About the Project
Bayesian methods allow us to combine mathematical models with data while quantifying uncertainty, and are widely used across science and engineering. However, for complex models, Bayesian inference can require enormous amounts of computation. This becomes particularly challenging in online applications, where new data arrive continuously and useful estimates may be needed in seconds or minutes rather than hours or days.
This PhD project will investigate how machine learning, posterior learning and modern parallel computing can be used to make Bayesian computation substantially more scalable. A particular motivation will be filtering and data assimilation: problems in which our understanding of an evolving system must be continually updated as new observations become available.
The project will build on recent work showing that machine-learning approximations of posterior distributions can be used to extract improved statistical estimates from limited and poorly converged computations. There is considerable freedom in how these ideas are developed. Possible approaches include methods such as surrogate modelling, Monte Carlo and sequential algorithms, machine-learning representations of probability distributions, and techniques designed to exploit modern parallel hardware.
A key application will be developed in collaboration with the National Physical Laboratory (NPL), concerning the analysis of the chemical composition of samples in real time. More broadly, the methods developed could be relevant to applications ranging from environmental forecasting to the monitoring of complex physical and engineering systems.
The project is particularly suited to a student with a strong background in statistics and scientific programming. Strong coding skills will be important, since a substantial part of the research will involve developing, implementing and testing new computational methods. A good background in applied mathematics and numerical analysis would also be valuable. The project will offer opportunities to work at the interface of applied mathematics, statistics, machine learning and scientific computing, combining theoretical ideas with substantial computational development.
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, Applied Mathematics, 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 a Statistics, Applied Mathematics, or a closely related quantitative discipline. A strong background in statistics and substantial experience in scientific programming/coding are essential. A good background in applied mathematics and numerical analysis would be highly desirable, together with any prior experience in Bayesian computation, machine learning or scientific computing.
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.
Funding Notes
Funding covers tuition fees, an annual stipend at the UKRI minimum rate (currently £21,805 per year), and a research training support grant of up to £2,500 per year for the full 3.5-year programme.