Fast Bayesian estimation using expectation propagation methods applied to inverse problems

Supervisor(s)

Contact Dr Robert G Aykroyd to discuss this project further informally.

Project description

The Bayesian modelling approach provides a natural framework within which many applied science problems can be considered. The resulting posterior distribution, derived from data likelihood and prior knowledge, is then the basis for inference. In many problems, however, it is not practical to work directly with the posterior distribution, as it is too complicated or complex, and hence it is popular to use Markov chain Monte Carlo (MCMC) methods. Such approaches are still computational expensive and so are impractical when rapid solution is needed. In contrast expectation propagation (EP) methods, based on suitable Gaussian approximations, are rapid with little reduction in accuracy.

There has been little research examining the use of EP methods for inverse problem yet if successful they have the potential to have dramatic impact. For example, in PET/MR medical imaging or ECT for industrial monitoring, existing methods work well for static problems which can be analysed “off-line”, but are too slow for dynamic studies. This means that “real-time” applications are not practical hence dramatically limiting their use. This project will consider a range of Bayesian modelling situations involving linear and nonlinear inverse problems from geophysics, engineering and medicine. The project will begin by exploring the basic ideas of variational Bayesian methods and expectation propagation before moving on to propose methods for inverse problems working from simple linear problems through to the more computationally challenging nonlinear and big data problems.

Where possible, the methods will be applied to real data examples. Through the project collaborators, the student will have access to real datasets covering a wide variety of applications and with significant practical experience. 

Entry requirements

Applications are invited from candidates with or expecting a minimum of a UK upper second class honours degree (2:1), and/or a Master's degree in a relevant mathematics or statistics.

If English is not your first language, you must provide evidence that you meet the University’s minimum English Language requirements.

How to apply

Formal applications for research degree study should be made online through the university's website. Please state clearly in the research information section that the PhD you wish to be considered for is the 'Fast Bayesian estimation using expectation propagation methods applied to inverse problems’ as well as Dr Robert G. Aykroyd as your proposed supervisor.

We welcome scholarship applications from all suitably-qualified candidates, but UK black and minority ethnic (BME) researchers are currently under-represented in our Postgraduate Research community, and we would therefore particularly encourage applications from UK BME candidates. All scholarships will be awarded on the basis of merit. 

If you require any further information please contact the Graduate School Office, e: maps.pgr.admissions@leeds.ac.uk