Topological methods for the assessment of statistical models
This research project develops new methodology. We base it on the fields of statistical topology and survival analysis. Our aim is to investigate how we can apply this methodology as a tool for both assessment of model fit, and comparison of two-dimensional random fields. This is of particular interest in the application to global wind intensities data from the CESM Large Ensemble. Our data set contains many realisations of simulated climate variables.
The work examines to what extent these methods for analysing random fields are more informative than conventional methods alone. It allows the discovery of more subtle differences between real data and model output, or between multiple realisations within a data set. This raises the challenge of applying standard survival analysis techniques to spatially correlated data. It is a problem that has not been subject to previous work. A range of spatial correlation structures are studied, including how to model and fit these structures on the surface of the globe, where possible. This is vital due to the global nature of the data set as many conventional methods are insufficient for modelling on the surface of a sphere.
Drawing on work from statistical topology, the research looks at one particular topological metric, connected components (apparent in the 1D and 2D cases as local maxima or minima). Of primary interest is whether the number of these components differs between random fields with different distributions or correlation structures. If so, whether it is possible to identify distributions by this topological metric. And whether it is possible to formulate their occurrence as event times, allowing the application of survival theory to the data. This allows a far more subtle analysis of data than is possible using a survival analysis approach alone.
