I started my career working on multiscale methods for stochastic differential equations, such as homogenization, which I later applied to modelling plant–soil interactions. That work set the theme for everything since: understanding how continuous-time dynamics — differential equations, deterministic and stochastic — relate to the discrete algorithms used to simulate, sample, or optimise them.
Today my main focus is computational statistics and Bayesian computation. I develop and analyse Markov chain Monte Carlo and Langevin-based sampling algorithms for large-scale inference, particularly in imaging inverse problems — denoising, deblurring, tomography, and low-photon imaging — often by drawing out the exact connections between sampling, optimisation, and the differential equations underneath them.
I also work in mathematical biology, on stochastic simulation of chemical reaction networks, and more recently in network science and data science, including spectral methods for graphs and hypergraphs and generative models for Bayesian inference.
The following video is a research overview I gave at the Alan Turing Institute in 2017.
This is a talk for the Sheffield SIAM-IMA student chapter conference in 2021.
This is a talk from the Stochastic Dynamical Systems in Biology: Numerical Methods and Applications programme at the Newton Institute.
This is a talk from the One World Virtual Seminar Series — Stochastic Numerics and Inverse Problems.
Watch the talk →