Functional data analysis models for count data

The aim of the project is to establish functional data analysis models for count data. The statistical analysis of count data is a specialized research area within statistics due to its high practical significance. Specifically the applications of count data are primarily in two directions. The first one is a statistical tool for counting, examples are number of passengers hospital admissions. The second one is to record the categorical data examples are classification of items in ordered and mutually exclusive quality categories depending on the level of defect. <br /> <br /> Functional count data occur frequently in real practice. The first motivating dataset is number of taxi passengers recorded over a few years among different zones in New York see Dubey and Müller (2022). The second motivating dataset is hospital admissions over a few years among different areas in Leeds see Liu et al. (2024). However, the methodology for functional count data is far behind. As far as we know, only two relevant works exist: Canale and Dunson (2012) and Sentürk et al. (2014). The main limitation of these two works is they cannot reduce dimension and therefore following-up regression, classification, clustering cannot be constructed in functional data analysis (FDA) way.<br /> <br /> Therefore, in this project, we aim to establish functional principal component analysis (FPCA) framework (including multiple FPCA) for functional count data. FPCA is an important tool in FDA, for its utility in dimensionality reduction and variation mode exploration.<br /> <br /> References:<br /> Canale, A., and Dunson, D. B. (2012). A Bayesian nonparametric model for count functional data. In XLVI Riunione Scientifica SIS (pp. 1-8). CLEUP-Coop. Libraria Editrice Universita di Padova.<br /> Dubey, P., and Müller, H. G. (2020). Functional models for time-varying random objects. Journal of the Royal Statistical Society Series B: Statistical Methodology, 82(2), 275-327.<br /> Liu, H., Aivaliotis, G., Kumar, V., and Houwing-Duistermaat, J. (2024). On Estimation of the Effect Lag of Predictors and Prediction in a Functional Linear Model. Statistics in Biosciences, 16(1), 1-24.<br /> Sentürk, D., Dalrymple, L. S., and Nguyen, D. V. (2014). Functional linear models for zero-inflated count data with application to modelling hospitalizations in patients on dialysis. Statistics in medicine, 33(27), 4825-4840.<br /> <br /> Student profile:<br /> The successful PhD candidate should have a solid background in mathematics and statistics, with a stong interest in statistical modelling of count data. Key skill required for the project is competent use of R.

<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 models for count data</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 in the finance section, please state clearly <em><strong>the funding 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/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-2022">Leeds Opportunity Research Scholarship</a> <strong>(closing date: 1 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: 7 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 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>