Simon Cotter is a senior lecturer in applied mathematics in the School of Mathematics at the University of Manchester. He attained his PhD in infinite dimensional Bayesian inverse problems from the University of Warwick in 2010 under Andrew Stuart. He then worked with Radek Erban at Oxford University on stochastic models of chemical reactions, before taking up a lectureship at the University of Manchester as a member of the numerical analysis group. He was promoted to senior lecturer in 2016. Simon is interested in working on problems in the interface between applied maths, statistics, probability and often with biological applications. In particular he is interested in a range of computational methods for characterising probability distributions, including Markov chain Monte Carlo methods.
Underlying almost all aspects of data science and artificial intelligence, is a need for the characterisation of probability distributions arising from epistemic uncertainties. Robust and efficient numerical methods for the sampling of such distributions is a key component of many approaches to understanding data, incorporating it into mechanistic models, and informing decision makers. This can range from sampling from the distributions arising from Bayesian inverse problems in data analytics within engineering and science, through to the distributions which form part of the machinery that allows AI algorithms to work, such as within Gaussian process construction. Within his research, Simon has focused, amongst other things, on the design, analysis and implementation of efficient Markov chain Monte Carlo (MCMC) methodologies for data analytics.
This powerful and increasingly important family of methods allow us to sample from complex probability distributions. There are a range of challenges in this arena, including the development of methods which can tackle problems in high dimensions, both in terms of the state-space, and in terms of the size of data. There are also challenges surrounding the efficient sampling of distributions with complex structures, for example multimodality, or the concentration of the probability density on lower dimensional curved manifolds. Each of these scenarios requires careful consideration, with specific methods being optimal in each case.