PhD in Statistics (Integrated): a four-year PhD programme which involves successful completion of postgraduate level (MSc) courses and a dissertation during the first year before progressing onto the PhD
PhD in Social Statistics: on subjects related to statistical approaches to social sciences problems
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.
Who we are
We are a highly active research School, 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 School 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.
Student research environment
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 School and wider university. We strongly encourage our students to develop peer support mechanisms, through shared offices, student-only seminars and social activities.
Entry date: our academic year starts in October and most students enter at this time. Entry in January or April is also possible. Applications are considered throughout the year.
Timeline: Applications for entry in October of the following year are normally considered between October and May.
Categories of candidates: Different studentships have different eligibility criteria but broadly cover 3 categories: UK students, UK/EU students and Overseas (non-EU) students. All eligible applicants are automatically considered for available studentships.
Studentships deadline: Due to high demand for studentships we have a deadline of 31st January. All applications received by this date will receive equal consideration. Applications received after this deadline will be considered for any remaining studentships. Final studentships decisions are usually made by April but please feel free to contact us to find out whether studentships are still available.
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.
Application Process
Identify and contact the prospective supervisor.
Complete an online application.
After an initial screening, all applicants who are under consideration for an offer will be invited to a half-hour online interview with a small panel of academic members of the Department.
Following the interviews, the Postgraduate Research Committee will decide which applicants will be offered a place.
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.
Apply online
All applicants for postgraduate study in the School of Mathematical Sciences 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.
Current Lancaster Students
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.
What to include
Postgraduate application form, available once you have created an account in the online portal and selected your mode of study.
Two references – you should include at least one academic referee who can comment on your academic quality, performance and potential to pursue independent research.
Transcripts of previous higher education degrees or other courses that you have completed or for which you are currently studying. Please note, for transcripts in languages other than English, a certified English translation will be required.
A detailed CV (up to 3 pages) – this should cover academic achievements, past projects and any employment history.
Personal statement (up to 2 pages) – you should include information on your research interests, relevant experiences and the subject area that you would like to work in, and if possible, the name of the supervisor(s) you would like to work with.
If English is not your first language, proof of English language competency is required.
IELTS is the recommended test but we consider tests from other providers; please refer to the university's information on language requirements. If you have any concerns or questions, please contact the Postgraduate Admissions team for clarification.
Our requirements for IELTS are an overall score of at least 6.5, with no individual element below 6.0. If your score is below our requirements but all individual elements are at least 5.5, we may consider you for one of our pre-sessional English language programmes.
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.).
Research Areas
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 mathematical sciences.
As a postgraduate research student, you can be funded from several different sources:
Research Council Studentships: full payment of tuition fees plus a stipend for living expenses are available for prospective students via the UKRI. As of 2021/2022, these studentships are now also available to international students. Please note that the University is limited to offering a maximum of 30% of these studentships to international students.
Department Studentships: normally full payment of tuition fees (at UK/EU level) plus a stipend for living expenses. No restrictions on applicants, unless specified, but overseas applicants would need to pay the difference in fees.
ESRC Studentship competition: The North West Social Science Doctoral Training Partnership (NWSSDTP) holds an annual competition for studentships, which can be used for study towards a PhD in Statistics or Social Statistics. The NWSSDTP is a collaboration between Lancaster, Manchester and Liverpool universities. Candidates may apply for funding towards master's and doctoral (1+3/2+2) study, or doctoral study only (+3/+2). If you are interested, you must contact the department with a PhD proposal and find a supervisor who can work with you towards making an application.
Studentships funded by industry and other external sources: normally full payment of tuition fees (at UK/EU level) plus a stipend for living expenses. No restrictions on applicants, unless specified but overseas applicants would need to pay the difference in fees.
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.
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Overview
The School of Mathematical Sciences at Lancaster University is inviting applications for fully-funded PhD positions in either Pure Mathematics or Statistics for the entry in October 2025. Please see the PhD in Mathematics and PhD in Statistics course pages for details.
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 2025. 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 (p.d.levy@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
Fully-funded CASE Studentship from the ESRC North West Social Science Doctoral Training Partnership to start in October 2025.
This is an exciting opportunity to develop new statistical methodology to better understand what information can be obtained from seizure data. The project is in partnership with TRAFFIC, a global NGO with a mission “to reduce illegal trafficking and enhance benefits to people from legal and sustainable trade of wild species”.
