Professor Stuart's research is focused on the development of foundational mathematical and algorithmic frameworks for the seamless integration of models with data. He works in the Bayesian formulation of inverse problems for differential equations, and in data assimilation for dynamical systems.
Bayesian inverse problems, Bayesian hierarchical models, geometric inverse problems, uncertainty quantification, imaging, reparametrization of models, model error approximation.
My research interests lie at the intersection of applied mathematics, probability and statistics. Broadly speaking, I work on the analysis, development and application of methods for estimating parameters and quantifying uncertainty. I am particularly interested in the Bayesian approach for solution of inverse problems. My interest in this field stems from industrial projects in atmospheric dispersion and focused ultrasound treatment.
Scalable Bayesian inference methods for problems of big data/large dimensions, particularly Markov Chain Monte Carlo (MCMC) methods, variational Bayes, and their geometric variants.