This studentship will develop a paradigm-changing theoretical underpinning of novel tools for assessing extremal dependence in high dimensions. It is based on extending a recently discovered link between classical principal component analysis and multivariate extreme value theory.
While most statistical tools that have a strong theoretical underpinning characterise the typical behaviour of a system, in many practical or safety-critical situations it is instead the extreme behaviours and their dependence, which require particular attention. Contrary to public perception, examples of such settings are ubiquitous and an improved understanding aided by sound statistical procedures is of utmost importance, for instance to assess risk related to environmental hazards, network failure or financial portfolio losses. What complicates such tasks is the lack of generic and interpretable, theoretically well-studied and computationally feasible statistical tools to explore the extremal dependence structure of high-dimensional data.
In recent years, Dr Kirstin Strokorb (KS), in collaboration with leading mathematicians, has established a better theoretical understanding of the dependence structure of extreme events. Now a novel approach by Professor Dan Cooley and Dr Emeric Thibaud (Biometrika 2019) provides an unprecedented link between classical principal component analysis and regular variation of random vectors. The latter opens up the opportunity to leverage knowledge from multivariate extreme value theory (KS) and spectral approximation in kernel-based models, of which Dr Bertrand Gauthier (BG) is an expert. Professor Marco Marletta (MM) completes the local supervisory team through his expertise in spectral problems. In addition, Professor Dan Cooley (DC, Colorado State University, College of Natural Sciences Professor Laureate) and Dr Christian Rohrbeck (CR, University of Bath) will be advisors for this project and ensure that the programme includes questions of high priority to end users.
Cardiff’s School of Mathematics provides an excellent postgraduate research environment. The latest PRES ranks its overall satisfaction 3rd and its professional development 1st (out of 22). While project-specific academic training will be provided by the supervisors, the student will also benefit from the School’s seminar culture, access to three national course centres in mathematics, statistics and OR (MAGIC, APTS, NATCOR) as well as Cardiff’s Doctoral Academy, which offers a comprehensive programme for postgraduate researchers to develop their professional skills. In addition, the SIAM-IMA Student Chapter is a valuable forum for exchange of ideas and public engagement.
The training in this project opens up outstanding career prospects both in academia and industry.
The 4 year studentship includes UK/EU fees, stipend (amount for 2020/21 is £15285) and a research training grant to cover costs such as research consumables, training, conferences and travel. HOW TO APPLY
Applicants should apply through the Cardiff University online application portal
, for a Doctor of Philosophy in Mathematics with an entry point of October 2020 UK Research Council eligibility conditions apply
In the research proposal section of your application, please specify the project title and supervisors of this project. In the funding section, please select "I will be applying for a scholarship / grant" and specify that you are applying for advertised funding from EPRSC DTP.
Shortlisted candidates will be invited to attend an interview in April