SEMINAR: Statistics Seminar

Statistical methods for analysing spatial data are important in many areas of science . There are many kinds of spatial data; in this project we are concerned with spatial patterns of points observed in a study region that covers all or part of the surface of a sphere. The points could represent the locations of animal sightings, gamma ray bursts, meteorite impacts, or other events.

Whilst the fundamental theory of point processes in general spaces is well-developed and can be applied easily to the sphere, little work has been done on models and methodology in this case. Indeed, most existing statistical methods for analysing spatial point patterns assume that the study region is a flat surface. However, this is not always appropriate. If a whale population survey covers a large area of ocean, it may be necessary to take account of the Earth’s curvature when calculating quantities such as the distance between whale sightings or the number of whales per unit area. Similarly, an astronomical survey of a large portion of the night sky needs to take account of the curvature of the celestial sphere. Other examples include surveys of cyclone initiation in the China Sea and gamma ray bursts in astronomy.

Curvature of the study region causes many complications. The effect of measurements and translations such as distance, area and rotation are more complex on curved surfaces than they are on flat surfaces. Similarly, many of the basic concepts of spatial statistics (e.g. point process intensity, stationarity, isotropy) require adaptation to deal with curved surfaces.

This project will develop a coherent set of statistical methods for spatial point patterns on curved surfaces. Existing statistical models and methodology will be reviewed and modified, and new methodology will be developed. The methods will be implemented in software, and applied to datasets from astronomy (galaxy surveys, gamma ray bursts), weather analysis (cyclone initiation) and other applications.