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 divided into three main branches (Cressie 1993):
In this section we focus on the branch of continuous spatial variation, commonly referred to as geostatistics.
- Continuous spatial variation: In this field, the spatial locations are treated as explanatory variables and the values attached to them as response variables. Many geostatistical methods aim to predict values at unobserved locations based on observations at a finite set of known sites. 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 a new, unobserved location \(x\).
The other branches of spatial statistics, spatial point patterns and discrete spatial variation, are discussed elsewhere. However, they can be briefly described as follows:
Spatial point patterns: The analysis of spatial point patterns is based on the data-generating mechanism, called a spatial point process, which describes how points are randomly distributed in space. A spatial point process is a type of stochastic process where each realization consists of a finite or countably infinite set of points located in a 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 to models generating clustered, random, or regularly spaced point patterns.
Discrete spatial variation: This branch of spatial statistics deals with observed entities that form a tessellation of the study area, sometimes called tiles, without overlaps or 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).
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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.