Overview

The Department of Mathematics and Statistics at Lancaster University is inviting applications for fully-funded PhD positions in either Pure Mathematics or Statistics for the entry in October 2024. Please see the PhD in Mathematics and PhD in Statistics course pages for details.

Research projects

Any research areas in Pure Mathematics or Statistics that are consistent with those of our staff members are considered and some examples of research topics and potential supervisors in statistics are available.

Entry Requirements

Applicants are expected to have a minimum of an upper-second class honours degree, or its equivalent, in Mathematics, Statistics or related fields. Preferably applicants will, or are expected to, hold a first class degree in MSci/MMath for Mathematics, MSc in Statistics/Data Science, though exceptional BSc students will also be considered.

Funding eligibility

The studentship normally covers full payment of tuition fees at UK/EU level plus a stipend for living expenses. All applicants from UK/EU/Overseas may apply. The funding is offered for 3.5 years of study for UK/EU candidates and 3 years of study for Overseas candidates.

Application process

The deadline for submitting applications for this studentship is 31 January 2024. The guidelines on the application process are found in the How to Apply section. Note that all eligible candidates from the standard PhD applications are automatically considered.

Contact

Those interested are encouraged to contact Dr Tony Nixon (a.nixon@lancaster.ac.uk) for applications in mathematics, or Dr Lloyd Chapman (l.chapman4@lancaster.ac.uk) for statistics. Please provide your CV and transcripts

About the Project

We are currently seeking a PhD researcher in Statistics and Machine Learning for the project "Probabilistic Linking in AI-Powered Knowledge Bases.” This project aims to advance the state-of-the-art in probabilistic algorithms for entity linkage in large language models (see detailed project description below).

Ideal candidates should have strong mathematical skills with an undergraduate degree in Mathematics or a related numerical discipline. A background and experience in Statistics, Machine Learning, or closely related fields, with a master’s degree in one of these areas, is highly desirable.

The successful candidate will be based in the Department of Mathematics and Statistics at Lancaster University. Supervision will be provided by Professor Chris Nemeth (Lancaster University), Professor Paul Fearnhead (Lancaster University) and Dr James Hensman (Microsoft Research). The candidate will join Lancaster’s vibrant Computational Statistics and Machine Learning research group and have the opportunity to work closely with researchers in MSR Cambridge.

Interested applicants are requested to submit their applications via email to c.nemeth@lancaster.ac.uk. The application should include a CV (including the names and contact details of two referees) and a short cover letter which demonstrates the applicant’s motivation for choosing this project.

We look forward to receiving your application. The position will remain open until a qualified candidate has been found.

Project description:

Large language models are transforming the world of work: at Microsoft, AI-powered co-pilots are being developed across many products. A key challenge is: how can language models work with private enterprise data? In the Alexandria team in Microsoft Research Cambridge, new technology is being developed to automatically construct knowledge bases that can then be used to augment AI’s abilities. A knowledge base construction can allow an AI co-pilot to work with private data that was not available at training time, include human annotations, and enable privacy preservation.

A key technical challenge in knowledge-base construction is linking. In Alexandria, knowledge is extracted form free-text into structured knowledge entities, and then a probabilistic program is used to link extractions. At its core, linking is an inference problem over a large number of binary random variables that denote repeated mentions of the same entity. A number of product requirements make the linking task challenging, the main one being scale: to ensure that linking techniques can be applied in real-world settings, we need to develop new tools which can perform inference online over millions of facts extracted from millions of documents every day. From a technical perspective, this can be likened to inference in a mixture model with hundreds of thousands of components, with online inference demanded over millions of observations daily.

This projects aims to develop new algorithms for linking, based on Sequential Monte Carlo (SMC) algorithms. Existing SMC methods will need to be adapted to cope with the demands of constructing huge knowledge bases, as well as product requirements such as privacy preservation. The candidate will work with Profs Nemeth and Fearnhead at Lancaster University, as well as Dr Hensman and researchers at Microsoft Research to develop new algorithms that achieve Bayesian linking at scale.

