Hierarchical Bayesian Model Selection for Inverse Problems in Applied Mathematics

We often have modelling choices to make when considering an inverse problem, which can have a big impact on the result. It is not always obvious which model might best represent our system. Model selection is often considered as a single choice for the whole of a particular dataset, but in some cases, different models may be the best representations in differing parts of the observation space. For example, one model may better represent boundary interactions, while another is better when the quantity of interest is small or big enough. In this project, we will explore how we can discover these regions, using novel Bayesian learning methods involving Gaussian Processes (GPs).

Eligibility

Applicants should have, or expect to achieve, at least a 2.1 honours degree or a master’s (or international equivalent) in a relevant science or engineering related discipline. The applicant must be fluent, competent and willing to write in a modern computing language (e.g. Python).

Before you apply

We strongly recommend that you contact the supervisor for this project before you apply.

How to apply

Apply online through our website: https://uom.link/pgr-apply-fap

When applying, you’ll need to specify the full name of this project, the name of your supervisor, if you already having funding or if you wish to be considered for available funding through the university, details of your previous study, and names and contact details of two referees.

Your application will not be processed without all of the required documents submitted at the time of application, and we cannot accept responsibility for late or missed deadlines. Incomplete applications will not be considered.

After you have applied you will be asked to upload the following supporting documents:

• Final Transcript and certificates of all awarded university level qualifications
• Interim Transcript of any university level qualifications in progress
• CV
• Contact details for two referees (please make sure that the contact email you provide is an official university/work email address as we may need to verify the reference)
• English Language certificate (if applicable)

If you have any questions about making an application, please contact our admissions team by emailing FSE.doctoralacademy.admissions@manchester.ac.uk.

Equality, diversity and inclusion is fundamental to the success of The University of Manchester, and is at the heart of all of our activities. We know that diversity strengthens our research community, leading to enhanced research creativity, productivity and quality, and societal and economic impact.

We actively encourage applicants from diverse career paths and backgrounds and from all sections of the community, regardless of age, disability, ethnicity, gender, gender expression, sexual orientation and transgender status.

We also support applications from those returning from a career break or other roles. We consider offering flexible study arrangements (including part-time: 50%, 60% or 80%, depending on the project/funder).