[School of Natural Sciences PhD Scholarships] Graph Gaussian Processes for Relational Dependence in Spatial Disease Risk Mapping

About the project

About the Project Mapping disease risk accurately is central to public health planning, but standard statistical models assume that risk in one location depends only on how physically close it is to another. In reality, risk can also be linked through non-geographic relationships. Places with similar environmental conditions, connected by mobility, or sharing ecological features can have linked disease dynamics even when they're far apart on a map. Recent research has shown that combining a classical geostatistical model with a graph neural network, a type of machine learning model that learns which locations are meaningfully "connected", captures this kind of relational dependence and substantially improves both the accuracy of disease-risk maps and how trustworthy their uncertainty estimates are. However, the way this combination currently works has a gap. The neural network is trained separately, and its output is then plugged into the statistical model as if it were known with certainty, so the uncertainty in what the network learned never makes it into the final risk map's confidence intervals. This project asks whether the same relational structure can instead be built directly into a single, fully probabilistic model using Gaussian processes, a well-established statistical tool for representing structured uncertainty, defined not over ordinary geographic space but over a network of relationships between locations. Doing so would remove the disconnect between the two modelling stages, produce more honestly calibrated uncertainty, and give a mathematically cleaner alternative to training a separate neural network. The student will develop new Gaussian process constructions for graph-structured data, integrate them with established spatial statistical methods (INLA/SPDE), and test the resulting models in simulation and on real malaria surveillance data. The project is jointly supervised across the Department of Mathematics (spatial statistics, disease mapping) and the Department of Computer Science (Gaussian processes, machine learning), giving the student training and expertise spanning both traditional statistical modelling and modern probabilistic machine learning. This is a strong project for a student who wants to work on methodologically rigorous, real-world-relevant statistics. It combines a well-defined mathematical problem, constructing valid, scalable covariance functions on graphs, with a clear applied motivation: better, more trustworthy disease-risk maps for public health decision-making. It offers training in both classical Bayesian spatial statistics and contemporary Gaussian process machine learning, skills in high demand in both academic and industry research settings. This project is expected to start in September 2027. Before you apply: We strongly recommend that you contact the supervisors for this project before you apply. How to apply: To be considered for this project you must complete a formal application through our online application portal. If you already have an applicant account this link will directly open an application for PhD School of Natural Sciences Scholarships . If you don’t already have an applicant account, please follow the instructions here . When applying, please specify the full title and supervisor/s of the project, details of your previous study, and names and contact details of two referees. You must also upload a Supporting Statement describing your motivation to apply to the project, your CV and transcripts of awarded and in-progress university qualifications . Please note late or incomplete applications will not be considered. Equality, diversity and inclusion are fundamental to the success of The University of Manchester and central to all our activities. A diverse research community strengthens creativity, productivity and quality, while increasing the societal and economic impact of our work. We welcome applicants from all career paths, backgrounds and sections of the community, regardless of age, disability, ethnicity, gender, gender expression, sexual orientation or transgender status. We welcome applications from candidates returning to study after a career break or experience in other roles. Flexible study arrangements may be available, including part-time study at 50%, 60% or 80%, subject to the requirements of the project and funder. Eligibility : The standard academic entry requirement for this PhD is an upper second-class (2:1) honours degree (or international equivalent) in Statistics, Mathematics, Computer Science, or a closely related quantitative discipline OR any upper-second class (2:1) honours degree and a Master’s degree at merit (or international equivalent) in Statistics, Mathematics, Computer Science, or a closely related quantitative discipline. Prior exposure to Bayesian statistics and/or Gaussian processes is desirable but not required. Programming experience in R and/or Python is expected. Interest in both the mathematical/computational side (kernel methods, scalable inference) and the applied side (spatial epidemiology, public health data) is welcomed. This project will remain open until filled. If your application is submitted by 1st November 2026, you can expect a decision by 18th December 2026. If your application is submitted by 15th January 2027, you can expect a decision by 30th March 2027. Self or externally funded students can also be considered for this project. FSESoNS

Research areas