Geostatistics

Geostatistics is a branch of statistics focusing on spatiotemporal datasets. Developed originally to predict probable distributions for mining operations, it is currently applied in diverse disciplines including petroleum geology, hydrogeology, hydrology, meteorology, oceanography, geochemistry, geometallurgy, geography, forestry, environmental control, landscape ecology, and agriculture (esp. in precision farming). Geostatistics is applied in varied branches of geography, particularly those involving the spread of disease (epidemiology), the practice of commerce and military planning (logistics), and the development of efficient spatial networks. Geostatistics are incorporated in tools such as geographic information systems (GIS) and digital elevation models.

Background
When any phenomena is measured, the observation methodology will dictate the accuracy of subsequent analysis; in geography, this issue is complicated by unique variables and spatial patterns such as geospatial topology. An interesting feature in geostatistics is that every location displays some form of spatial pattern, whether in the form of the environment, climate, pollution, urbanization or human health. This is not to state that all variables are spatially dependent, simply that variables are incapable of measurement separate from their surroundings, such that there can be no perfect control population. Whether the study is concerned with the nature of traffic patterns in an urban core, or with the analysis of weather patterns over the Pacific, there are always variables which escape measurement; this is determined directly by the scale and distribution of the data collection, or survey, and its methodology. Limitations in data collection make it impossible to make a direct measure of continuous spatial data without inferring probabilities, some of these probability functions are applied to create an interpolation surface - predicting unmeasured variables at innumerable locations.

Computational Geometry

 * See main article Computational Geometry

Topography

 * See main article Topography

Sampling methodology
See Statistics
 * Statistical sampling
 * Geospatial sampling

Criticism
Jan W Merks, a mineral sampling expert consultant from Canada, has strongly criticized geostatistics since 1992. Referring to it as "voodoo science" and "scientific fraud", he claims that geostatistics is an invalid branch of statistics. Merks submits that geostatistics Furthermore, Merks claims geostatistics inflates mineral reserve and resources such as in the case of Bre-X's fraud. Merks's expertise and credibility are supported by several company executives, who regularly hire his consulting services.
 * ignores the variance of Agterberg's distance-weighted average point grade,
 * ignores the concept of degrees of freedom of a data set when testing for spatial dependence by applying Fisher's F-test to the variance of a set and the first variance term of the ordered set,
 * abuses statistics by not using analysis of variance properly,
 * replaced genuine variances of single distance-weighted average point grades with pseudo-variances of sets of distance-weighted average point grades, violating the one-to-one correspondence between variances and functions such as Agterberg's distance-weighted average point grade.

Philip and Watson have also criticized geostatistics in the past.

There is a consensus that inappropriate use of geostatistics makes the method susceptible to erroneous reading of results.

Related software

 * gslib is a set of fortran 77 routines (open source) implementing most of the classical geostatistics estimation and simulation algorithms
 * sgems is a cross-platform (windows, unix), open-source software that implements most of the classical geostatistics algorithms (kriging, Gaussian and indicator simulation, etc) as well as new developments (multiple-points geostatistics). It also provides an interactive 3D visualization and offers the scripting capabilities of python.
 * gstat is an open source computer code for multivariable geostatistical modelling, prediction and simulation. The gstat functionality is also available as an S extension, either as R package or S-Plus library.
 * besides gstat, R has at least six other packages dedicated to geostatistics and other areas in spatial statistics.