[School of Natural Sciences PhD Scholarships] Reliable Inference from High-Dimensional Data

About the project

About the Project Modern scientific studies often measure thousands of variables from relatively few individuals. Statistical methods can identify patterns in such data, but producing trustworthy confidence intervals and hypothesis tests is much harder, particularly when variability and dependence are not correctly modeled. This project will develop methods for reliable inference on a small number of scientifically important effects. The central idea is to construct an estimation procedure tailored to the question of interest, balancing statistical precision with robustness to covariance misspecification and correcting for bias induced by high-dimensional regularization. Potential applications include identifying genetic or imaging biomarkers, estimating environmental and public health effects, analyzing repeated measurements from digital health devices, and studying high-dimensional data collected across groups or regions. The research will involve high-dimensional probability, asymptotic theory, and convex optimization. Key questions include when valid inference is possible, whether adaptive procedures can improve efficiency, and whether they can perform nearly as well as the best method in a chosen class. The project would particularly suit a student who enjoys rigorous, proof-based mathematics and wants to apply it to modern scientific problems. Training will be provided in high-dimensional statistics, robust inference, optimization, and scientific computing, supported by regular supervision, research-group activities, and conference participation. This project is expected to start in September 2027. Before you apply: We strongly recommend that you contact the supervisors for this project before you apply. How to apply: To be considered for this project you must complete a formal application through our online application portal. If you already have an applicant account this link will directly open an application for PhD School of Natural Sciences Scholarships . If you don’t already have an applicant account, please follow the instructions here . When applying, please specify the full title and supervisor/s of the project, details of your previous study, and names and contact details of two referees. You must also upload a Supporting Statement describing your motivation to apply to the project, your CV and transcripts of awarded and in-progress university qualifications . Please note late or incomplete applications will not be considered. Equality, diversity and inclusion are fundamental to the success of The University of Manchester and central to all our activities. A diverse research community strengthens creativity, productivity and quality, while increasing the societal and economic impact of our work. We welcome applicants from all career paths, backgrounds and sections of the community, regardless of age, disability, ethnicity, gender, gender expression, sexual orientation or transgender status. We welcome applications from candidates returning to study after a career break or experience in other roles. Flexible study arrangements may be available, including part-time study at 50%, 60% or 80%, subject to the requirements of the project and funder. Eligibility : The standard academic entry requirement for this PhD is an upper second-class (2:1) honours degree (or international equivalent) in Mathematics, Statistics, Physics or Engineering OR any upper-second class (2:1) honours degree and a Master’s degree at merit (or international equivalent) in Mathematics, Statistics, Physics or Engineering. This project will remain open until filled. If your application is submitted by 1st November 2026, you can expect a decision by 18th December 2026. If your application is submitted by 15th January 2027, you can expect a decision by 30th March 2027. Self or externally funded students can also be considered for this project. FSESoNS

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