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>To apply for this project you will need to make a formal application for research degree study through the <a href="https://www.leeds.ac.uk/research-applying/doc/applying-research-degrees">University website</a>. You will need to create a login ID with a username and PIN. </p> <p>•    For <strong>Application type</strong> please select <strong>Research Degrees – Research Postgraduate</strong>. <br /> •    The admission year for this project is <strong>2027/28</strong> Academic Year. <br /> •    You will need to select your <strong>Planned Course of Study</strong> from a drop-down menu. For this project, scroll down and select <strong>PHP Statistics Full Time.</strong> <br /> •    The project start date for this project is <strong>1 October 2027</strong>, please use this as your <strong>Proposed Start Date of Research</strong>. <br /> •    Please state clearly in the<strong> Research Information Section</strong> that the research degree you wish to be considered for is <strong>Functional data analysis with informative missingness </strong>as well as <a href="https://eps.leeds.ac.uk/maths/staff/4053/dr-haiyan-liu">Dr. Haiyan Liu</a> as your proposed supervisor.</p> <p><strong>Please state clearly in the Finance section</strong>, <strong>the funding that you are applying for, if you are self-funding or externally sponsored</strong>.</p> <p>More information on how to apply is available on our website <a href="https://www.leeds.ac.uk/research-applying/doc/applying-research-degrees">here</a>. You will be required to provide a personal statement which outlines your interest in the project you are applying for, why you have chosen it and how your skills map onto the requirements of the project.</p> <p>We will assess applications continuously as we receive them. We welcome and strongly encourage any potential applicants to contact the supervisor(s) for an informal discussion, prior to applying, and recommend submitting your application early.</p> <p><strong>If you are applying 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>If English is not your first language, you must provide evidence that you meet the University's minimum English language requirements (below).</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>This is a non funded PhD project. Applicants are expected to be self funded or to secure external funding.</p> <p>You can find out more about our Funding Opportunities on our <a href="https://phd.leeds.ac.uk/">Postgraduate Research Opportunities</a> website.</p> <p><strong>Important: </strong>Please note that all costs associated with your arrival at Leeds (<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>For questions related to the application process and eligibility, please contact PGR Admissions by email to <a href="mailto:epspgradmissions@leeds.ac.uk">epspgradmissions@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>