Spatial Statistics

Spatial Statistics

Spatial Statistics


Spatial statistics is concerned with statistical analysis of data collected over a spatial region, possibly including the study of a development over time. Research in spatial statistics mainly deals with spatial point processes, lattice processes and geostatistics. Spatial point processes are models for locations of objects randomly dispersed in space. On a large scale, such objects may be trees in a rain forest while on a micro-scale, objects may represent cells in the brain or protein molecules within a cell. Many important biological hypotheses are concerned with the nature of the spatial patterns - e.g. whether they are clustered or regular. Geostatistics and statistics for lattice processes are concerned with statistical analysis of observations where the locations associated with the observations play a crucial role. In geostatistics observations can in principle be observed at any location in space. One example could be observations of the content of potassium in the soil and one objective could be to map the potassium content over a spatial region based on a finite set of potassium observations. Lattice data are restricted to observations on a fixed lattice. Digital images are important examples of lattice data where the pixels of the images represent light intensities.

The research of the spatial statistics group is concerned with construction of flexible parametric statistical models for spatial data as well as computational and theoretical aspects of parameter estimation and inference procedures for such models. Another important research topic is non-parametric summary statistics that allows to study scientific hypotheses without the need to posit a specific statistical model for the data. The spatial statistics group also conducts research in stochastic geometry which is concerned with probabilistic aspects of random geometric structures. Spatial point processes are important in stochastic geometry, e.g. for modeling random locations of objects or for generating random tesselations like Voronoi and Johnson-Mehl tesselations.