In this paper we consider the problem of quickly detecting changes in hidden Markov models (HMMs) in a Bayesian setting, as well as several structured generalisations including changes in statistically periodic processes, quickest detection of a Markov process across a sensor array, quickest detection of a moving target in a sensor network and quickest change detection (QCD) in multistream data. Our main result establishes an optimal Bayesian HMM QCD rule with a threshold structure. This framework and proof techniques allow us to elegantly establish optimal rules for the structured generalisations by showing that these problems are special cases of the Bayesian HMM QCD problem. The threshold structure enables us to develop bounds to characterise the performance of our optimal rule and provide an efficient method for computing the test statistic. Finally, we examine the performance of our rule in several simulation examples and propose a technique for calculating the optimal threshold.
翻译:在本文中,我们考虑了在巴伊西亚环境中迅速发现隐蔽的Markov模型变化的问题,以及若干结构化的概略,包括统计周期过程的变化,在传感器阵列中最迅速地探测Markov过程,在传感器网中最迅速地探测移动目标,在多流数据中最迅速的改变探测(QCD),我们的主要结果确立了一种带有门槛结构的最佳的Bayesian HMM QCD规则。这一框架和验证技术使我们能够通过显示这些问题是巴伊西亚HMM QCD问题的特殊案例,来优雅地为结构化的概略制定最佳规则。这一阈值结构使我们能够制定界限,以描述我们最佳规则的性能,并为计算测试统计数据提供有效的方法。最后,我们在若干模拟实例中审视了我们的规则的性能,并提出了计算最佳阈值的技术。