For more details download Alexandria project

Funding Notes

This PhD studentship is sponsored by Microsoft Research (MSR) and will involve close collaboration with researchers based at MSR in Cambridge. The successful candidate for this position will receive a tax-free studentship stipend of £21,622 per year, along with relevant tuition fees, for up to 3.5 years, subject to satisfactory progress. A training budget and funds for attending international conferences will also be provided. Due to tuition fee restrictions, this position is only available to applicants who are eligible for UK fee status. This position will be available from October 2023 onwards.

University of Western Australia, Australia

University of Wollongong, Australia

Lancaster University , UK

PhD Scholarships are available in the area of statistical/machine learning with applications to metocean and ocean engineering. Research topics in statistics/machine learning identified as PhD projects include (1) sequential decision making and optimal design to augment targeted and efficient data acquisition; (2) data driven spatio-temporal inference/prediction of complex ocean dynamic processes; (3) statistical analyses, emulation, and uncertainty quantification of physical models. The student will be a member of the Australian Research Council’s (ARC) Industrial Transformation Research Hub for Transforming energy Infrastructure through Digital Engineering (TIDE), situated in the Indian Ocean Marine Research Centre (IOMRC) at the University of Western Australia (UWA). TIDE brings together a vibrant international team of researchers in statistics, data science, and ocean engineering. The data science team within the Hub is comprised of researchers located at the University of Western Australia, University of Wollongong, Australia, and University of Lancaster, UK, with expertise in statistics, machine learning, and applied mathematics. Successful applicants will be hosted at one of the aforementioned institutions, depending on research interests and student circumstances, and will engage in collaboration across, and travel between, institutions.

A generous scholarship will be made available to fund the student’s studies for three years full-time. An additional top-up scholarship is also available for outstanding candidates. Tuition fees for outstanding international students (for up to 4 years) will be waived. The successful applicant will have the opportunity to work with both Australian and international collaborators, and funding is available for conference travel.

Applications are invited from domestic and international students who are able to commence their PhD studies in early 2024. Applicants should hold, or be close to completing, an Honours undergraduate degree or a Master's degree in Statistics, Machine Learning, or a closely related field. The ideal candidate will have an interest in the development of statistical learning/machine learning methodology and computation, excellent mathematical and programming skills, and an interest in using them to model and predict environmental or engineering phenomena. Self-motivation, strong research potential, and good oral and written communication skills are essential criteria.

To apply, please send in academic transcripts, a CV, and a cover letter outlining your motivation for conducting research in one of the above areas to Kath Lundy (tide@uwa.edu.au). For informal queries, please contact A/Professor Andrew Zammit Mangion (azm@uow.edu.au), A/Professor Edward Cripps (edward.cripps@uwa.edu.au) or Professor David Leslie (d.leslie@lancaster.ac.uk)

Supervisors

• Dr Gabriel Wallin (Mathematics and Statistics)
• Dr Emanuele Giorgi (Lancaster Medical School)

Dates

• Deadline for applications: 15th March 2024
• Provisional Interview Date: Mar - April 2024
• Start Date: October 2024

Project description

In the social and behavioural sciences, latent variable models are popular for modelling variables that are not directly measurable, such as latent abilities, political attitudes, and mental health indicators. In recent years, they have been gaining popularity in the machine learning community as they offer a dimension-reduction of the data with an interpretable structure. However, since they were developed for relatively small and low-noise datasets, they have important limitations.

This project aims to develop flexible, robust, and computationally efficient statistical methods based on latent variable models for complex, large-scale data. The focus will be on model-based clustering and outlier detection for multivariate data, where applications range from cheating detection in educational testing to accurate mental health diagnoses in health surveys. Collaborating with researchers at the Centre for Health Informatics, Computing, and Statistics (CHICAS) at Lancaster Medical School, we will integrate these new methods to address questions in public health.