This project will develop novel statistical approaches to enhance an understanding of what may be reliably inferred from open-source, non-mandated, at-times opportunistically collected seizure data and explore improved data collection strategies. The work will assist TRAFFIC to obtain reliable estimates of trends in illegal trade across a wide range of taxa, helping to inform law enforcement and policy interventions at a variety of national and international levels.
Keywords: Bayesian hierarchical models, latent variable modelling, data collection strategies
Supervision: Professor Rachel McCrea and Dr Gabriel Wallin (Lancaster); Dr Sharon Baruch-Mordo (TRAFFIC)
Wider Supervisory Team: Dr Graham Laidler (TRAFFIC), Dr Fiona Underwood (Independent Statistical Consultant) and Dr Oscar Morton (Sheffield)
Funding: UK Home Fees paid in full; Annual maintenance stipend to the student (this was £19,237 in 2024/25, the exact rate for 2025/26 subject to confirmation from UKRI). Access to a Research Training Support Grant for research-related expenses (e.g. conference attendance, training courses). An extra 3 months of funding are provided for the student to undertake a three-month Research in Practice placement during the studentship.
Student Academic Eligibility: Applicants should be completing or have completed a taught master’s degree in a strongly quantitative subject.
To apply: Please send a copy of your CV and a copy of your degree transcripts to Rachel McCrea on r.mccrea@lancaster.ac.uk
We are now accepting applications for our fully-funded MARS PhD programmes in Applied Mathematics and Mathematical AI for October 2025 entry. Interviews and offers will occur on an ongoing basis so early applications are strongly encouraged.
Research Projects
Please consult our list of indicative PhD projects for a flavour of the exciting PhD research opportunities that MARS is offering. For more information about a potential project, please contact the lead supervisor.
Entry requirements
We are looking for PhD researchers who have demonstrated excellence in their studies and who are expecting to hold, or already hold, a first class honours undergraduate degree or 2:1 undergraduate degree with amaster’s with substantial mathematical content (for example, in mathematics, statistics, physics, computer science or engineering).
Funding
MARS has 4-year fully-funded, full-time PhD studentships available for UK students and a limited number of places for overseas students. These include an enhanced tax-free stipend, tuition fees and a research, training and support grant. The stipend is approximately £22,814 for 2025, rising to approximately £24,651 in the final year.
A current copy of your CV (no more than two sides of A4in Word or PDF format).
A covering letter (no more than two sides of A4 in Word or PDF format) outlining which MARS PhD programme you are applying for, which of the potential projects you are interested in, and your motivation for undertaking a PhD with MARS.
An up-to-date copy of the degree courses you have studied including marks awarded.
Your current fees status (UK or overseas including EU).
Details of where you saw the opportunity.
As places on the MARS PhD programmes are limited, and will be allocated on a rolling basis, we encourage all UK (including Republic of Ireland) applicants to apply by 31 March 2025, and all overseas applicants to apply by 31 January 2025.
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 School of Mathematical Sciences 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.
Self-Funded Opportunities
The School also considers applications from self-funded students. Please contact the PhD admissions team - Dr Paul Levy (pure mathematics) and Dr Lloyd Chapman (statistics) - to discuss this possibility.
PhD Supervisors
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I an interested in supervising PhDs in the following topics: Random matrices, high dimensional phenomena, and optimal transportation theory.
Specifically, I would be willing to supervise a project `Integrating differential equations in random matrix theory'. This would involve using methods from the theory of linear systems to analyze various operators which arise in random matrix theory. In particular, the aim is to extend ideas of Tracy and Widom to new matrix models. To pursue this project, a student would need a sound background in analysis. While the results have applications to statistical physics, the student would not require much background in physics or probability. This project develops a theme from some previous PhD thesis which I have supervised at Lancaster. Further information is available on request.
Two fully-funded PhD projects currently advertised through MARS:
(1) Numerical continuation and deflation techniques in atomistic modelling of materials
(2) Minimisation diagrams, optimal transport and logistic regression, with applications to microstructure modelling in metals
Please get in touch if you are interested!
I am happy to take on PhD students and have the following potential projects.
Schur-Weyl duality and variants for Spin groups, Deformed Howe Duality, Cohomology of Grassmannians, Clifford algebras and exterior algebras of Lie algebra pairs.
