Functional data analysis with informative missingness

The increasing availability of extensive datasets with variables measured over a continuum, such as time, space, or frequency, has opened new frontiers in research across disciplines. These datasets, known as functional data, are prevalent in fields ranging from environmental monitoring and education to biomedical sciences and engineering. However, analysing such data remains challenging due to their high dimensionality, multivariate structure, and, critically, the presence of missingness that is not completely at random. Functional data analysis (FDA) offers a powerful framework for extracting meaningful insights from these infinite-dimensional data. A first step in FDA is typically functional principal component analysis (FPCA), which reduces dimensionality by capturing dominant modes of variation. For multivariate functional data, multivariate FPCA (MFPCA) extends this approach to model covariation among multiple functional variables. These methods are essential for understanding complex systems where multiple variables evolve over time or space. However, real-world datasets often suffer from different types of informative missingness. Applying FPCA or MFPCA without accounting for these issues can lead to biased results, misrepresenting relationships among variables and undermining downstream analyses such as prediction, classification, and thus decision-making.<br /> <br /> This project aims to fill that gap by developing FPCA and MFPCA frameworks for functional data with informative missingness. The application will be within biomedical studies, such as Alzheimer's disease and scleroderma.

<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 data analysis with informative missingness</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 that you are applying for, if you are self-funding or externally sponsored.</strong></em></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 grading scheme</li> <li>Personal Statement outlining your interest in the project</li> <li>CV</li> </ul> <p><strong>If English is not your first language, you must provide evidence that you meet the University's minimum English language requirements (below). Please note that if you are applying to the China Scholarship Council-University of Leeds Scholarship, evidence of meeting English Language requirements must be provided by the closing date of Wednesday 7 January 2026 at 17:00 (UK Time).</strong></p> <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>A highly competitive School of Mathematics Scholarship offering the award of fees, together with a tax-free maintenance grant (currently £20,780 for academic session 2025/26) for 3.5 years. Training and support will also be provided. <strong>Please note the closing date for this scholarship is Friday 27 February 2026.</strong><br /> <br /> This opportunity is open to both UK and international applicants. All candidates will be placed into the School of Mathematics Scholarship Competition and selection is based on academic merit.<br /> <br /> Please note that there is only 1 funded place available. Please note that whilst you may be successful in securing an academic offer for any project linked to this funding opportunity, this does not mean that you have been successful in securing an offer of funding. Funding is awarded on a competitive basis.</p> <p><em><strong>Important:</strong></em> Please note that that the award does <em><strong>not</strong></em> cover the costs associated with moving to the UK.  All such costs (visa, Immigration Health Surcharge, 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><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/209-leeds-doctoral-scholarships-2024">Leeds Doctoral Scholarship</a> <strong>(closing date: 1 April 2026)</strong> and <a href="https://phd.leeds.ac.uk/funding/234-leeds-opportunity-research-scholarship-2026">Leeds Opportunity Research Scholarship</a> <strong>(closing date: 1 April 2026)</strong> are available to UK applicants.  Alumni Bursary 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-2026">China Scholarship Council-University of Leeds Scholarship</a> is available to nationals of China <strong>(closing date: 7 January 2026)</strong>. The Leeds Marshall Scholarship is available to support US citizens. Alumni Bursary 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><em><strong>Important:</strong></em> Please note that that the award does <em><strong>not</strong></em> cover the costs associated with moving to the UK.  All such costs (visa, Immigration Health Surcharge, 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 UKCISA website for information regarding Fee Status for Non-UK Nationals.</p>

<p>For general enquiries about your application, please contact PGR Admissions by email to <a href="mailto:phd@engineering.leeds.ac.uk">phd@engineering.leeds.ac.uk</a>.</p> <p>For questions about this research project, please contact Dr Haiyan Liu by email to <a href="mailto:h.liu1@leeds.ac.uk">h.liu1@leeds.ac.uk</a>.</p>