General eligibility criteria

Applicants would normally be expected to hold a minimum of a UK Honours degree at 2:1 level or equivalent in a relevant degree course.

Project specific criteria

The ideal candidate will have an interest in statistical modelling and computational statistics. Strong programming skills, preferably in R and/or Python, are important.

Studentship funding

A tax-free stipend will be paid at the standard UKRI rate; currently £18,622. This is a fully funded studentship of 3.5 years for UK/Home students.

Enquiries

Interested applicants are welcome to get in touch to learn more about the PhD project. Please contact Gabriel Wallin (g.wallin@lancaster.ac.uk) for more information.

Further reading

• Wallin, G., Chen, Y., & Moustaki, I. (2023). DIF Analysis with Unknown Groups and Anchor Items. arXiv preprint arXiv:2305.00961. Accepted for publication in Psychometrika.
• Liu, X., Wallin, G., Chen, Y., & Moustaki, I. (2023). Rotation to sparse loadings using Lp losses and related inference problems. Psychometrika, 88(2), 527-553.

Application process

1. Download the Natural Sciences Funded PhD Application Form  and Natural Sciences Funded PhD Reference Form‌.
2. Complete the Application Form, renaming the document with your 'Name and Application Form' e.g., Joe Bloggs Application Form.
3. Submit the completed Application Form and a CV to naturalsci@lancaster.ac.uk
4. Please note only Word or PDF files are accepted.
5. Rename the referee form with your ‘Name and Reference’, e.g., Joe Bloggs Reference. Send the renamed reference form to two referees and request them to forward the referee document to naturalsci@lancaster.ac.uk
6. Please note only Word or PDF files are accepted. It is important that you ensure references are submitted by the closing date or as soon as possible.
7. You will receive a generic acknowledgement in receipt of successfully sending the application documents.
8. Please note that only applications submitted as per these instructions will be considered.
9. Please note that if English is not your first language, you will be required to provide evidence of your proficiency in English. This evidence is only required if you are offered a funded PhD and is not required as part of this application process.
10. Please note that if you do not hear from us within four weeks of the closing date, then you have been unsuccessful on this occasion. If you would like feedback on your application, please contact the supervisors of the project.

Project description

Climate change has led to an increased risk for many natural, such as flooding, storms, coastal erosion, and drought, resulting in significant challenges for communities and potential damage to the economy. To prevent or mitigate damage from such events, it is crucial to accurately predict the behaviour of future events.  

This PhD project develops a statistical modelling framework for flood events using a functional time series approach. Unlike existing methods, which model only the peak and magnitude of events, the proposed approach will provide new scientific insights into how floods evolve over time and space and pave the way for new operational tools for risk prediction, particularly for multi-hazard events.  

This PhD project is cross-disciplinary with LEC and JBA. Thus, the student will have the opportunity to work with JBA to apply the methodology to compound hazards problems. 

General eligibility criteria:  Applicants would normally be expected to hold a minimum of a UK Honours degree at 2:1 level or equivalent in a relevant undergraduate degree course.

Project specific criteria: The ideal candidate will have a master’s level understanding of statistical modelling, including generalised linear models and either time series analysis or geostatistics. You should be confident with at least one of likelihood and Bayesian inference and undergraduate-level multivariate probability. We encourage students who do not have this experience to make informal enquiries prior to making an application.  

Studentship funding: A tax-free stipend will be paid at the standard UKRI rate; £17,668 in 2023/24. This is a fully funded studentship of 3.5 years for UK/Home students.

Supervisors: Israel Martinez Hernandez (Mathematics and Statistics), Emma Eastoe (Mathematics and Statistics), Suzana Ilic (Lancaster Environment Centre), and Rob Lamb (JBA Trust, Ltd and LEC).    

Enquiries: Interested applicants are welcome to get in touch to learn more about the PhD project. Please contact Israel Martinez Hernandez (i.MartinezHernandez@lancaster.ac.uk) or Emma Eastoe (e.eastoe@lancaster.ac.uk) for more information. 

