Sequential multiple testing and quickest change detection for dependent data streams

Chaudhuri, Anamitra

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https://hdl.handle.net/2142/121480 Copy

Description

Title

Sequential multiple testing and quickest change detection for dependent data streams

Author(s)

Chaudhuri, Anamitra

Issue Date

2023-07-12

Director of Research (if dissertation) or Advisor (if thesis)

Fellouris, Georgios

Doctoral Committee Chair(s)

Fellouris, Georgios

Committee Member(s)

• Chatterjee, Sabyasachi
• Veeravalli, Venugopal
• Martinsek, Adam

Department of Study

Statistics

Discipline

Statistics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• Sequential multiple testing
• Detection and isolation
• Anomaly detection
• Asymptotic optimality
• Dependence structure
• Sequential change point detection
• Sampling constraint
• CUSUM
• quickest detection

Abstract

The area of sequential analysis considers the statistical procedures which are applied to the scenarios where neither the sample size nor the complete collection of data is available to the practitioners in advance. Instead, the observations are collected sequentially in real-time, and we stop sampling according to some pre-specified stopping criterion which suggests that we have enough evidence to make certain decisions. The general objective in this discipline is to make reliable decisions as quickly as possible while keeping the probability of erroneous decisions under control. This dissertation addresses two research problems in this field. In the first chapter, we consider the problem of joint sequential detection and isolation in the context of multiple, not necessarily independent, data streams. A multiple testing framework is proposed, where each hypothesis corresponds to a different subset of data streams, the sample size is a stopping time of the observations, and the probabilities of four kinds of error are controlled below distinct, user-specified levels. Two of these errors reflect the detection component of the formulation, whereas the other two the isolation component. The optimal expected sample size is characterized to a first-order asymptotic approximation as the error probabilities go to 0. Different asymptotic regimes, expressing different prioritizations of the detection and isolation tasks, are considered. A novel, versatile family of testing procedures is proposed, in which two distinct, in general, statistics are computed for each hypothesis, one addressing the detection task and the other the isolation task. Tests in this family, of various computational complexities, are shown to be asymptotically optimal under different setups. The general theory is applied to the detection and isolation of anomalous, not necessarily independent, data streams, as well as to the detection and isolation of an unknown dependence structure. In the second chapter, we consider the problem of sequentially detecting a change in the joint distribution of multiple information sources when it is possible to sample only some of them at each time instance. Specifically, it is assumed that the random vectors, each of whose elements are generated from the individual sources, are independent over time and that the global marginal distribution of this random vector is changed at some unknown time. The problem is to stop sampling as quickly as possible after the change while controlling the false alarm rate and with/without assuming any prior information on the nature of the change. A computationally efficient joint sampling and change-detection rule is proposed and is shown to achieve the smallest possible worst-case conditional expected detection delay among all processes that satisfy the same constraints to a first-order approximation as the false alarm rate goes to 0 if under every possible global post-change distribution, whenever the local distribution of any samplable subsets is affected, it is affected in the most informative and homogeneous way. When it is not the case, we further extend this rule and provide an upper bound for its asymptotic relative efficiency.

Graduation Semester

2023-08

Type of Resource

Thesis

Copyright and License Information

Copyright 2023 Anamitra Chaudhuri

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