Uncertainty Quantification and Data Science
The quantity and complexity of data available to researchers continues to increase rapidly. The group seek to develop the mathematical methods for working with large and / or complex datasets, such as networks, biological and industrial data. One example is designing algorithms such as Markov chain Monte Carlo (MCMC) methods so that modern computational resources can be efficiently leveraged. Another is to obtain theoretical understanding of data based on mathematical analysis of models of the process that generated it. This can lead to application-specific improvements in inference and data analysis.
Thomas works primarily on mathematical epidemiology, an area of interdisciplinary applied mathematics that involves a large number of quantitative techniques applied to the study of patterns of disease at the population level. Epidemiology is the science of counting ill people - a simple description that hides major mathematical complexity. A tremendous number of different factors combine to determine the risk that any of us might become ill, however if we could disentangle these from each other then it might be possible to target the most important factors systematically. His work is mainly on the mathematical, statistical and computational methods that are needed to understand these phenomena. Thomas currently works on the EPSRC-funded project 'Operationalising Modern Mathematical Epidemiology'.
Tim is a lecturer in statistics with the University, his research interest primarily include (optimal) statistical design of experiments, together with associated modelling and uncertainty quantification problems. In design of experiments, he seek methods and strategies for choosing a good allocation of the limited resources in a physical or computational experiment in order to maximize the 'information' gained. An important consideration is how to quantify the amount of information that will likely be obtained.
He alternates between Bayesian and non-Bayesian, e.g. minimax, approaches. Some particular problems of interest include design for models for grouped discrete data (GLMMs), methodology for Bayesian and pseudo-Bayesian design, computer model calibration, and random design strategies, especially as applied to model-robust design theory.
Catherine is a Reader in Applied Maths and Numerical Analysis in the School of Mathematics. Her research is mainly concerned with numerical analysis (linear algebra, fast solvers, error estimation) related to the numerical solution of partial differential equations (PDEs). In particular, she is interested in the numerical solution of PDE models with uncertain/random inputs, and efficient algorithms for uncertainty quantification (UQ). The applications she deals with typically give rise to mathematical models consisting of PDEs with uncertain inputs. Catherine is also an associate editor for the SIAM/ASA journal on Uncertainty Quantification and the SIAM journal on Numerical Analysis.
Oliver is the Sir Horace Lamb Professor in Applied Mathematics, his research interests span continuum mechanics, transport processes, multiscale methods and mathematical modelling in medicine and biology. He applies these techniques in studies of cell and tissue biomechanics, physiological flows and systems biology, with applications ranging from the human respiratory and cardiovascular systems to plant growth and development. His interests also include energy-related applications such as carbon sequestration and photosynthesis.
Simon is a senior lecturer in applied mathematics within the School of Mathematics. His research interests lie in the interface between applied probability, statistics and numerical analysis. He is particularly interested in the development of numerical algorithms which allows him to simulate and analyse complex stochastic systems, ranging from Markov chain Monte Carlo (MCMC) methods for Bayesian inverse problems, to multiscale methods for stochastic biochemical reaction networks.
Mark is a Reader in the School of Mathematics, who works on applications of mathematics to the Life Sciences. He collaborates closely with experimental groups to develop ODE and Markov-process models of biochemical reaction networks and other cellular and biophysical processes. He is interested in essentially all aspects of the associated mathematical problems, from dynamics through to statistical problems associated with fitting parameters and on to the algebraic structure of some of the systems of ODEs. He has also worked on molecular evolution, which is essentially an optimisation problem over a combinatorially vast forest of potential evolutionary trees.