Spatial dependence

Spatial dependence is the spatial relationship of variable values (for themes defined over space, such as rainfall) or locations (for themes defined as objects, such as cities). Spatial dependence is measured as the existence of statistical dependence in a collection of random variables, each of which is associated with a different geographical location. Spatial dependence is of importance in applications where it is reasonable to postulate the existence of corresponding set of random variables at locations that have not been included in a sample. Thus rainfall may be measured at a set of rain gauge locations, and such measurements can be considered as outcomes of random variables, but rainfall clearly occurs at other locations and would again be random. Because rainfall exhibits properties of autocorrelation, spatial interpolation techniques can be used to estimate rainfall amounts at locations near measured locations.

As with other types of statistical dependence, the presence of spatial dependence generally leads to estimates of an average value from a sample being less accurate than had the samples been independent, although if negative dependence exists a sample average can be better than in the independent case. A different problem than that of estimating an overall average is that of spatial interpolation: here the problem is to estimate the unobserved random outcomes of variables at locations intermediate to places where measurements are made, on that there is spatial dependence between the observed and unobserved random variables.

Tools for exploring spatial dependence include: spatial correlation, spatial covariance functions and semivariograms.

Methods for spatial interpolation include Kriging, which is a type of best linear unbiased prediction.

The topic of spatial dependence is of importance to geostatistics and spatial analysis.

## See also

* Spatial analysis
* Geostatistics

## References

* Journel, A G and Huijbregts, C J, Mining Geostatistics, Academic Press Inc, London

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