Functional regression models with application in neuroimaging data analysis

We are looking for strong candidates to work on this exciting project with a multidisciplinary team described below!<br /> <br /> In today's world, clinicians and researchers have access to a wealth of data to support diagnosis and treatment in a huge range of brain-related disorders. Specifically, data from Magnetic Resonance Imaging systems (fMRI and MRI) offers a wealth of information waiting to be unlocked, but requires tools and significant expertise for the analysis and interpretation of these data sets. In this project, we aim to develop novel statistical approaches (with corresponding software) for exploring these datasets to further understand the dynamical behaviour behind cognitive-related deficits aiming to improve diagnosis and treatment. Given the important societal and clinical need to address Dementia that has now become the leading cause of death within the UK (ONS, UK), the initial focus of the project will be Alzheimer’s disease with the opportunity to diversify our models into other cognitive/neurodegenerative related disorders. <br /> <br /> The challenge for understanding brain data lies in analysing multi-dimensional time-varying images (e.g. MRI, fMRI) and simultaneously extracting high-resolution structures and dynamic information for which existing methods are limited. To address this, the project aims to develop novel functional regression models based on Karhunen-Loeve decomposition (Li et al. 2019) and tensor decomposition (Zhou et al. 2013) and machine learning methods based on vibrational auto encoder (Sauty & Durrleman2022), which will leverage the advantages of time and space data to unlock new insights for understanding the brain. In particular, the proposed models are expected to be able to identify region-of-interest, and quantify its rate of change in the brain over time, thus will make accurate predictions of disease progression and provide insight into earlier diagnosis. <br /> <br /> This proposed PhD project is related to our on-going Royal Society International Exchanges project and therefore has exciting UK-China collaborations.<br /> <br /> References:<br /> Li, Y., Huang, C., & Härdle, W. K. (2019). Spatial functional principal component analysis with applications to brain image data. Journal of Multivariate Analysis, 170, 263-274.<br /> <br /> Sauty, B., & Durrleman, S. (2022, September). Progression models for imaging data with longitudinal variational auto encoders. In International Conference on Medical Image Computing and Computer-Assisted Intervention (pp. 3-13). Cham: Springer Nature Switzerland. <br /> <br /> Zhou, H., Li, L., & Zhu, H. (2013). Tensor regression with applications in neuroimaging data analysis. Journal of the American Statistical Association, 108(502), 540-552.<br />

<p>Formal applications for research degree study should be made online through the <a href="https://www.leeds.ac.uk/research-applying/doc/applying-research-degrees">University's website</a>. Please state clearly in the Planned Course of Study section that you are applying for <em><strong>PHD Statistics FT,</strong></em> in the research information section that the research degree you wish to be considered for is <em><strong>Functional regression models with application in neuroimaging data analysis</strong></em> as well as <a href="https://eps.leeds.ac.uk/maths/staff/4053/dr-haiyan-liu">Dr. Haiyan Liu</a> as your proposed supervisor and <em><strong>in the finance section, please state clearly the funding source 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 an appropriate discipline. The criteria for entry for some research degrees may be higher, for example, several faculties, also require a Masters degree. Applicants are advised to check with the relevant School prior to making an application. Applicants who are uncertain about the requirements for a particular research degree are advised to contact the School or Graduate School prior to making an application.

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. Some schools and faculties have a higher requirement.

<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://phd.leeds.ac.uk/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://phd.leeds.ac.uk/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://phd.leeds.ac.uk/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://phd.leeds.ac.uk/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://phd.leeds.ac.uk/funding/73-leeds-marshall-scholarship">Leeds Marshall Scholarship</a> is available to support US citizens. <a href="https://phd.leeds.ac.uk/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 <em><strong>not</strong></em> cover the costs associated with moving to the UK.  All such costs (<a href="https://www.leeds.ac.uk/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 general enquiries about applications, contact our admissions team by email to <a href="mailto:phd@engineering.leeds.ac.uk">phd@engineering.leeds.ac.uk</a> <br /> For questions about the research project, contact Dr. Haiyan Liu by email to <a href="mailto:h.liu1@leeds.ac.uk">h.liu1@leeds.ac.uk</a>.</p>