[School of Natural Sciences PhD Scholarships] Conformal Prediction for Uncertainty Quantification in Machine Learning with Applications to Precision Medicine

About the project

About the Project Precision medicine aims to tailor treatment decisions to individual patients based on their characteristics, predicted outcomes and likely responses to treatment. A fundamental challenge is to estimate how much an individual patient would benefit from one treatment compared with another. This quantity, known as the individual treatment effect (ITE), depends on a counterfactual outcome: the outcome that would have been observed had the patient received a different treatment. Since this counterfactual cannot be directly observed, reliable statistical inference is particularly challenging. Modern machine-learning methods, including random forests, gradient boosting and neural networks, offer powerful tools for modelling complex relationships and heterogeneous treatment effects. However, accurate predictions alone are not sufficient for clinical decision-making. It is equally important to understand how uncertain those predictions are and how much confidence can be placed in an estimated treatment effect or treatment recommendation. This PhD project will investigate conformal prediction and conformal inference as flexible approaches to uncertainty quantification for counterfactual outcomes and individual treatment effects. Conformal methods can be combined with a wide range of machine-learning algorithms and, under suitable assumptions, can provide rigorous finite-sample coverage guarantees without requiring a fully specified parametric model. The project will combine methodological development, statistical theory and computation. Possible research directions include developing new conformal methods for counterfactual prediction and ITEs; integrating conformal inference with different machine-learning models; investigating coverage, efficiency and robustness; studying the effects of sample size, treatment-effect heterogeneity, covariate imbalance and model misspecification; comparing conformal approaches with alternative uncertainty-quantification methods; and extending the methodology to personalised treatment selection and optimal treatment decision-making. The student will conduct simulation studies and apply the methods to publicly available clinical or healthcare datasets. Depending on the student's interests and progress, the project may also investigate theoretical properties such as finite-sample validity, efficiency and asymptotic behaviour. This project is particularly suitable for a student with an interest in statistics, machine learning, causal inference, uncertainty quantification, statistical computing and precision medicine. It will provide training in modern statistical methodology, R and/or Python programming, simulation studies, machine-learning techniques, reproducible research and the analysis of healthcare data. The student will join an active research environment and will be encouraged to participate in seminars, specialist training, research collaborations and national and international conferences. 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 Statistics, Mathematics, Data Science, Machine Learning, Computer Science, Biostatistics or a closely related discipline OR any upper-second class (2:1) honours degree and a Master’s degree at merit (or international equivalent) in Statistics, Mathematics, Data Science, Machine Learning, Computer Science, Biostatistics or a closely related discipline. 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