Tom graduated from Durham University in 2015 with a BSc in Mathematics. His interests in computational and applied maths led him to the Modern Applications of Mathematics MSc offered by Bath, which included a placement writing numerical software in the oil industry. While between universities, he undertook a summer research placement at York focused on Mathematical Biology. During the next four years of SAMBa, he hopes to expand his understanding of applied maths and maybe even learn some stats along the way. Outside of maths he enjoys listening to music, cycling and hiking.

Research project title:
Large scale differential geometric MCMC

Supervisor(s):
Karim Anaya-Izquierdo, Rob Scheichl

Project description:
Uncertainty Quantification (UQ) concerns both propagation of uncertainty through a physical model, known as the forward problem, and the inverse problem of inferring uncertain model parameters from noisy measurements. Markov Chain Monte Carlo (MCMC) methods 30are the most widely used tools for computing expectations in UQ and large statistical models in general. Conventional approaches to MCMC are often inefficient and must compute many samples for a high accuracy. Geometric ideas can be used to improve the methods’ statistical performance; two prominent algorithms in this line of thinking are Riemann Manifold Hamiltonian Monte Carlo (RMHMC) and Riemann Manifold Metropolis Adjusted Langevin Algorithm (RMMALA). Tom is interested in extending these ideas to exploit more general ideas from differential geometry, with a focus on developing methods that are suited to problems from UQ.