Statistics PhD/iPhD/MPhil/MSc (Research)

The School of Mathematics & Statistics combines world-leading research expertise in pure mathematics, applied mathematics and statistics. Our research in statistics impacts across a range of areas including the energy sector, the environment, medicine and public health, teaching practice and public policy.

PhD: 3-4 years full-time; 6-8 years part-time; Thesis of Max 80,000 words
MSc (Research): 1-2 years full-time; 2-3 years part-time;
MPhil: 2-3 years full-time; 3-4 years part-time;
IPhD: 4 years full-time;

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Research projects

Statistics thesis topics

Overview

The School of Mathematics and Statistics is one of the largest in the UK. In the 2021 Research Excellence Framework (REF) the school was ranked 5^th in Mathematical Sciences, the highest ranking of any university in Scotland. Our research interests cover a wide range of topics, with our AI3 initiative, of analytics and inference innovation for impact, aiming to create a world-class environment for research and teaching that transforms the practice of Statistics, Data Analytics and Data Science.

With regular seminars and events, we have a lively and mutually supportive research environment, which has led to the award of coveted prizes and competitive fellowships for several of our junior staff and postgraduate research students.

Our main areas of research (AI3 intiative)

Study options

	full-time (years)	part-time (years)
Phd	3-4	6-8
Integrated PhD	4	n/a
MSc (Res)	1-2	2-3
MPhil	2-3	3-4

Integrated PhD programme (4 years)

Our PhD with Integrated Study in Mathematical Sciences is a four-year PhD programme in the School of Mathematics and Statistics.

Completion of taught Masters level courses in the first nine months will provide you with a valuable introduction to academic topics and research methods, whilst providing key training in the critical evaluation of research data.

Upon successful completion of the taught component, you will progress to your research degree. You will submit a thesis to be examined by the end of your fourth year.

Entry requirements

Our regular standard of admission is usually a 2.1 honours degree.

Required documents

Applicants should submit:

Academic Transcripts and Degree Certificates
CV
Two References

English language requirements

For applicants from non-English speaking countries, as defined by the UK Government, the University sets a minimum English language proficiency level.

Accepted English language tests

We accept a wide range of English language tests for entry to this programme. Tests must have been taken within 2 years 5 months of programme start date, and requirements must be met using a single test.

International English Language Testing System (IELTS) Academic and Academic Online (not General Training)

6.5 with no subtests under 6.0
IELTS One Skill Retake Accepted
We do not accept General Training

TOEFL iBT (including MyBest and Home Edition)

Tests taken up to 20 January 2026

90 Overall, no subtest lower than Reading 20; Listening 19; Speaking 19; Writing 21

Tests taken from 21 January 2026

92 Overall, no subtest lower than 4.5

Pearsons PTE Academic (test centre only)

65 overall with no subtest less than Reading 60; Listening 60; Speaking 65; Writing 60

Cambridge C1 Advanced and C2 Proficiency

176 overall, no subtest less than 169

Oxford ELLT

7 overall with no subtest less than 6

LanguageCert Academic SELT/Academic/Academic Online

70 overall with no subtest less than 60

Password Skills Plus

6.5 overall with no subtest less than 6.0

Trinity College Integrated Skills in English II

96 overall with no subtest less than 90

Kaplan Test of English

Any two subtests at 480 or higher, and any two subtests at 450 or higher

PSI Skills for English

B2 Pass with Merit

Duolingo English Test

120 overall with Writing at 120 and no subtest less than 110

Oxford Test of English Advanced

140 Overall with any two subtests at 126 or higher, and any two subtests at 136 or higher

Alternatives to English Language qualification

Degree from majority-English speaking country (as defined by the UKVI including Canada if taught in English)

Students must have studied for a minimum of their final year at Undergraduate level, or 9 months at Master's level, and must have completed their degree in that majority-English speaking country within 6 years of programme start.

TNE degree for UK University taught at a campus outside of the UK.

Students must be awarded the degree by the UK university and must have completed the degree within 6 years of programme start.

Pre-sessional courses

The University of Glasgow accepts evidence of the required language level from the English for Academic Study Unit Pre-sessional courses. We would strongly encourage you to consider the pre-sessional courses at the University of Glasgow's English for Academic Study (EAS) Unit. Our Pre-sessional courses are the best way to bring your English up to entry level for University study. Our courses give you:

direct entry to your University programme for successful students (no need to take IELTS)
essential academic skills to help you study effectively at University
flexible entry dates so you can join the right course for your level.

