多源贝叶斯序贯变化检测

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摘要翻译：
假设几个独立的复合Poisson和Wiener过程的局部特征在某个不可观测的无序时间突然同时发生变化。问题是在故障发生后尽可能快地检测出故障时间，同时最大限度地降低误报警率。这些问题产生于生产系统中的产品质量管理和防止传染病的传播。如果有多个独立的信息源，则检测规则的快速性和准确性将大大提高。早期关于连续时间序列变化检测的工作没有为几个标记计数数据和连续变化信号同时可观察的情况提供最佳规则。本文针对这类问题，提出了当标记计数数据为独立的复合泊松过程，连续变化的信号为多维Wiener过程时的最优贝叶斯序列检测规则。首先利用跳跃算子将跳跃扩散过程的辅助最优停止问题转化为纯扩散过程的一系列最优停止问题，从而解决了一个跳跃扩散过程的辅助最优停止问题。这种方法是新的，在其他应用中也非常有用，因为它允许使用强大的扩散最优停止理论。
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英文标题：
《Multisource Bayesian sequential change detection》
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作者：
Savas Dayanik, H. Vincent Poor, Semih O. Sezer
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最新提交年份：
2008
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分类信息：

一级分类：Mathematics        数学
二级分类：Statistics Theory        统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Computer Science        计算机科学
二级分类：Information Theory        信息论
分类描述：Covers theoretical and experimental aspects of information theory and coding. Includes material in ACM Subject Class E.4 and intersects with H.1.1.
涵盖信息论和编码的理论和实验方面。包括ACM学科类E.4中的材料，并与H.1.1有交集。
--
一级分类：Mathematics        数学
二级分类：Information Theory        信息论
分类描述：math.IT is an alias for cs.IT. Covers theoretical and experimental aspects of information theory and coding.
它是cs.it的别名。涵盖信息论和编码的理论和实验方面。
--
一级分类：Mathematics        数学
二级分类：Probability        概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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一级分类：Statistics        统计学
二级分类：Statistics Theory        统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
--

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英文摘要：
  Suppose that local characteristics of several independent compound Poisson and Wiener processes change suddenly and simultaneously at some unobservable disorder time. The problem is to detect the disorder time as quickly as possible after it happens and minimize the rate of false alarms at the same time. These problems arise, for example, from managing product quality in manufacturing systems and preventing the spread of infectious diseases. The promptness and accuracy of detection rules improve greatly if multiple independent information sources are available. Earlier work on sequential change detection in continuous time does not provide optimal rules for situations in which several marked count data and continuously changing signals are simultaneously observable. In this paper, optimal Bayesian sequential detection rules are developed for such problems when the marked count data is in the form of independent compound Poisson processes, and the continuously changing signals form a multi-dimensional Wiener process. An auxiliary optimal stopping problem for a jump-diffusion process is solved by transforming it first into a sequence of optimal stopping problems for a pure diffusion by means of a jump operator. This method is new and can be very useful in other applications as well, because it allows the use of the powerful optimal stopping theory for diffusions.
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PDF链接：
https://arxiv.org/pdf/708.0224

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关键词：贝叶斯 Experimental Applications SIMULTANEOUS Transforming 防止 Wiener 计数 复合 序列