Bayesian inference methods for epidemic models, e.g. data augmentation MCMC, particle MCMC; spatiotemporal and individual-level modelling of infectious diseases
Subject to my existing commitments: I am always keen to hear from applicants with a strong background in functional analysis. Some previous exposure to representation theory of groups or the general theory of (matrix) Lie groups would be desirable, but is not essential.
Current ideas for PhD projects
Here are four possible areas in which I am willing to supervise: each of these is not a specific PhD project, but a setting in which there are various possible research problems that a student could work on. If you would like to know more, then please feel free to get in touch.
Ulam stability for Banach and operator algebras
Banach algebras associated to group actions on Lp spaces
Fourier algebras of locally compact groups
Non-selfadjoint subalgebras of Type I C*-algebras
Warning notes.
Themes 3 and 4 will require a student to start by learning the basic theory of C*-algebras, before getting on to the actual PhD project(s). C*-algebra theory is also valuable context for Themes 1 and 2, but in those cases there are "sub-projects" where one can get started on research without pre-existing C*-background.
It is possible that you are reading this and have had some exposure to various structural properties of Banach algebras known as "approximate amenability", "character amenability", or "module amenability". I will not, for the foreseeable future, supervise on any of these three, nor on any hybrid of these.
I am happy to supervise PhD students in the area of Functional Analysis and Operator Algebras, with particular interests in the study of algebras arising from topological groups and locally compact quantum groups. I am interested in applications of these areas to Quantum Information Theory, such as the study of Quantum Graphs and Non-Local games, and (quantum) symmetries thereof.
Interested in supervising doctoral students working on topics in the spectral theory of partial differential operators, particularly those arising in mathematical physics and/or with connections to other areas of mathematics. Potential projects could focus on zero modes of Pauli and Dirac operators, operators with periodic or quasi-periodic coefficients and the stability of embedded eigenvalues.
I am open to discussing with individuals considering pursuing a PhD program, especially students keen on creating novel time series and spatio-temporal models for environmental data science or developing novel statistical models for brain data analysis.
Projects in Algebraic Number Theory and related areas (in particular projects concerning the arithmetic of Modular Forms and Galois Representations). Interested in projects concerning applications to Cryptography and Cyber Security.
I am currently offering PhD projects in three areas:
1. Quantum groups, including producing novel quantum groups from the double bosonisation construction.
2. Cluster algebras, their quantizations and representation theory.
3. Relationships with mathematical physics, including Verlinde algebras, quantum cohomology and integrable systems and their relationships to quantum cluster algebras.
Students with interests in discrete probability and/or graph theory are welcome. My current interests include: models for randomly evolving graphs such as preferential attachment; systems of interacting particles moving ballistically or by random walks on graphs; percolation on planar graphs; and extremal problems in graph theory, for example those related to average graph parameters or topological indices.
Potential PhD candidates interested in any of the following should feel encouraged to contact me.
- Estimation of complexity (e.g. leverage and effective degrees of freedom) of non-standard estimators (clustering models, linear projections, etc.)
- Methodology for and analysis of non-parametric regression and classification problems
- Methodology and theory for cluster analysis and /or unsupervised dimension reduction
- Applications of (modified) flexible regression models in spatial; temporal and spatio-temporal problems
I am interested in supervising PhD students who have a strong interest and background in discrete probability. My current research is in the theory of interacting particle systems. One potential project is to study the second class particle behaviour of certain reversible interacting particle systems.
Interacting particle systems have been shown to have strong links to other areas of mathematics such as combinatorics (via partitions) and algebra (some systems can be constructed from certain quantum groups). I would be happy to discuss the potential for interested students to work on a jointly supervised project studying these links further.
If you would like to know more, please feel free to get in touch!
I am interested in discussing PhD projects in two research areas:
a. Graph Rigidity. I am particularly interested in rigidity properties of partially triangulated orientable and non-orientable surfaces. In a more analytic approach, I have worked on the study of periodic and symmetric structures.
b. Non-selfadjoint operator algebras. My research interests involve reflexivity and chirality of operator algebras generated by unitary semigroups.
PhD proposals are welcome in the broad areas of time series analysis, nonstationarity, changepoints, wavelets, streaming data as well as environmental and health applications.
I am happy to supervise PhD students who wish to work on a project related to my research expertise in Operator Theory and Non-commutative Analysis. Possible topics include: ideals of the algebra of bounded operators on a Banach space; the existence of approximate identities in such ideals; commutators and traces.