For more detail on our pre-sessional courses please see:

Pre-sessional courses

We can also consider the pre-sessional courses accredited by the below BALEAP approved institutions to meet the language requirements for admission to our postgraduate taught degrees:

Heriot Watt
Kingston Upon Thames
Middlesex University
Manchester University
Reading University
Edinburgh University
ST Andrews University
UCL
Durham

Fees and funding

Fees

2027/28

UK: To be confirmed [26/27 fee was £5,238]
International & EU: £33,708

Prices are based on the annual fee for full-time study. Fees for part-time study are half the full-time fee.

Irish nationals who are living in the Common Travel Area of the UK, EU nationals with settled or pre-settled status, and Internationals with Indefinite Leave to remain status can also qualify for home fee status.

Fee status and policies

Alumni discount

We offer a 15% tuition fee discount to eligible self-funded alumni starting a Postgraduate Taught (PGT) Masters or Postgraduate Research (PGR) programme in the 2027/28 academic year.

This includes University of Glasgow graduates and those who have completed a Study Abroad programme, Exchange programme, International Summer School or Erasmus programme with us. This discount can be awarded alongside most University scholarships. No additional application is required.

Full details of our Alumni Discount

Possible additional fees

Re-submission by a research student £540
Submission for a higher degree by published work £1,355
Submission of thesis after deadline lapsed £350
Submission by staff in receipt of staff scholarship £790

Depending on the nature of the research project, some students will be expected to pay a bench fee (also known as research support costs) to cover additional costs. The exact amount will be provided in the offer letter.

Funding

View a full list of our current scholarships

Support

Our postgraduate students join a community of academic experts across a wide range of pure and applied mathematics and statistics and develop a mature understanding of fundamental theories and analytical skills applicable to many solutions.

There is a lively seminar program with members of the Schools involved in a number of networks including the North British Functional Analysis Seminar, The North British Differential Equations Seminar and the LMS Network on Classical and Quantum Integrability.

The School also welcomes many guest speakers from the UK and overseas. We hold regular postgraduate seminars, where our PhD students can develop their presentation skills, and international conferences and workshops.

Students can also attend our hugely popular week-long training course each year, which provides practically motivated training in key statistical analysis and modelling skills.

You will be part of a Graduate School which provides the highest level of support to its students.

The overall aim of our Graduate School is to provide a world-leading environment for students which is intellectually stimulating, encourages them to contribute to culture, society and the economy and enables them to become leaders in a global environment.

We have a diverse community of over 750 students from more than 50 countries who work in innovative and transformative disciplinary and interdisciplinary fields. An important part of our work is to bring our students together and to ensure they consider themselves an important part of the University’s academic community.

Being part of our Graduate School community will be of huge advantage to you in your studies and beyond and we offer students a number of benefits in addition to exceptional teaching and supervision, including:

A wide-ranging and responsive research student training programme which enables you to enhance your skills and successfully complete your studies.
Mobility scholarships of up to £4000 to enable you to undertake work in collaboration with an international partner.
A diverse programme of activities which will ensure you feel part of the wider-research community (including our biannual science slam event).
A residential trip for all new research students.
The opportunity to engage with industry-partners through training, placements and events.
Professionally accredited programmes.
Unique Masters programmes run in collaboration with other organisations.
State-of-the-art facilities including the James Watt Nanofabrication Centre and the Kelvin Nanocharacterisation Centre.
Highly-rated support for international students.

Over the last five years, we have helped over 600 students to complete their research studies and our students have gone on to take up prestigious posts in industries across the world.

Email: scieng-gradschool@glasgow.ac.uk

Collaborations

Our research group has strong connections with environmental agencies such as the Scottish Environment Protection Agency (SEPA), the Environment Agency in England and the Centre for Ecology and Hydrology.

These collaborations have led to research secondments for postgraduate students, and other opportunities have seen students travelling abroad to work with high-profile scientific groups such as the Commonwealth Scientific Industrial Research Organisation in Australia.

How to apply

Identify potential supervisors

All Postgraduate Research Students are allocated a supervisor who will act as the main source of academic support and research mentoring. You may want to identify a potential supervisor and contact them to discuss your research proposal before you apply. Please note, even if you have spoken to an academic staff member about your proposal you still need to submit an online application form.

You can find relevant academic staff members with our staff research interests search.

Gather your documents

Before applying please make sure you gather the following supporting documentation:

Final or current degree transcripts including grades (and an official translation, if needed) – scanned copy in colour of the original document.
Degree certificates (and an official translation, if needed): scanned copy in colour of the original document.
Two references on headed paper and signed by the referee. One must be academic, the other can be academic or professional. References may be uploaded as part of the application form or you may enter your referees contact details on the application form. We will then email your referee and notify you when we receive the reference. We can also accept confidential references direct to pg-research-admissions@glasgow.ac.uk, from the referee’s university or business email account.
Research proposal, CV, samples of written work as per requirements for each subject area.