computes a variogram using binned values.
generates the same result.
Details and Options
- BinnedVariogramList is also known as empirical variogram or sample variogram.
- BinnedVariogramList is typically used to get an initial assessment of the spatial data dependence in data. It is also used as a first stage in estimating high-quality EstimatedVariogramModel.
- The variogram for a spatial process at locations and is given by . It is a measure of how quickly the process varies spatially.
- When a process is weakly stationary, then the variogram depends only the difference of locations, i.e. . And when the process is isotropic, it only depends on the distance between locations where .
- The value of for is computed as , where . The result is a binned variogram:
- The resulting binned variogram is typically not a valid variogram. It needs to be conditionally negative definite for all weights wi such that and locations pi. However, it can be used to fit a variogram model that will be a valid variogram, as is done in EstimatedVariogramModel.
- From the binned variogram, one can detect whether there is a trend in the data, which will result in an unbounded variogram.
- The following options can be given:
DistanceFunction Automatic specify the function to compute distance Method "NonLattice" specify the shape of the locations for binning SpatialTrendFunction None specify the global trend model
- The following settings can be used for Method:
"NonLattice" locations are given as a collection
- The following Method options can be used:
"BinCenter" "Centroid" how to compute bin centers "MaxDistanceRatio" 1/3 data pairs for which the ratio of their distance to the max pair distance is greater are dropped "MinPairs" 30 bins containing fewer pairs are dropped "ScaleEstimator" "Cressie" which scale estimator to use
- The following settings can be used for "ScaleEstimator":
"Cressie" use the fourth moment of square root "Matheron" use the second moment "Qn" use QnDispersion "Sn" use SnDispersion
- BinnedVariogram returns two-dimensional WeightedData, with weights being the number of pairs for each distance bin.
Examplesopen allclose all
Basic Examples (2)
Basic Uses (3)
Use HistogramList specs for binning:
Compute binned variogram with Automatic bin specification:
Compute BinnedVariogramList for geographical data:
Compute BinnedVariogramList for various "BinCenter" specifications:
Compute BinnedVariogramList for various "MaxDistanceRatio" specifications:
Compute BinnedVariogramList for various "MinPairs" specifications:
Compute BinnedVariogramList for various "ScaleEstimator" specifications:
Binned variogram can be used to get initial visual shape idea for EstimatedVariogramModel:
BinnedVariogramList can be used to indicate the presence of trend in the data:
Possible Issues (1)
BinnedVariogramList will fail if there is not enough data to meet the minimum number of pairs per bin requirement:
Wolfram Research (2021), BinnedVariogramList, Wolfram Language function, https://reference.wolfram.com/language/ref/BinnedVariogramList.html.
Wolfram Language. 2021. "BinnedVariogramList." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/BinnedVariogramList.html.
Wolfram Language. (2021). BinnedVariogramList. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/BinnedVariogramList.html