Markwick, Dean;
(2020)
Bayesian Nonparametric Hawkes Processes with Applications.
Doctoral thesis (Ph.D), UCL (University College London).
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Abstract
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.
| Type: | Thesis (Doctoral) |
|---|---|
| Qualification: | Ph.D |
| Title: | Bayesian Nonparametric Hawkes Processes with Applications |
| Event: | UCL (University College London) |
| Open access status: | An open access version is available from UCL Discovery |
| Language: | English |
| Additional information: | Copyright © The Author 2020. Original content in this thesis is licensed under the terms of the Creative Commons Attribution 4.0 International (CC BY 4.0) Licence (https://creativecommons.org/licenses/by/4.0/). Any third-party copyright material present remains the property of its respective owner(s) and is licensed under its existing terms. Access may initially be restricted at the author’s request. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10109374 |
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