Quickest Detection under False Discovery Rate and Communication Constraints

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http://urn.fi/URN:NBN:fi:hulib-202109293767
Julkaisun nimi: Quickest Detection under False Discovery Rate and Communication Constraints
Toissijainen nimi: Reaaliaikainen käännepisteiden havainta hylkäysvirheaste- ja kommunikaatiorajoitteilla
Tekijä: Halme, Topi
Muu tekijä: Helsingin yliopisto, Matemaattis-luonnontieteellinen tiedekunta
University of Helsinki, Faculty of Science
Helsingfors universitet, Matematisk-naturvetenskapliga fakulteten
Julkaisija: Helsingin yliopisto
Päiväys: 2021
Kieli: eng
URI: http://urn.fi/URN:NBN:fi:hulib-202109293767
http://hdl.handle.net/10138/334692
Opinnäytteen taso: pro gradu -tutkielmat
Koulutusohjelma: Matematiikan ja tilastotieteen maisteriohjelma
Master's Programme in Mathematics and Statistics
Magisterprogrammet i matematik och statistik
Opintosuunta: Tilastotiede
Statistics
Statistik
Tiivistelmä: In a quickest detection problem, the objective is to detect abrupt changes in a stochastic sequence as quickly as possible, while limiting rate of false alarms. The development of algorithms that after each observation decide to either stop and declare a change as having happened, or to continue the monitoring process has been an active line of research in mathematical statistics. The algorithms seek to optimally balance the inherent trade-off between the average detection delay in declaring a change and the likelihood of declaring a change prematurely. Change-point detection methods have applications in numerous domains, including monitoring the environment or the radio spectrum, target detection, financial markets, and others. Classical quickest detection theory focuses settings where only a single data stream is observed. In modern day applications facilitated by development of sensing technology, one may be tasked with monitoring multiple streams of data for changes simultaneously. Wireless sensor networks or mobile phones are examples of technology where devices can sense their local environment and transmit data in a sequential manner to some common fusion center (FC) or cloud for inference. When performing quickest detection tasks on multiple data streams in parallel, classical tools of quickest detection theory focusing on false alarm probability control may become insufficient. Instead, controlling the false discovery rate (FDR) has recently been proposed as a more useful and scalable error criterion. The FDR is the expected proportion of false discoveries (false alarms) among all discoveries. In this thesis, novel methods and theory related to quickest detection in multiple parallel data streams are presented. The methods aim to minimize detection delay while controlling the FDR. In addition, scenarios where not all of the devices communicating with the FC can remain operational and transmitting to the FC at all times are considered. The FC must choose which subset of data streams it wants to receive observations from at a given time instant. Intelligently choosing which devices to turn on and off may extend the devices’ battery life, which can be important in real-life applications, while affecting the detection performance only slightly. The performance of the proposed methods is demonstrated in numerical simulations to be superior to existing approaches. Additionally, the topic of multiple hypothesis testing in spatial domains is briefly addressed. In a multiple hypothesis testing problem, one tests multiple null hypotheses at once while trying to control a suitable error criterion, such as the FDR. In a spatial multiple hypothesis problem each tested hypothesis corresponds to e.g. a geographical location, and the non-null hypotheses may appear in spatially localized clusters. It is demonstrated that implementing a Bayesian approach that accounts for the spatial dependency between the hypotheses can greatly improve testing accuracy.
Avainsanat: Quickest detection
Multiple hypothesis testing
False discovery rate
Sequential inference


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