy Observations
摘要：
提出了一种新的最快检测设置，它是著名的贝叶斯变点检测模型的推广。设\{（X_i，Y_i）\}_{i \geq 1}是随机变量对序列，S是关于\{X_i\}_{i \geq 1}的停时.问题是找到一个关于\{Y_i\}_{i \geq 1}的停时T，它最优地跟踪S，在这个意义上，T最小化预期反应延迟E（T-S）^+，同时保持虚警概率P（T<S）低于给定的阈值α \in [0，1]。这个问题公式适用于几个领域，如通信，检测，预测和质量控制。我们的结果涉及到X_i和Y_i取值于有限字母表的情形，以及S被某个正整数κ有界的情形.通过对停时树结构的分析，利用初等方法给出了一个计算所有α \in [0，1]的最优平均反应延迟的算法，并构造了相应的最优停时T.在\{（X_i，Y_i）\}_{i \geq 1}和S的一定条件下，算法的运行时间是关于κ的多项式.
英文摘要：
A novel quickest detection setting is proposed which is a generalization of the well-known Bayesian change-point detection model. Suppose \{(X_i,Y_i)\}_{i\geq 1} is a sequence of pairs of random variables, and that S is a stopping time with respect to \{X_i\}_{i\geq 1}. The problem is to find a stopping time T with respect to \{Y_i\}_{i\geq 1} that optimally tracks S, in the sense that T minimizes the expected reaction delay E(T-S)^+, while keeping the false-alarm probability P(T<S) below a given threshold α\in [0,1]. This problem formulation applies in several areas, such as in communication, detection, forecasting, and quality control. Our results relate to the situation where the X_i's and Y_i's take values in finite alphabets and where S is bounded by some positive integer κ. By using elementary methods based on the analysis of the tree structure of stopping times, we exhibit an algorithm that computes the optimal average reaction delays for all α\in [0,1], and constructs the associated optimal stopping times T. Under certain conditions on \{(X_i,Y_i)\}_{i\geq 1} and S, the algorithm running time is polynomial in κ.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
