During my internship in STOR-i, I investigated (supervised by Chris Nemeth) the use of particle filters algorithms for parameter estimation. The motivation of the project lied in the common necessity to estimate hidden processes. They, in fact, are at the heart of many problems in statistics, signal processing, engineering. In particular, my project was inspired by the need to estimate the state of a target (defined, for example, by its position and velocity). When tracking targets, it is often possible to only have partial and noisy observations, on which we need to work in order to estimate the real underlying process. I first looked into the current literature on the subject, and later assess some of the existing models by using particle filters methods. For an introduction to the topic and an account of my work, please refer to the presentation I gave at the end of my experience , and the poster I produced.
As part of my BSc, I undertook, supervised by Dr. Andreas Grothey a project on Semidefinite Programming and its application to the Pooling problem.
Semidefinite programming (or SDP), a popular field since the 1990s, is an extension of linear programming over the cone of positive semidefinite matrices. My project provides an overview of the main theoretical notions, and proceeds to apply them to the pooling problem, a common problem in the petroleum industry. This models the production of blends according to some given requirements, using intermediate mixes of the original raw materials. My research looked into approaching the pooling problem, originally modelled as a nonconvex and nonlinear program, with a semidefinite programming relaxation.
Here you can find the report providing an account of the work done.
Before starting my MRes in Statistics and OR, I spent the summer on placement in Shellís Statistic and Chemometrics department in Thornton. Supervised by Phil Jonathan, I worked on extreme value statistics applied to the understanding of extreme wave conditions in a variety of ocean basins. I specifically looked into the use of spline based methodology to incorporate spatial, directional and temporal effects in extreme value models.
STOR-i MRes - Markov Decision Processes
During my MRes I did some research on Markov Decision Processes.
A brief report on the subject is available here here, together with the poster I presented on the topic.
I have just started my MRes year of the STOR-i program, and I do not currently have any research projects underway. I will update this section with a record of all research projects undertaken.