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 continuous spatial variation.

1. 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. The prediction of continuous attributes in space is often referred to as interpolation.

For a given sample of measurements $\{z_1, z_2,..., z_n\}$ at locations $\{x_1, x_2,..., x_n\}$ the main goal is to estimate the value $z$ at some new point $x$.

---

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

2. Spatial point patterns: The analysis of spatial point patterns 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.

3. 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-Py was developed at the Department of Earth Sciences by Annette Rudolph, Joachim Krois and Kai Hartmann. 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: Rudolph, A., Krois, J., Hartmann, K. (2023): Statistics and Geodata Analysis using Python (SOGA-Py). Department of Earth Sciences, Freie Universitaet Berlin.