Statistical research involves developing and applying methods to learn from data.
The Modelling and Inference group focusses on developing novel approaches that can be applied to generic classes of data. For example, we have been at the forefront of research looking at how to estimate the probability of future extreme events - work that feeds into applications ranging from the design of flood defences to appropriately quantifying risk of investments - and have one of the largest groups in the UK investigating methods for detecting changes in time-series data. Full details of the range of research areas are given below.
Much of our work is motivated by real-life applications from a range of scientific and industrial areas. In particular, we are currently collaborating with BT, DSTL, Shell, Unilever and the Met Office. The group also has strong links with the Operational Research group based in the Department of Management Science and plays a leading role in the running of the STOR-i Centre for Doctoral Training.
Extreme Value Modelling
Quantifying risk often involves estimating the frequency of rare events. These events may be much rarer than those observed in data, and thus estimating their frequency will involve extrapolation. Extreme value theory gives a justified way of performing this extrapolation. Our group is at the forefront of theoretical developments of extremes, such developing methods for spatial extremes or dealing with non-stationarity over time. Much of our research is motivated by important real-life environmental applications, such as designing flood-defences or offshore installations.
Wavelets and Locally-Stationary Time Series
Many of the time series which we generate are characterised by abrupt or evolving changes in statistical structure. Failing to account for such realities can result in serious consequences. Our work seeks to develop more realistic analysis methods which explicitly account for such time-varying structure. This includes the development of novel methods for both changepoints and locally stationary time series. A particular current focus is on the development of accurate and computationally efficient changepoint search methods.
Most real-life applications of statistics require the use of computational methods. We have expertise in a range of such methods, including MCMC, sequential Monte Carlo and approximate Bayesian computation. Of particular focus is how to implement such methods in modern settings where we wish to fit complex stochastic models to large datasets.
Functional Data Analysis
Typical functional data will be in the form of curves, or densely observed longitudinal data, such as spectrometric curves or cardiac frequency profiles. Our group has interest in all aspects of data analysis and its application, such as curve alignment and registration, variability decomposition, regression and classification. We focus on developing new methodologies that take structural information into account to overcome high-dimensional problems associated with functional data.
Robust estimation for Finance
Our research focuses on the analysis of robust estimators of the parameters associated with volatility model of financial time series, such as GARCH models. We study them both theoretically and empirically based on simulated and real datasets.