10th World Congress in Probability and Statistics

Organized Contributed Session (live Q&A at Track 3, 10:30PM KST)

Organized 29

Sequential Analysis and Applications (Organizer: Alexander Tartakovsky)

Conference
10:30 PM — 11:00 PM KST
Local
Jul 21 Wed, 9:30 AM — 10:00 AM EDT

Asymptotically optimal control of FDR and related metrics for sequential multiple testing

Jay Bartroff (University of Southern California)

3
I will discuss asymptotically optimal multiple testing procedures for sequential data in the context of prior information on the number of false null hypotheses, for controlling FDR/FNR, pFDR/pFNR, and other metrics. These procedures are closely related to those proposed and shown by Song & Fellouris (2017) to be asymptotically optimal for controlling type 1 and 2 familywise error rates (FWEs). We show that by appropriately adjusting the critical values of the Song-Fellouris procedures, they can be made asymptotically optimal for controlling any multiple testing error metric that is bounded between multiples of FWE in a certain sense. In addition to FDR/FNR and pFDR/pFNR this includes other metrics like the per-comparison and per-family error rates, and the false positive rate. Our setup includes asymptotic regimes in which the number of null hypotheses approaches infinity.

Nearly optimal sequential detection of signals in correlated Gaussian noise

Grigory Sokolov (Xavier University)

3
Detecting an object in AR(p) noise assuming the intensity of the signal is not specified is a problem of interest to many practitioners.
To this end we examine three procedures: (i) an adaptive version of the sequential probability ratio test (SPRT) built upon one-stage delayed estimators of the unknown signal intensity; (ii) the generalized SPRT; and (iii) the non-adaptive double SPRT (2-SPRT). The generalized SPRT has certain drawbacks in selecting thresholds to guarantee the upper bounds on error probabilities, but may appear to be slightly more efficient than the adaptive SPRT.
However, simulations show that the loss in performance of the adaptive SPRT compared to the generalized SPRT is very minor, so—coupled with the error probability guarantee—the adaptive SPRT can be recommended for practical applications.
And although the non-adaptive 2-SPRT is not asymptotically optimal for all signal strength values, it does offer benefits at the worst point in the indifference zone.

Acknowledgement: The work of Alexander Tartakovsky was supported in part by the Russian Science Foundation Grant 18-19-00452 at the Moscow Institute of Physics and Technology.

A unified approach for solving sequential selection problems

Yaakov Malinovsky (University of Maryland)

2
In this work we develop a unified approach for solving a wide class of sequential selection problems. This class includes, but is not limited to, selection problems with no-information, rank-dependent rewards, and considers both fixed as well as random problem horizons. We demonstrate that our approach allows exact and efficient computation of optimal policies and various performance metrics thereof for a variety of sequential selection problems, several of which have not been solved to date.

Sequential change detection by optimal weighted l2 divergence

Yao Xie (Georgia Institute of Technology)

2
We present a new non-parametric statistic, called the weighed l2 divergence, based on empirical distributions for sequential change detection. We start by constructing the weighed l2 divergence as a fundamental building block for two-sample tests and change detection. The proposed statistic is proved to attain the optimal sample complexity in the offline setting. We then study the sequential change detection using the weighed l2 divergence and characterize the fundamental performance metrics, including the average run length (ARL) and the expected detection delay (EDD). We also present practical algorithms to find the optimal projection to handle high-dimensional data and the optimal weights, which is critical to quick detection since, in such settings, there are not many post-change samples. Simulation results and real data examples are provided to validate the good performance of the proposed method.

Detection of temporary disorders

Michael Baron (American University)

2
Change-point detection methods are proposed for the case of temporary failures, or transient changes, when an unexpected disorder is ultimately followed by an adjustment and return to the initial state. A known base distribution of the in-control state changes to different unknown distributions for unknown periods of time. Sequential and retrospective methods are proposed for the detection and estimation of each pair of change-points. Examples of similar problems are shown in quality and process control, energy finance, and statistical genetics, although the meaning of disorder and adjustment change-points is quite different in these applications.

Q&A for Organized Contributed Session 29

1
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Session Chair

Alexander Tartakovsky (Moscow Institute of Physics and Technology )

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