Sequential multiple testing with generalized error control: An asymptotic optimality theory

Song, Yanglei; Fellouris, Georgios

doi:10.1214/18-aos1737

Cited by 30 publications

(27 citation statements)

References 43 publications

(145 reference statements)

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“…By a similar argument as we developed when proving (25), the RHS of (35) decreases exponentially with n. Hence, (22) follows.…”

Section: A Proof Of Theoremsupporting

confidence: 53%

“…In this paper, we focus on asymptotically optimal strategies with low computational complexity for sequential search of a target over multiple processes. Different models considered the case of searching for targets without constraints on the probing capacity, whereas all processes are probed at each given time (i.e., K = M, which is a special case of the setting considered in this paper) [17], [22], [23], [35].…”

Section: B Related Workmentioning

confidence: 99%

See 1 more Smart Citation

Searching for Anomalies Over Composite Hypotheses

Hemo

Gafni

Cohen

et al. 2020

IEEE Trans. Signal Process.

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The problem of detecting anomalies in multiple processes is considered. We consider a composite hypothesis case, in which the measurements drawn when observing a process follow a common distribution with an unknown parameter (vector), whose value lies in normal or abnormal parameter spaces, depending on its state. The objective is a sequential search strategy that minimizes the expected detection time subject to an error probability constraint. We develop a deterministic search algorithm with the following desired properties. First, when no additional side information on the process states is known, the proposed algorithm is asymptotically optimal in terms of minimizing the detection delay as the error probability approaches zero. Second, when the parameter value under the null hypothesis is known and equal for all normal processes, the proposed algorithm is asymptotically optimal as well, with better detection time determined by the true null state. Third, when the parameter value under the null hypothesis is unknown, but is known to be equal for all normal processes, the proposed algorithm is consistent in terms of achieving error probability that decays to zero with the detection delay. Finally, an explicit upper bound on the error probability under the proposed algorithm is established for the Bar Hemo, Tomer Gafni and Kobi Cohen are with the

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“…By a similar argument as we developed when proving (25), the RHS of (35) decreases exponentially with n. Hence, (22) follows.…”

Section: A Proof Of Theoremsupporting

confidence: 53%

Section: B Related Workmentioning

confidence: 99%

Searching for Anomalies Over Composite Hypotheses

Hemo

Gafni

Cohen

et al. 2020

IEEE Trans. Signal Process.

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show abstract

“…We assume that the prior distribution for the change points, and the pre-and post-change distributions are known, which is a standard assumption in single-stream Bayesian sequential change detection (e.g., Shiryaev, 1963). Similar assumptions are adopted in recent developments on multi-stream sequential multiple testing (Song and Fellouris, 2019) and Statistica Sinica: Newly accepted Paper (accepted author-version subject to English editing) 2.1 Bayesian Change-point Model for Parallel Streams multi-stream sequential change detection (Chen, Zhang and Poor, 2020).…”

Section: Bayesian Change-point Model For Parallel Streamsmentioning

confidence: 99%

Compound Sequential Change-point Detection in Parallel Data Streams

Chen¹,

Li²

2023

STAT SINICA

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We consider sequential change-point detection in parallel data streams, where each stream has its own change point. Once a change is detected in a data stream, this stream is deactivated permanently. The goal is to maximize the normal operation of the pre-change streams, while controlling the proportion of post-change streams among the active streams at all time points. Taking a Bayesian formulation, we develop a compound decision framework for this problem. A procedure is proposed that is uniformly optimal among all sequential procedures which control the expected proportion of post-change streams at all time points. We also investigate the asymptotic behavior of the proposed method when the number of data streams grows large. Numerical examples are provided to illustrate the use and performance of the proposed method.

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“…Different from our goal in developing dynamic statistical inference, their settings are completely from ours because they aim to minimize the overall expectation delay while controlling the average run length under the null hypothesis that none of the datastreams experience changes. Recent works on sequential testing based on the sequential probability ratio test (SPRT) rules such as Bartroff (2018) and Song and Fellouris (2019) are computationally intensive, making it infeasible for large-scale studies such as those arising from IHS where millions of tests are conducted simultaneously at each time.…”

Section: Connections To Existing Workmentioning

confidence: 99%

Dynamic statistical inference in massive datastreams

Wang¹,

Du²,

Zou³

et al. 2021

Preprint

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Modern technological advances have expanded the scope of applications requiring analysis of large-scale datastreams that comprise multiple indefinitely long time series. There is an acute need for statistical methodologies that perform online inference and continuously revise the model to reflect the current status of the underlying process. In this manuscript, we propose a dynamic statistical inference framework-named dynamic tracking and screening (DTS)-that is not only able to provide accurate estimates of the underlying parameters in a dynamic statistical model, but also capable of rapidly identifying irregular individual streams whose behavioral patterns deviate from the majority. Concretely, by fully exploiting the sequential feature of datastreams, we develop a robust estimation approach under a framework of varying coefficient model. The procedure naturally accommodates unequally-spaced design points and updates the coefficient estimates as new data arrive without the need to store historical data. A data-driven choice of an optimal smoothing parameter is accordingly proposed. Furthermore, we suggest a new multiple testing procedure tailored to the streaming environment. The resulting DTS scheme is able to adapt time-varying structures appropriately, track changes in the underlying models, and hence maintain high accuracy in detecting time periods during which individual streams exhibit irregular behavior. Moreover, we derive rigorous statistical guarantees of the procedure and investigate its finite-sample performance through simulation studies. We demonstrate the proposed methods through a mobile health example to estimate the timings when subjects' sleep and physical activities have unusual influence upon their mood.

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Sequential multiple testing with generalized error control: An asymptotic optimality theory

Cited by 30 publications

References 43 publications

Searching for Anomalies Over Composite Hypotheses

Searching for Anomalies Over Composite Hypotheses

Compound Sequential Change-point Detection in Parallel Data Streams

Dynamic statistical inference in massive datastreams

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