Most statistical methods within the field of spatial statistics developed independently and grew out of different areas of application, including mining engineering, agriculture and forestry (see Gelfand at al. 2010). As a consequence of its scattered history the field of spatial statistics is generally viewed as being comprised of three major branches (Cressie 1993):

In this section we focus on the branch of **spatial point
patterns**.

**Spatial point patterns**: The analysis of spatial point pattern is based on the underlying data generation process, denoted as*spatial point process*. Spatial point processes are regarded as*stochastic processes*each of whose realizations consists of a finite or countably infinite set of points in the plane (Gelfand at al. 2010). In spatial point pattern analysis both, the spatial locations and the values attached to them, are treated as response variables. In many applications the observed relative position of points within a study region is compared with clustered, random, or regular generating point processes.

The other branches of spatial statistics, **continuous spatial
variation** and **discrete spatial variation**, are
discussed elsewhere. Though, these two branches can be roughly described
as following:

**Continuous spatial variation**: In this field, often denoted as*geostatistics*, the spatial locations are treated as explanatory variables and the values attached to them as response variables. Many geostatistical methods were developed to predict values over a spatial region from observations at a finite set of locations. An example application is the computation of spatially continuous weather maps from spatially discrete observations on the ground.**Discrete spatial variation**: In this branch of spatial statistics the observed entities form a tessellation of the study area, sometimes referred to as tiles, with no overlaps and no gaps. Examples include lattice data, pixel data, and areal unit data (including irregular areal units both in size and shape). The goals of inference for discrete spatial variation are explanation, smoothing and prediction rather than interpolation (Gelfand at al. 2010).

**Citation**

The E-Learning project SOGA-R was developed at the Department of Earth Sciences by Kai Hartmann, Joachim Krois and Annette Rudolph. You can reach us via mail by soga[at]zedat.fu-berlin.de.

You may use this project freely under the Creative Commons Attribution-ShareAlike 4.0 International License.

Please cite as follow: *Hartmann,
K., Krois, J., Rudolph, A. (2023): Statistics and Geodata Analysis
using R (SOGA-R). Department of Earth Sciences, Freie Universitaet Berlin.*