Homological algebra and derived categories Higher structures and noncommutative geometry Deformation theory of geometric and algebraic structures Operads and Topological Field Theories Rational homotopy theory
Bandits in real systems
Multi-armed bandit theory [https://en.wikipedia.org/wiki/Multi-armed_bandit] is extremely well-studied in situations where there is a very direct link between actions and rewards. However in many situations where we may wish to deploy these techniques, the choice of an action leads to outcomes in a complex and partially-understood way. For example, choosing the price of a finitely-available product for the following day will result in a semi-predictable sales pattern, and consequent amount of stock left at the end of the day. And choosing some hyper-parameters of a learning method for a period of time will result in a semi-predictable performance improvement of the method. This project will develop techniques for such problems, where there is a (semi-)parameterised model of the world, and sequential decisions must be taken to simultaneously learn the model and optimise outcomes.
I would be interested in taking a PhD student who has some familiarity with algebraic geometry and representation theory. A PhD student of mine would address open questions in the theory of linear algebraic groups over fields. I have potential PhD projects in mind related to birational invariant theory, and also to linear representation theory in positive characteristic.
I am interested in supervising the following topics:
1. Nonstationary functional time series methods
2. Methodologies for large spatio-temporal data
3. Factor models for complex spatio-temporal data
4. Methodologies for large environmental data
5. Methodologies for Point Processes
I would be happy to supervise PhD students for a research project in modular representation theory of finite, infinite discrete and profinite groups and related topics (such as group cohomology), on Mackey functors and Burnside rings, or on (pro-)fusion systems and related topics.
I am happy to supervise enthusiastic PhD statistics students in areas developing new statistical methodology for real data problems. My areas of current research include statistical ecology, multiple systems estimation and illegal wildlife trade.
I welcome new PhD students with strong background in statistics and probability to work on projects related to robust estimation in nonlinear time series models and resampling.
I would be happy to supervise a PhD student who is interested in computational methods for Bayesian inference or probabilistic machine learning. In particular, the development of new MCMC and SMC algorithms for big data and intractable likelihood problems. Or projects which explore the intersection of sampling and optimisation algorithms.
I would be interested in discussing PhD opportunities with a student interested in graph theory, matroid theory, discrete geometry, algebraic geometry, algebraic statistics or matrix/tensor product completions. Specifically I work in combinatorial rigidity which combines ideas from combinatorics, algebra and geometry to study problems related to each of the above topics. Unifying these topics is the study of geometric graphs and their configuration spaces.
As well as the above theoretical topics, I am interested in applications of these topics, for example to biophysical materials and control of robotic formations.
I am interested in supervising topics in changepoint regression, anomaly detection and related applied projects. Many topics will have links to artificial intelligence, machine learning, non-parametric statistics, high-dimensional statistics or time series analysis.
More information can be found: https://qiyaopeng.github.io/index.html
(1) Quantification of the impact of incomplete surgical resection on future tumor evolution by mathematical modelling
(2) Agent-based model of wound healing in epidermis and dermis with finite-element methods
(3) Modelling and analysis of traction force microscopy experiments
(4) Analysis of a bulk-surface reaction-diffusion model for cell polarisation: biological validation and cell migration
I would be happy to supervise a PhD student who is interested in graph theory, combinatorics and/or discrete geometry (in particular rigidity and flexibility of geometric constraint systems, geometric graphs, count matroids, and symmetry in discrete structures). I have purely mathematical projects as well as projects that are motivated by applications and are interdisciplinary (involving areas such as robotics, structural and mechanical engineering, biophysics, and materials science).
Projects are available in combinations of (1) MCMC theory: efficiency as a function of tuning parameters, and convergence; (2) MCMC methodology: developing new algorithms or variations on existing algorithms; (3) MCMC applications in e.g. the environment, ecology or epidemiology; (4) particle filters and bridges for stochastic processes.
Example MCMC areas include: pseudo-marginal, delayed acceptance, HMC, non-reversible, and MCMC and variations for tall data.
I am happy to supervise students in topics related to medical statistics. I would particularly welcome applicants interested in developing methodology for the analysis of event history data using multi-state models.
I am happy to supervise PhD topics in all aspects of extreme value theory. In particular multivariate and spatial extremes are exciting areas with lots of work to be done on relaxing assumptions so that models are more realistic.
