[School of Natural Sciences PhD Scholarships] Bayesian Monte Carlo Methods for Complex Generative Time-Series Models

About the project

About the Project Time series arise throughout finance, economics science and technology, and are increasingly modelled using sophisticated generative systems. Classical examples include stochastic-volatility, regime-switching and high-frequency market-microstructure models, where latent states can make likelihood-based inference computationally demanding or even intractable. More recently, large pretrained generative models and time-series foundation models have created new opportunities for modelling complex sequential data, but it remains challenging to condition these models on specific features or constraints of interest. This PhD project will develop new Monte Carlo methodology for reliable inference and conditional simulation in such complex time-series models. A central theme will be to connect modern Bayesian computational methods with emerging generative modelling approaches. One direction will focus on scalable Bayesian computation for complex state-space and financial econometric models. The student will investigate methods including sequential Monte Carlo (SMC), importance sampling, particle MCMC, approximate Bayesian computation and neural posterior methods. Particular attention will be given to challenging settings involving long or multivariate time series and high-dimensional latent states. The research will study new computational strategies together with their theoretical properties, including consistency, Monte Carlo error and computational scaling. A second direction will investigate how SMC and related methods can be used to condition modern generative sequence models, including time-series foundation models. The aim is to generate paths satisfying user-specified conditions while maintaining a principled probabilistic interpretation. In financial applications, such conditions could include terminal returns, drawdowns, volatility levels, stress scenarios or other path-dependent features. Possible approaches include guided SMC, tempering or annealing strategies, and learned proposal mechanisms. The project will combine statistical methodology, mathematical analysis and computational experimentation. It would particularly suit a student interested in the interface between Bayesian statistics, Monte Carlo computation, time-series modelling and modern machine learning. Training will be provided in Bayesian computation, state-space modelling, sequential Monte Carlo methods, time-series analysis and modern generative models. The student will also develop skills in high-performance scientific computing and the implementation and evaluation of advanced statistical algorithms. 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 1 st November 2026, you can expect a decision by 18 th December 2026. If your application is submitted by 15 th January 2027, you can expect a decision by 30 th March 2027. Self or externally funded students can also be considered for this project. FSESoNS

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