What is geostatistics?

Geostatistics is a class of statistics used to analyze and predict the values associated with spatial or spatiotemporal phenomena. It incorporates the spatial (and in some cases temporal) coordinates of the data within the analyses. Many geostatistical tools were originally developed as a practical means to describe spatial patterns and interpolate values for locations where samples were not taken. Those tools and methods have since evolved to not only provide interpolated values, but also measures of uncertainty for those values. The measurement of uncertainty is critical to informed decision making, as it provides information on the possible values (outcomes) for each location rather than just one interpolated value. Geostatistical analysis has also evolved from uni- to multivariate and offers mechanisms to incorporate secondary datasets that complement a (possibly sparse) primary variable of interest, thus allowing the construction of more accurate interpolation and uncertainty models.

Geostatistics is widely used in many areas of science and engineering, for example:

• The mining industry uses geostatistics for several aspects of a project: initially to quantify mineral resources and evaluate the project's economic feasibility, then on a daily basis in order to decide which material is routed to the plant and which is waste, using updated information as it becomes available.
• In the environmental sciences, geostatistics is used to estimate pollutant levels in order to decide if they pose a threat to environmental or human health and warrant remediation.
• Relatively new applications in the field of soil science focus on mapping soil nutrient levels (nitrogen, phosphorus, potassium, and so on) and other indicators (such as electrical conductivity) in order to study their relationships to crop yield and prescribe precise amounts of fertilizer for each location in the field.
• Meteorological applications include prediction of temperatures, rainfall, and associated variables (such as acid rain).
• Most recently, there have been several applications of geostatistics in the area of public health, for example, the prediction of environmental contaminant levels and their relation to the incidence rates of cancer.

In all of these examples, the general context is that there is some phenomenon of interest occurring in the landscape (the level of contamination of soil, water, or air by a pollutant; the content of gold or some other metal in a mine; and so forth). Exhaustive studies are expensive and time consuming, so the phenomenon is usually characterized by taking samples at different locations. Geostatistics is then used to produce predictions (and related measures of uncertainty of the predictions) for the unsampled locations. A generalized workflow for geostatistical studies is described in The geostatistical workflow.