Spatial dependence
Encyclopedia
In applications of statistics
, spatial dependence is the existence of statistical dependence
in a collection of random variables or a collection time series
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 only at a set of raingauge locations, and such measuements can be considered as outcomes of random variables, but rainfall clearly occurs at other locations and would again be random.
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 idependent 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
.
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
, spatial dependence is the existence of statistical dependence
Statistical independence
In probability theory, to say that two events are independent intuitively means that the occurrence of one event makes it neither more nor less probable that the other occurs...
in a collection of random variables or a collection time series
Time series
In statistics, signal processing, econometrics and mathematical finance, a time series is a sequence of data points, measured typically at successive times spaced at uniform time intervals. Examples of time series are the daily closing value of the Dow Jones index or the annual flow volume of the...
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 only at a set of raingauge locations, and such measuements can be considered as outcomes of random variables, but rainfall clearly occurs at other locations and would again be random.
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 idependent 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 Correlation
Theoretically, the performance of wireless communication systems can be improved by having multiple antennas at the transmitter and the receiver. The idea is that if the propagation channels between each pair of transmit and receive antennas are statistically independent and identically...
, spatial covariance functions and semivariograms.
Methods for spatial interpolation include Kriging
Kriging
Kriging is a group of geostatistical techniques to interpolate the value of a random field at an unobserved location from observations of its value at nearby locations....
, which is a type of best linear unbiased prediction
Best linear unbiased prediction
In statistics, best linear unbiased prediction is used in linear mixed models for the estimation of random effects. BLUP was derived by Charles Roy Henderson in 1950 but the term "best linear unbiased predictor" seems not to have been used until 1962...
.
The topic of spatial dependence is of importance to geostatistics
Geostatistics
Geostatistics is a branch of statistics focusing on spatial or spatiotemporal datasets. Developed originally to predict probability distributions of ore grades for mining operations, it is currently applied in diverse disciplines including petroleum geology, hydrogeology, hydrology, meteorology,...
and spatial analysis
Spatial analysis
Spatial analysis or spatial statistics includes any of the formal techniques which study entities using their topological, geometric, or geographic properties...
.
See also
- Spatial analysis
- GeostatisticsGeostatisticsGeostatistics is a branch of statistics focusing on spatial or spatiotemporal datasets. Developed originally to predict probability distributions of ore grades for mining operations, it is currently applied in diverse disciplines including petroleum geology, hydrogeology, hydrology, meteorology,...