Mathematical data science and statistics
We focus on the analysis of real-world dynamical systems that generate large data sets. We apply a broad range of mathematical techniques to identify system characteristics, and to make predictions using data and mathematical models.
Research leads
Dr Werner Bauer
Using stochastic models for predictions
Dr Naratip Santitissadeekorn
Data assimilation for urban crime models
Professor Anne Skeldon
Data assimilation in the neighbourhood of bifurcations
Data assimilation methods
Data analysis and statistical techniques are an essential element in many cross-disciplinary projects. Within our group, we have expertise in the design of experiments, the development of new data assimilation methods and novel methods for the analysis of physiological time series.
Data assimilation for urban crime models
Recent mathematical research has developed several crime models such as agent-based model (ABM) for urban burglary that incorporate well-known interactions between individual criminals and environment at the neighbourhood level. These models provide an important tool to establish the links between hypothesised criminal behaviours embedded in the models and observed crime data.
Naratip Santitissadeekorn is developing a nonlinear filtering algorithm technique that can statistically merge model predictions with crime data, mathematically modelled a point process, in order to make better projections of future crime patterns such as crime hot spots. His research will also provide a non-invasive tool to quantify some well-known criminal behaviours (eg. near-repeat victimisation).
Data assimilation in the neighbourhood of bifurcations
Data assimilation involves fusing models and data to estimate model parameters or to predict state variables, or both. In order to develop robust algorithms, it is important to understand both the data and the model structure.
Motivated by models of the carbon cycle in forests, project lead Anne Skeldon is analysing and evaluating the performance of data assimilation schemes in the neighbourhood of tipping points.
Uncertainty quantification for weather and climate modelling
We are developing prediction systems for weather and climate that consider unknown processes and errors in the mathematical models and measurements, to estimate uncertainties in forecasts.
Using stochastic models for predictions
When using numerical models for predictions of weather and climate we face various problems such as errors in the mathematical formulations of the phenomena of interest, unresolved scales, and limited computational resources. This might lead to significant errors in the prediction because, for example, unresolved physical processes might have a significant influence on the large scale atmospheric flow. Traditionally, parameterisations have been used in deterministic weather and climate models to represent subgrid processes to increase the accuracy of simulations.
To capture these different sources of errors, led by Werner Bauer, we use stochastic models for predictions because they provide promising alternatives to classical, deterministic prediction systems. These models describe the uncertainty in processes and their effects on the large scale flow by random variables.
We apply this approach to predict, rather than one deterministic solution (which might differ significantly from the “truth”), an ensemble of solutions. The forecasting error is then expressed through the spread of this ensemble. This allows us to provide weather and climate forecasts and an estimation of their uncertainty.
