General asymptotic Bayesian theory of quickest change detection
General asymptotic Bayesian theory of quickest change detection
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DOI：
10.1137/s0040585x97981202
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发表时间：
2004-01-01
影响因子：
0.6
通讯作者：
Veeravalli, VV
中科院分区：
文献类型：
--
作者：
Tartakovsky, AG;Veeravalli, VV
最佳检测程序检测独立同分布（i.i.d.）在贝叶斯设置中的序列是由Shiryaev在20世纪60年代导出的。然而，这个过程中的平均检测延迟和虚警概率的性能分析一直是一个悬而未决的问题。在本文中，我们开发了一个一般的渐近变点检测理论，不限于一个限制性的独立同分布。假设特别是，我们调查的性能一般离散时间随机模型的Shiryaev过程中的渐近设置，其中虚警概率接近零。我们证明了Shiryaev方法在一般非独立同分布情形下是渐近最优的。在温和的条件下。我们还表明，两个流行的非贝叶斯检测程序，即页面和Shiryaev-Roberts-Pollak程序，一般不是最佳的（甚至渐近）贝叶斯准则下。本研究的结果被证明是特别重要的，在研究的渐近分散变化检测程序。
The optimal detection procedure for detecting changes in independent and identically distributed (i.i.d.) sequences in a Bayesian setting was derived by Shiryaev in the 1960s. However, the analysis of the performance of this procedure in terms of the average detection delay and false alarm probability has been an open problem. In this paper, we develop a general asymptotic change-point detection theory that is not limited to a restrictive i.i.d. assumption. In particular, we investigate the performance of the Shiryaev procedure for general discrete-time stochastic models in the asymptotic setting, where the false alarm probability approaches zero. We show that the Shiryaev procedure is asymptotically optimal in the general non-i.i.d. case under mild conditions. We also show that the two popular non-Bayesian detection procedures, namely the Page and the Shiryaev-Roberts-Pollak procedures, are generally not optimal (even asymptotically) under the Bayesian criterion. The results of this study are shown to be especially important in studying the asymptotics of decentralized change detection procedures.