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Title: Bayesian nonparametric Hawkes processes with applications
Author: Markwick, Dean
ISNI:       0000 0004 9359 5911
Awarding Body: UCL (University College London)
Current Institution: University College London (University of London)
Date of Award: 2020
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Many statistical problems involve modelling the times at which events occur. There are cases where events can occur in clusters with sudden jumps in the total number of occurrences. To model such data an intensity function can be constructed which describes the probability of an event occurring at a specific time. The Hawkes process is a point process model with a conditional intensity function that provides a change in intensity for each event occurrence and as such the Hawkes process can be used to explain event clustering. The flexibility and extendability of the Hawkes process will be highlighted in this thesis. I extend the Hawkes process by using nonparametric Bayesian methods where different components of the Hawkes process are constructed using a Dirichlet process which is a Bayesian prior for distributions. This allows for a data driven approach and removes the need for parametric assumptions. This Bayesian approach also allows for a hierarchical structure to be integrated in the models where appropriate. These extended Hawkes process are applied to different application domains including: extreme value theory, financial trading and soccer goal occurrence modelling. Each new application introduces a different extension to the Hawkes process and illustrates how it improves on existing methodology. From this research I also wrote a new software package for using Dirichlet processes. This software enables users to easily construct Dirichlet process objects that can incorporated into existing inference workflows. This allows users to introduce nonparametric methods without needing to program their own inference methods.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available