PhD and Postgraduate Research
The Department offers the opportunity to study for a research degree in any of the areas of interest of our staff members.
The Department offers the opportunity to study for a research degree in any of the areas of interest of our staff members.
We offer several fully-funded PhD studentships on the following PhD programmes in the department
Lancaster is also home to the Statistics and Operational Research Centre (STOR-i) and is a participant in the North West Social Science Doctoral Training Partnership. Details on these programmes, and how to apply, can be found on their respective websites.
Regardless of your preferred programme, the conventional entry point is at the start of the academic year in October. We recommend that you apply 6-12 months in advance of this to maximise your chance of being offered a place and funding.
We are a highly active research department, achieving 7th place overall and 1st for impact in REF2021. Our research is regularly published in top international academic journals and many members of the department have been successful in obtaining research grant income from highly competitive funding bodies.
Our research interests cover Pure Mathematics and Statistics. The web pages for each of the two areas provide specific details of research interests and activities, and we encourage you to use these pages to identify which of our research topics interest you. A good starting point is to look at the research groups, which reflect broad areas of interest. Once you have narrowed down your interests, we suggest that you get in touch with potential supervisors using the PhD Supervisors list.
For many people, their PhD studies will be the first time that they undertake independent research and supporting the transition from taught programme to trainee researcher to fully independent researcher is integral to our PhD programmes. Our graduates are equipped with highly specialist subject knowledge and skills, but also the broader set of research skills which are essential to any research-led career pathway, whether in industry or academia. As well as regular contact with your supervisor, who will be your main point of contact and academic support, you will be given the opportunity to further your subject knowledge and awareness by engaging in research activities in the department and wider university. We strongly encourage our students to develop peer support mechanisms, through shared offices, student-only seminars and social activities.
There are additional special funding routes available in Statistics which have their own deadlines. Please visit the websites of the STOR-i Centre for Doctoral Training and North West Social Science Doctoral Training Partnership for more information.
The most important considerations when choosing to study for a PhD or MPhil are the project and supervisor. For this reason, we invite all applicants to discuss research projects with potential supervisors. Whilst we welcome proposals for research projects from applicants, most research projects are developed by academics taking into consideration applicants’ strengths and knowledge. We suggest mentioning the name of your prospective supervisor in your personal statement.
At the bottom of this page, you can see a sample of possible projects offered by our staff, but please note that this list is only indicative and is not exhaustive. You should contact members of staff directly for more details. You might also wish to look at our research pages, to learn more about our specialisms.
Applicants who are eligible for UK studentship funding: the departmental studentships are awarded according to a competitive process. Allocation is made by the Postgraduate Research Committee at the meeting at which offers of places are decided.
Applicants who are not eligible for UK studentship funding: will also be invited for an interview. If you are successful in being offered a place, this will be made conditional on you obtaining funding from elsewhere.
Note that occasionally studentships are tied to a specific project. In these cases, candidates should follow the application instructions provided on the project advert.
All applicants for postgraduate study in the Department of Mathematics and Statistics need to complete an online application via the University Postgraduate Admissions Portal.
Once you have created an account at our Postgraduate Admissions Portal you will be able to fill in your personal details, background and upload supporting documentation.
If you are a current Lancaster student, or you have recently graduated from Lancaster, and are made an offer, you will only need to provide one reference.
Please note that the Department does not require applicants to submit a research proposal. This is optional, but if an applicant would like further guidance on this issue, please contact the relevant PhD admissions tutor with the subject line your intended programme (e.g. PhD Mathematics or PhD Statistics etc.).
With 100% of our research being rated world-leading or internationally excellent (REF2021), Lancaster is one of the UK's top departments for research in mathematics and statistics.
As a postgraduate research student, you can be funded from several different sources:
Details of currently advertised funded PhD studentships are given below. You are strongly encouraged to contact the prospective supervisor before making an application.
Note that the majority of funding opportunities for October entry in any given year close before March of that year.
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.
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.
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.
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.
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.
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
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.
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
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)
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.
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.
The ideal candidate will have an interest in statistical modelling and computational statistics. Strong programming skills, preferably in R and/or Python, are important.
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.
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.
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
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:
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.
The Department also considers applications from self-funded students. Please contact the PhD admissions team - Dr Anthony Nixon (pure mathematics) and Dr Lloyd Chapman (statistics) - to discuss this possibility.
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