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There is now a CONTENT FREEZE for Mercury while we switch to a new platform. It began on Friday, March 10 at 6pm and will end on Wednesday, March 15 at noon. No new content can be created during this time, but all material in the system as of the beginning of the freeze will be migrated to the new platform, including users and groups. Functionally the new site is identical to the old one. webteam@gatech.edu
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Dr. Mark Davenport, ECE , Advisor
Dr. Christopher Rozell, ECE
Dr. Le Song, CoC
Dr. Eva Dyer, BME
Dr. Yao Xie, ISyE
Abstract:
The purpose of this work is to improve our ability to extract information from data generated by Poisson and Hawkes processes. Our principal focus is to provide improvements to the theory for parameter estimation under these models. To this end, we present novel bounds on the estimation of model parameters for linear Poisson processes. Earlier results applied to Poisson counting processes, but we improve upon these while addressing the broader class of Poisson arrival processes. For Hawkes processes, we present asymptotic parameter estimation bounds. These provide an enhanced understanding of how the structure of a Hawkes process affects our ability to estimate its parameters. We explore the capability of Hawkes processes to model telecommunication networks and to aid in the discovery of connections within such networks. We also discuss the considerations and extensions that should be employed when utilizing this model for this application. Finally, we discuss a way that the Hawkes process can be used to recognize event cascades within a network, rather than mere nodal connectivity. This is particularly relevant to telecommunication applications, as relay nodes often serve as intermediaries between others.
