Bayesian Inference and Approximations of High-Dimensional Network Models

Supervisor: Professor Istvan Kiss and Dr Masoumeh Dashti

The PhD studentship is part of a research project funded by the Leverhulme Trust which involves further openings for Postdoctoral Research and Teaching Fellow positions. The start date of the project is September 1 2018. It involves a team led by Professor Istvan Kiss with local (Dr Masoumeh Dashti and Dr Luc Berthouze) and international collaborators (Professor Andrew Stuart, Caltech).
The use of networks to model complex systems has revolutionised the way in which brains, epidemics, social interactions and more generally the flow of information are modelled. However, many of the resulting mathematical models suffer from high model dimensionality and therefore limited analytical tractability, sensitivity to incomplete information about the network, and inaccuracies due to simplifying assumptions or approximations. The aim of this project is to develop a new modelling paradigm capable of tackling these challenges. This paradigm relies on the specification of a new class of parametric models that are flexible enough to handle networks currently out of reach of state-of-the-art models. The inference of the parameters is formulated as Bayesian inverse problems, which in turn makes it possible to rigorously quantify the uncertainty introduced by simplifying assumptions and incomplete network data.
This research will seek to harness a novel combination of techniques from stochastic analysis, partial differential equations (PDEs) and uncertainty quantification and could prove a step change in the ability of network science to deal with real-world applications. You will be expected to play a key role in developing rigorous and efficient stochastic simulation techniques on networks as well as being responsible for developing a statistically sound network-coefficient classification. You will also be expected to contribute to the theory and computational techniques underpinning the Bayesian inference framework to be implemented within the project. The project will also provide opportunities to get familiar with elements of Uncertainty Quantification and Bayesian Inverse problems.

Eligibility:
To be eligible, you must:
- Be a UK/European Union (EU) student.
- Have or expect to have a UK undergraduate/master’s degree, or equivalent, in Mathematics or a related subject.

How to apply:
Apply through the online postgraduate application system (http://www.sussex.ac.uk/study/phd/apply) and select the full time PhD in Mathematics with a September 2018 start date.
When you apply, you should include:
• The supervisor’s name (Professor Istvan Kiss) in the ‘Suggested supervisor’ section
• Bayesian Inference and Approximations of High-Dimensional Network Models in the ‘Award detail’ section
• A research proposal/personal statement which describes your suitability for the project
• Two academic references
• Your transcripts from any previously obtained degrees. If you have not yet completed your undergraduate degree, you can provide an interim transcript or record of any marks obtained so far.

The position will be filled as soon as a suitable candidate is found so you are encouraged to apply as soon as you are able to.

Due to the high volume of applications received, you may only hear from us if your application is successful.

Contact us:
Email Professor Istvan Kiss ([Email Address Removed]) and Dr Masoumeh Dashti ([Email Address Removed]) if you have a question about the project. If you have any informal enquiries about applying or funding eligibility, email [Email Address Removed].