## My Research

Below you will find examples of my current work and research. As I progress through my MRes and PhD I will keep this page updated regularly.

For those who are interested, a copy of my CV can be found here.

My PhD is titled 'Novel Methods for the Detection of Emergent Behaviour in Streamed Data'. This project is in partnership with BT, and the requirement is to detect the anomalous data in real time as this may correspond to a fault on the BT network. The fastest possible detection of these faults will allow for BT to reconnect customers quicker, minimising downtime and maximising customer satisfaction.

On a technical level the project requires the fastest possible detection of an anomaly in a high dimensional data stream. As in the literature, a balance must be struck between minimsing the average detection delay whilst also controlling the false alarm rate. Furthermore, a decision must be made of how to handle the high dimensionality; indeed, having more data points than data streams means that inference can be more challenging than in the typical low dimensional setting.

One unique challenge the project possesses is that the data streams exhibit smooth changes over time. This means that, in contrast to the existing online changepoint detection literature, the anomalies are not clearly defined by jump discontinuities but instead by continuous, emergent changes. This means that existing tools such as the CUSUM, MOSUM, or NP-PELT are ineffective at solving this problem.

On the other hand, several approaches exist for the detection of smoothly emerging anomalies for data that has been observed in full. The issue with this, however, is that this means that detection can only take place at the end of a day when the data has been observed in full. This is of no interest to BT, as it does not allow detection of the anomalies in real time.

The goal of this PhD, then, is to combine these two fields to allow for detection of smooth changes in an online setting. This will be a novel contribution of the project, unseen before in the existing change detection literature.

The first term of the MRes year involves studying modules that form the foundations of research in STOR. These are:

- Probability and Stochastic Processes
- Likelihood Inference
- Bayesian Inference
- Computational Intensive Methods
- Optimisation

In addition to this skills such as programming, presenting, and problem solving are taught.

In the second term specialisation begins as topics research in STOR is focussed on are covered. My research projects were focussed on the field of functional data in particular. This provided me with an excellent platform for which to build upon as I started my PhD project.

Prior to joining STOR-i I completed a project investigating a vehicle routing problem. In particular this involved modelling risk for road transportation of hazardous materials. A key part of this was first building a model for a road network, and then using various methods to model the risk before using Policy Iteration to find the route with the minimum risk.

Further work involved finding routes with the least time, or cost, associated with their journey as well as modelling different forms of risk.

Finally, work was done to try and model the accidents in the network as Poisson Processes in order to pinpoint both the impact of the incident, and the precise location of the accident. Further details of my work in this area can be found to the right, and also in this presentation.

My main interests lie in the field of Functional Data, and in particular how functional data can be used to model perform te detection of anomalous data. This relates to my PhD, and also fits in with my broader interest in the use of functional data to deal with other high dimensional problems.

I also have an interest in the broader field of anomaly detection, in both machine learning and statistics based settings. Furthermore, I have an interest in the solving of these - and other related - problems in the online setting. This is where the problems are solved in real time.

I also have an interest in problems related to the field of integer programming. One particular problem I am very interested in is the Travelling Salesperson problem. I find it fascinating how this problem can seem so simple and yet can be difficult to solve. I am have interests in other similar combinatorial optimization problems, for example the knapsack problem.