Research being undertaken by our current postgraduates:

Curvature in Spatial Statistics

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. The points could represent the locations of bird nests, meteorite impacts, accidents, petty crimes or other events.

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 Earthâ€™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. Formulae for measurements such as distance and area and the effect of transformations such as translation 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, interpoint distance distributions, K-functions, pairwise interaction models, 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.

Spatial statistics can be applied to many important areas of research, such as climatology and astronomy. However, the candidate is not aware of models or methodology for spatial statistics having been developed for data on the surface of a sphere (such as the planet Earth, or the Celestial Sphere), or on some part (such as an ocean, continent, or similar region). This research aims to fill at least part of this void, by providing methods for refined analysis of data from large-sized study areas. It will also address the question of when it is more appropriate to consider e.g. a part of the Earth's surface as a part of the surface of a sphere rather than a flat surface.

Assistance in statistics is available for Postgraduates students by research at the UWA Centre for Applied Statistics.