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><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> <p class="MsoNoSpacing"><strong>Please note that you must provide the following documents in support of your application by the closing date of Monday 6 January 2025 if applying for the China Scholarship Council-University of Leeds Scholarship, Monday 3 February 2025 if applying for Leeds Doctoral Scholarship or Tuesday 1 April 2025 for Leeds Opportunity Research Scholarship.</strong></p> <p><strong>If you are applying for the School of Mathematics Scholarship 2025/26, or 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</li> <li>Personal Statement outlining your interest in the project</li> <li>CV</li> </ul>

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 style="margin-bottom:12px"><strong>Self-Funded or externally sponsored students are welcome to apply.</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: Monday 3 February 2025)</strong>, <a href="https://phd.leeds.ac.uk/funding/234-leeds-opportunity-research-scholarship-2022">Leeds Opportunity Research Scholarship</a> <strong>(closing date: Tuesday 1 April 2025)</strong> and <a href="https://phd.leeds.ac.uk/funding/55-school-of-mathematics-scholarship-2025-26">School of Mathematics Scholarship 2025/26</a> <strong>(open from October 2024)</strong> are available to UK applicants.</p> <p><strong>Non-UK</strong> – <a href="https://phd.leeds.ac.uk/funding/55-school-of-mathematics-scholarship-2025-26">School of Mathematics Scholarship 2025/26</a> <strong>(open from October 2024)</strong> are available to all International applicants.  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> <strong>(closing date: Monday 6 January 2025)</strong> is available to nationals of China. 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>You will be responsible for paying the overtime fee in full in your writing up/overtime year (£320 in Session 2024/25), 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:maps.pgr.admissions@leeds.ac.uk">maps.pgr.admissions@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>