Statistical inference for Shannon and Rényi entropies for ambit-type processes

About the project:

The School of Mathematics at Cardiff University is delighted to offer a fully funded studentship starting in October 2022.

 Project Summary:

During the last decade, Ambit processes have become an exciting new approach to model space-time phenomena with successful applications e.g. in energy systems, finance, biology and neuroscience. Key developments so far culminated in the recent monograph Ambit Stochastics (Springer, NY 2018). An advantage of the Ambit approach over conventional (e.g. SPDE) approaches is their interpretable definition, which makes them highly analytically tractable.

However, statistical inference techniques for Ambit processes are still underexplored, in particular for dependent and multidimensional processes that are needed in many practical problems. Entropy and divergences estimation arises also as a central problem in image processing. Mutual information, which is strongly related to Shannon entropy and Kullback-Leibler divergence, is a widely used measure of similarity between images. Similar divergences are known for Rényi type entropies.

This studentship will develop new methodology for estimation of Shannon and Rényi entropies and related information divergences for dependent multidimensional Ambit processes. It will leverage recent advances in using the nearest-neighbour distances between observations, e.g. Leonenko et al. 2008 (Annals of Statistics), Penrose and Yukich 2013 (Annals of Applied Probability), Berrett et al. 2019 (Annals of Statistics), Leonenko et al. 2021 (Electronic Journal of Statistics). The implemented methods will be made publicly available on CRAN (the central software repository of the statistical computing environment R).

The student will be supervised by Prof. Nikolai Leonenko and Dr Kirstin Strokorb, whose research interests include stochastic processes, the nearest-neighbour distances methods, Ambit stochastics, extreme value theory and statistical computing.

Cardiff’s School of Mathematics provides an excellent postgraduate research environment. Project-specific academic training will be provided by the supervisors. The student will also benefit from the School’s excellent research culture, access to national course centres in mathematical training (MAGIC, APTS, NATCOR), the Doctoral Academy, which offers a comprehensive programme for postgraduate researchers to develop their professional skills, and the SIAM-IMA Student Chapter, a valuable forum for exchange and public engagement.

The training in this project opens up outstanding career prospects both in academia and industry.

Research Environment:

The School of Mathematics at Cardiff provides an excellent environment for a research student to develop professionally. The student will have an office space with their own computers in the newly build state-of-the-art ABACWS building which houses the School of Mathematics and the School of Computer Science and Informatics, providing the right environment to foster collaborations.  The supervisory team will support the research and professional development of the student. The student has access to nationwide centres with courses in mathematics (MAGIC), statistics (APTS) and Operations Research (NATCOR) and further professional development courses through the Doctoral Academy. Moreover, the School has five different research groups, each with individual seminars and School-wide Colloquia and interdisciplinary lectures as well as the Welsh Mathematics Colloquium which provide plenty of opportunities to mix with research leaders in different areas of Mathematics.  

The School of Mathematics has a very active PGR student group which includes weekly PGR organized seminars, the SIAM-IMA Chapter and the Women in Mathematics group.  Academic staff in the School organize a number of workshops/conferences in Cardiff where students get the opportunity to network with leading researchers around the world.

Training and/or Development Opportunities:

This studentship is an outstanding opportunity to conduct cutting-edge research across disciplinary boundaries in Mathematics as part of an international team and in an excellent PGR environment on a topic of theoretical and practical importance.

To ensure the student is well-supported in all aspects of their research and personal development, the team will identify individual needs and provide project-specific training in at least weekly meetings. For academic training the student has access to three national course centres (MAGIC, APTS, NATCOR) that is complemented by the professional skills training of Cardiff's Doctoral Academy. The School’s research culture includes weekly seminars, global collaborations and an active participation in the Welsh Mathematics Colloquium, during which students gain first valuable feedback beyond their project team.

  As the student progresses, they will learn how to disseminate their work in high-quality journals and during conferences enabling them to become part of a research community. In addition the SIAM-IMA Chapter provides a unique forum for public engagement. To further strengthen their CV, the student may gain teaching practice, whilst being mentored by an experienced lecturer.

Collectively, these activities will empower the student to work successfully in various environments that are currently affected by skills-shortage and provide them with excellent career prospects both in academia and industry.

How to apply:

Applicants should apply through the Cardiff University online application portal, SIMS. Applicants should select Doctor of Philosophy in Mathematics, with a start date of October 2022. In the research proposal section of your application, please specify the project title “Statistical inference for Shannon and Rényi entropies for ambit-type processes” and supervisor/Lead supervisor “Prof Nikolai Leonenko”.

In the funding section, please specify that you are applying for advertised funding.

Academic criteria:

 A 1st or upper 2nd class UK Honours degree (or equivalent) and/or a Master’s degree is required in mathematics or a related subject.

Please upload the following supporting documents on SIMS :

·        Curriculum vitae

·        A personal statement

·        Two completed references

·        Degree certificates and transcripts

Deadline for applications:

 27 May 2022

Eligibility:

This studentship is available to home students.

Cardiff University is committed to supporting and promoting equality and diversity and to creating an inclusive environment for all. We welcome applications from all members of the global community irrespective of age, disability, sex, gender identity, gender reassignment, marital or civil partnership status, pregnancy or maternity, race, religion or belief and sexual orientation.

Short-listed applicants will be invited to interview w/c shortly after the application deadline.

As part of the interview process, applicants will be asked to answer a series of questions by a panel of academics. 

Interviews are expected to take place remotely via Zoom/Teams on within one month after the application deadline.