PhD project : Structured Multivariate Extreme Value Models for Flood Risk Estimation

Supervisor(s): Prof Jenny Wadsworth and Prof Thordis Thorarinsdottir

The aim of the project is to develop statistical methodologies that will allow us to analyse extremes of river flows at multiple points on river networks simultaneously. We approach this problem through the novel framework of geometric extreme value theory, since this has the potential to handle the complex dependence structures that may be observed in river flow extremes. However, current methodologies within this framework are limited to a relatively low number of dimensions. This is insufficient for the purposes of flood risk estimation, since for these types of analyses, we utilise river flow data from gauge stations on a river network, which is often of the order 10-20. In the project we will focus on extending the current methodologies by addressing some of the issues associated with inference in higher dimensions, exploiting the structure of the river network and incorporating covariates such as rainfall or geographical location within our model.

MPhys project in collaboration with Manchester City Group (MCG): Developing a Dynamical System to Rank Footballers Based on Duel Performance

Supervisor(s): Prof Terry Wyatt and Dr Lewis Whitehouse

  • Implemented Elo rating system to rank players who took part in duels in all games of the Premier League from the 2019 season until Nov 2022.
  • Optimised the performance distribution, the free parameters, and the burn-in period.
  • Investigated the impact of external factors, such as home advantage or pitch position on the win percentage.
  • Future work – investigate further external factors and extend the rating system to more leagues.
  • Presented the work to the data analysts in the MCG and wrote a 20-page report.

STOR-i research internship: Time Series Analysis via Kalman Filtering

Supervisor(s): Dr Maddie Smith

  • Applied Dynamic Linear Models (DLMs) to time series that do not show a particular trend or seasonal variation.
  • Used the local level model to generate observed data.
  • Applied the Kalman filter to perform inference on the unknown state vector and forecast.
  • Tested the performance of the Kalman filter on multiple observation sequences and sequences of missing data.