Department of Mathematical Sciences

Studentship Opportunities

Interested in doing a PhD in mathematical sciences at Bath? There are many ways to join our excellent and welcoming department.

4-year SAMBa PhD Studentships

Applications are open from 1 October to 30 June for an October start in our Centre for Doctoral Training in Statistical Applied Mathematics. SAMBa is a four year programme, including a first year MRes programme, during which you will scope your own research programme. Apply early as places are competitive. 

Project Specific Studentships

Fully funded research projects available in the Department of Mathematical Sciences are described below. Often these are SAMBa aligned projects where you will become part of the SAMBa cohort, and will have access to SAMBa training opportunities, but will not complete the MRes training year. 

Novel methods for analysis of nonstationary time series

Supervisors: Matt Nunes 

Starting October 2019

Many time series observed in practice are nonstationary in nature, meaning their second order (variance) properties vary over time. These time series often arise in data streams, where "on-the-fly" or online analysis is required. In addition, the complex dependence structure (memory) within series can make it difficult to perform analysis in a efficient manner, and time series with different sampling rates often need different approaches to model them. This project will look at developing new tools for efficient estimation for multivariate nonstationary data streams with potentially mixed sampling regimes, for analysis tasks such as forecasting of economic time series.

Stochastic mixing in many-particle systems

Supervisors: Kit Yates and Tim Rogers in collaboration with Syngenta.

Starting October 2019 or before.

Tackling this project will require the development of individual-based stochastic models for individual seed motion, and derivation of macro-scale partial differential equations for fluid-like flow of the bulk. In order to enable optimisation of the process, ultimately, these disparate modelling regimes must be coupled to each other and further to a stochastic model for the spread of coating. Each of these steps is mathematically significant, allowing the project student to develop expertise in cutting-edge techniques across applied mathematics and probability. 

Multivariate Regression on High Dimensional Networks

Supervisors: Sandipan Roy and Evangelos Evangelou 

Starting October 2019

A key feature of many modern datasets is the inherent network structure present in it. Examples include social networks, biological networks, spatial networks among others. Graphical models (Wainwright and Jordan (2008)) are widely used to describe the multivariate relationship among interacting individuals. In this case, each individual corresponds to a node in the graph and the edges represent correlations. Often, there are multivariate observations available on each node of the graph and it is essential to infer about the parameters of a joint model. For example, in biomedical studies, multiple clinical characteristics are measured across several patients and it is essential to understand how those different characteristics are correlated.

We would like to integrate the variations across the observations and the individuals in a joint optimization framework that would allow us estimate the parameters in the model and learn the graph structure as well. Often network structures are sparse in nature and we would like to extend the high dimensional sparse estimation techniques to learn the underlying structure combining across variables over nodes.

This project is motivated by several applications in biology and in social sciences. Examples include understanding how different diseases show similar pattern in the number of deaths across spatially nearby states, mapping crime patterns across neighbouring counties/states (Hӓrdle and Simmer (2003)).

There has been growing interest recently to analyse network structures with covariates/meta data (Latouche et al. (2018)). However, most of these methods focus on understanding the interactions through multiple regression based on the covariates. The objective of the project is to extend this framework to multivariate responses and perform multivariate regression utilizing the network structure. Further there are some recent literature (Zhu et al. (2014)) on joint estimation of multiple graph structure (motivated by gene regulatory networks for different subtypes of genes). The regression framework developed in this project will be applied in the case of multiple graph structures as well.

This PhD offers the chance to develop –(i) a joint parameter estimation framework for graphical models with multiple observations on each node when the graph structure is known (spatial network) and (ii) a joint framework for multiple sparse graph estimation (biological network) using techniques available on sparse graphical models, high dimensional estimation and multivariate multiple regression.