Dates

Deadline for applications: 15th March 2024

Provisional Interview Date: Mar - April 2024

Start Date: October 2024

Application process

1. Download the Natural Sciences Funded PhD Application Form and Natural Sciences Funded PhD Reference Form‌.
2. Complete the Application Form, renaming the document with your 'Name and Application Form' e.g., Joe Bloggs Application Form.
3. Submit the completed Application Form and a CV to naturalsci@lancaster.ac.uk
4. Please note only Word or pdf files are accepted.
5. Rename the referee form with your ‘Name and Reference’, e.g., Joe Bloggs Reference. Send the renamed reference form to two referees and request them to forward the referee document to naturalsci@lancaster.ac.uk
6. Please note only Word or pdf files are accepted. It is important that you ensure references are submitted by the closing date or as soon as possible.
7. You will receive a generic acknowledgement in receipt of successfully sending the application documents.
8. Please note that only applications submitted as per these instructions will be considered.
9. Please note that, if English is not your first language, you will be required to provide evidence of your proficiency in English. This evidence is only required if you are offered a funded PhD and is not required as part of this application process.
10. Please note that, if you do not hear from us within four weeks of the closing date then you have been unsuccessful on this occasion. If you would like feedback on your application, please contact the supervisors of the project.

We are currently seeking a number of PhD researchers in areas of Probability, Statistics and Machine Learning for the £8.5m EPSRC-funded hub on Probabilistic AI (Prob_AI Hub). This is a large-scale, multi-institution project led by Lancaster University and involves the Universities of Bristol, Cambridge, Edinburgh, Manchester and Warwick, with a number of supporting industrial partners.

The vision of the Prob_AI Hub is to develop a world-leading, diverse and UK-wide research programme in probabilistic AI. The hub will develop the next generation of mathematically-rigorous, scalable and uncertainty-aware AI algorithms. This will be achieved through: bringing together world-leading researchers across Applied Mathematics, Computer Science, Probability and Statistics, who engage with a range of non-academic partners; transforming the people pipeline; and producing a culture change within the mathematical sciences more broadly, so that cross-disciplinary mathematics research in AI is the norm.

Ideal PhD candidates should have strong mathematical skills with an undergraduate degree in Mathematics or a related numerical discipline. A background and experience in Mathematics, Statistics, Machine Learning, or closely related fields, with a master’s degree in one of these areas, is highly desirable.

The successful candidate for this position will receive a tax-free studentship stipend of £18,622 per year, along with paid tuition fees, for up to 3.5 years, subject to satisfactory progress. A training budget and funds for attending international conferences will also be provided. Due to tuition fee restrictions, these positions are only available to applicants who are eligible for UK fee status (see https://www.lancaster.ac.uk/study/fees-and-funding/fee-status/ for further details).

The successful candidate will be based in the Department of Mathematics and Statistics at Lancaster University. Supervision will be provided by one of the Lancaster academics within the Prob_AI Hub and supervisors will be allocated based on the alignment between the PhD project and the student’s research interests. A list of indicative research areas include:

• AI-scale probabilistic reasoning: This could include topics such as scalable Monte Carlo methods; conditional sampling for diffusion-generative models; application of AI-methods within Markov chain Monte Carlo (MCMC) algorithms.
• Mathematical underpinning of generative models: Developing a deeper understanding of generative models and their links to statistical methods such as tempering, conditional simulation of diffusions and sequential Monte Carlo algorithms. Extending generative models to new data types and applications.
• Structure-constrained and informed AI: How can we improve AI methods and models by forcing them to impose known structural information? For example, an AI emulator of a physical system should impose known constraints from physics.

Interested applicants are requested to submit their applications via email to Prof Paul Fearnhead (p.fearnhead@lancaster.ac.uk) or Prof Chris Nemeth (c.nemeth@lancaster.ac.uk). The application should include a CV (including the names and contact details of two referees) and a short cover letter which demonstrates the applicant’s motivation for choosing a PhD project in Probabilistic AI.