Functional data analysis with informative missingness (UK Only)

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 <strong><em>EPSRC DTP Engineering & Physical Sciences</em></strong><em><strong>,</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>EPSRC Doctoral Landscape Award 2026/27: Statistics and School of Mathematics Scholarships 2026/27</strong></em>.</p> <p>Applications will be considered on after the closing date of Friday 30 January 2026.  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>Please note that you must provide the following documents in support of your application by the closing date of Friday 30 January 2026:</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).</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 class="MsoNoSpacing" style="text-align:start; margin-bottom:24px">A highly competitive EPSRC Doctoral Landscape Award providing full academic fees, together with a tax-free maintenance grant at the standard UKRI rate (£20,780 in academic session 2025/26) for 3.5 years.  Training and support will also be provided. You will also be automatically considered for a School of Mathematics Scholarship.</p> <p>This opportunity is open to UK applicants only.  All candidates will be placed into the EPSRC Doctoral Landscape Award and School of Mathematics Scholarship competitions. Selection is based on academic merit.</p> <p>Please note that there are up to 2 funded places available.  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>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 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>