Asymptotic Exponentiality of the Distribution of First Exit Times for a Class of Markov Processes with Applications to Quickest Change Detection

Pollak, Moshe; Тартаковский, Александр Г; Tartakovskii, Alexander G

doi:10.4213/tvp2444

Cited by 11 publications

(13 citation statements)

References 15 publications

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“…With a constant threshold, as the example shows, P 0 (τ ≤ N) ≤ α can only be achieved if P 0 (τ = 1) ≤ α. This is true more generally; recall that for independent or weakly dependent observations, it has been shown, for example, in Pollak and Tartakovsky (2009) that the distribution of τ is approximately exponential when the threshold b is large but constant.…”

Section: More Control Over False Alarmsmentioning

confidence: 89%

“…as a performance criterion. It has, however, since been shown that the probability in (1) is approximately exponential for small α, if observations are independent or weakly dependent (Pollak and Tartakovsky 2009). Therefore, by the memoryless property of the exponential distribution, we have P 0 (n ≤ T < n + N) ≈ P 0 (T ≤ N).…”

Section: Introductionmentioning

confidence: 96%

“…Since such expressions are not known in general, we first show how the distribution of the window-limited stopping time can be described in terms of recursive integral equations. For detection procedures without windows, integral equations have been derived based on renewal theory (Page 1954;Pollak and Tartakovsky 2009;Siegmund 1985); here we follow a different approach, using results on the maximum of autoregressive processes (Withers and Nadarajah 2014). We remark that the obtained recursions are not restricted to CUSUM but hold for a broad class of testing procedures including exponentially weighted moving average schemes (EWMA, see Roberts 1959).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Practical Aspects of False Alarm Control for Change Point Detection: Beyond Average Run Length

Kühn

Mandjes

Taimre

2018

Methodol Comput Appl Probab

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A popular method for detecting changes in the probability distribution of a sequence of observations is CUSUM, which proceeds by sequentially evaluating a loglikelihood ratio test statistic and comparing it to a predefined threshold; a change point is detected as soon as the threshold is exceeded. It is desirable to choose the threshold such that the number of false alarms is kept to a specified level. Traditionally, the number of false alarms is measured by the average run length-the expected stopping time until the first false alarm. However, this is does not in general allow one to control the number of false alarms at every particular time instance. Thus, in this paper two stronger false alarm criteria are considered, for which approximation methods are investigated to facilitate the selection of a threshold.

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Section: More Control Over False Alarmsmentioning

confidence: 89%

Section: Introductionmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Practical Aspects of False Alarm Control for Change Point Detection: Beyond Average Run Length

Kühn

Mandjes

Taimre

2018

Methodol Comput Appl Probab

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“…For large threshold values, asymptotically sharp approximations can be derived as follows. It follows from Pollak and Tartakovsky (2008a) and Tartakovsky (2005) and c 5 = 5v 2 . In order to derive an asymptotic approximation for SADD T min , note that 1 T min h ≤ 1 i h for all i = 1 N and, hence,…”

Section: Tartakovsky and Veeravallimentioning

confidence: 99%

“…The asymptotic performance (2.13) is attained again for the centralized CUSUM and Shiryaev-Roberts tests given in (2.9), with the thresholds h chosen so that PFA T c h = and PFA T ˆ c h = . To this end, we may use the results of Pollak and Tartakovsky (2008a) and Tartakovsky (2005) …”

Section: Uniform Formulationmentioning

confidence: 99%

Asymptotically Optimal Quickest Change Detection in Distributed Sensor Systems

Tartakovsky

Veeravalli

2008

Sequential Analysis

125

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State-of-the-Art in Sequential Change-Point Detection

Polunchenko

Tartakovsky

2011

Methodol Comput Appl Probab

114

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We provide an overview of the state-of-the-art in the area of sequential change-point detection assuming discrete time and known pre- and post-change distributions. The overview spans over all major formulations of the underlying optimization problem, namely, Bayesian, generalized Bayesian, and minimax. We pay particular attention to the latest advances in each. Also, we link together the generalized Bayesian problem with multi-cyclic disorder detection in a stationary regime when the change occurs at a distant time horizon. We conclude with two case studies to illustrate the cutting edge of the field at work.Comment: 34 pages, accepted for publication in Methodology and Computing in Applied Probabilit

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Asymptotic Exponentiality of the Distribution of First Exit Times for a Class of Markov Processes with Applications to Quickest Change Detection

Cited by 11 publications

References 15 publications

Practical Aspects of False Alarm Control for Change Point Detection: Beyond Average Run Length

Practical Aspects of False Alarm Control for Change Point Detection: Beyond Average Run Length

Asymptotically Optimal Quickest Change Detection in Distributed Sensor Systems

State-of-the-Art in Sequential Change-Point Detection

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