Statistics is heavily used in GIS, and there is a special branch of statistics that deals with field data specifically. This special branch of statistics uses spatial data with a continuous index. It is able to provide methods to model spatial correlation and predict values at arbitrary locations, which is also known as interpolation.
When geographic phenomena are measured, the observation methods can dictate the accuracy of any analysis. There are limits caused by the nature of some data, where there is a constant or dynamic degree of precision that is always lost in measurement. This loss of precision is determined by the scale and distribution of the data collection.
When determining the statistical relevance of any analysis, the average has to be determined so that the points outside of any measurement can be included to their predicted behavior. Applied statistics and data collection methods have a limitation to predicting the behavior of particles, points, and locations, which causes them to not be directly measurable.
Interpolation is where a surface is created by raster datasets through the input of data collection at a certain number of sample points. There are, however, several different forms of interpolation, and each of them treats data differently, which is dependent on the properties of the dataset. When interpolation methods are compared, several points need to be considered. The first is whether or not that data source will change and whether exact or approximate data collection will be used. The next is whether a method is subjective, which essentially means whether human interpretation or objective interpretation methods will be used. Next is the nature of transitions between the points: are they gradual or abrupt? Finally, checking to see whether a method is local or global.
A global method utilizes the entire dataset to form the model, and a local method uses an algorithm to repeat for a small section of terrain. Interpolation is utilized as the fundamental technique for estimation because of the spatial autocorrelation rule, which says that information gathered at any position will have comparability to or impact over those areas inside its prompt region.
The mathematical methods to produce interpolative data are as follows:
- Digital elevation models
- Triangulated irregular networks
- Edge finding algorithms
- Thiessen polygons
- Fourier analysis
- Weighted moving averages
- Inverse distance weighting
- Kriging
- Spline
- Trend surface analysis