[School of Natural Sciences PhD Scholarships] Quantitative Limit Theorems in Mathematical Statistics via Stein’s Method

About the project

About the Project Distributional approximations arise throughout probability and statistics. Here one is interested in approximating the (possibly intractable) distribution of a quantity of interest by a simpler, well-understood distribution, allowing one to make inference. For example, the normal approximation of the standardised sample mean, formalised by the central limit theorem, is one of the most fundamental results in probability and statistics. In this project, the powerful (and rather beautiful!) probabilistic technique Stein’s method will be used to derive explicit error bounds for important distributional approximations in mathematical statistics, such as the normal approximation of the maximum likelihood estimator, the chi-square approximation of the log-likelihood ratio statistic and the multivariate delta method. 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 in Mathematics (or international equivalent) OR any upper-second class (2:1) honours degree and a Master’s degree at merit in Mathematics (or international equivalent). We are looking for an enthusiastic and highly motivated graduate holding a first-class undergraduate degree in Mathematics or a closely related discipline. Applicants are preferred to have a background in probability and excellent communication skills (written and oral). 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

Research areas