PhD Studentship: Monte Carlo Methods for Constrained and Aggregated Data

The University of Birmingham invites applications for a fully or partially funded PhD studentship within the School of Mathematics. The research focuses on designing and analysing innovative Monte Carlo methods, specifically exploring fusion techniques under exact constraints and optimal scaling in constrained domains. The successful candidate will work closely with leading researchers to build rigorous mathematical frameworks and computational algorithms for Bayesian inference. Applicants have the flexibility to shape the balance between mathematical theory, methodology, and practical computation according to their research interests. The position aims to produce methodological breakthroughs with theoretical guarantees on accuracy and computational cost.

• Develop and analyse novel Monte Carlo fusion methods that enforce exact aggregate constraints efficiently
• Derive diffusion limits and optimal tuning rules for samplers such as random-walk Metropolis and MALA on constrained domains
• Investigate the theoretical guarantees on accuracy and computational cost for newly designed sampling algorithms
• Implement computational experiments and algorithms using programming languages such as Python or R
• Synthesize research findings into high-quality publications and present results at academic conferences
• Contribute to the academic life of the School of Mathematics and collaborate with research peers