VariogramModel

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`VariogramModel`

[Experimental]

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VariogramModel["model",{params}]

represents the function for the variogram model specified by "model".

Details and Options

VariogramModel is also known as variogram and semivariogram.
VariogramModel[…] represents a function generated by EstimatedVariogramModel.
VariogramModel is typically used as a local model of spatial dependence when predicting values of a spatial field, as in SpatialEstimate.
The following tables enumerate valid variogram model families grouped into tables with similar features.
Variogram models that reach the sill within a finite range:

		{"Askey",a,b,c}
		{"BoundedLinear",a,b}
		{"Circular",a,b}
		{"Cubic",a,b}
		{"EuclidsHat",a,b,c}
		{"Pentaspherical",a,b}
		{"Spherical",a,b}
		{"WhiteNoise",a}

Variogram models that reach the sill asymptotically where the effective range is defined at 95% of the sill:

		{"Dagum",a,b,c,d}
		{"Exponential",a,b}
		{"Gaussian",a,b}
		{"GeneralizedCauchy",a,b,c,d}
		{"Matern",a,b,c}
		{"PoweredExponential",a,b,c}

Variogram models oscillating around the sill and reaching the sill asymptotically. The range is defined at the first crossing of the sill:
{"GaussianLaguerre",a,b,c,d}

{"Poisson",a,b,c}

{"SineHoleEffect",a,b}
Variogram models that are unbounded. These occur when data has a global trend:
{"Linear",a}

{"Power",a,b}
VariogramModel works like Function.
VariogramModel[…]["prop"] can be used to access different properties for the variogram model.
The following properties "prop" can be used:

	"ModelFormula"	model function without variance noise
	"Name"	name of the variogram model
	"SpatialNoiseLevel"	value of the spatial noise variance
	"Parameters"	parameters of the variogram model function
	"Properties"	list of available properties
	"Range"	range of the function model
	"Sill"	sill of the function model
	"Visualization"	plot of the function model

Additional properties "prop" can be used when VariogramModel is obtained from EstimatedVariogramModel:
"BinnedVariogram" binned variogram used for model fitting

"WeightedSumOfResiduals" weighted sum of residuals from the fitting procedure
The following option can be given:
SpatialNoiseLevel Automatic specify the noise level in the model

Examples

open allclose all

Basic Examples (1)Summary of the most common use cases

Gaussian model:

In[4]:=4

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https://wolfram.com/xid/0ixk51ut6s6bhlp-73gj1l

Out[4]=4

Value at a distance:

In[5]:=5

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https://wolfram.com/xid/0ixk51ut6s6bhlp-xtectv

Out[5]=5

Variogram range:

In[9]:=9

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https://wolfram.com/xid/0ixk51ut6s6bhlp-hvkx4g

Out[9]=9

Plot as a function of distance:

In[12]:=12

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https://wolfram.com/xid/0ixk51ut6s6bhlp-wahhco

Out[12]=12

Scope (3)Survey of the scope of standard use cases

Basic Uses (2)

Explicit spherical model:

In[1]:=1

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https://wolfram.com/xid/0ixk51ut6s6bhlp-ekub80

Out[1]=1

With noise variance:

In[2]:=2

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https://wolfram.com/xid/0ixk51ut6s6bhlp-m9079x

Out[2]=2

Estimate a variogram model for random data:

In[1]:=1

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https://wolfram.com/xid/0ixk51ut6s6bhlp-xttwcl

In[2]:=2

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https://wolfram.com/xid/0ixk51ut6s6bhlp-fw7x7

Out[2]=2

White noise model:

In[3]:=3

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https://wolfram.com/xid/0ixk51ut6s6bhlp-w2dpeu

Out[3]=3

In[4]:=4

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https://wolfram.com/xid/0ixk51ut6s6bhlp-xq9wod

Out[4]=4

Variogram Models (1)

Spherical model:

In[1]:=1

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https://wolfram.com/xid/0ixk51ut6s6bhlp-6ujgwf

Out[1]=1

In[2]:=2

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https://wolfram.com/xid/0ixk51ut6s6bhlp-vxcty7

Out[2]=2

With noise variance:

In[3]:=3

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https://wolfram.com/xid/0ixk51ut6s6bhlp-7o2pu0

Out[3]=3

In[4]:=4

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https://wolfram.com/xid/0ixk51ut6s6bhlp-tx40i2

Out[4]=4

In[7]:=7

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https://wolfram.com/xid/0ixk51ut6s6bhlp-n8im46

Out[7]=7

Possible Issues (1)Common pitfalls and unexpected behavior

For symbolic variogram representation, not all properties are defined:

In[1]:=1

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https://wolfram.com/xid/0ixk51ut6s6bhlp-3evbho

Out[1]=1

List all the properties:

In[2]:=2

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https://wolfram.com/xid/0ixk51ut6s6bhlp-63tfdy

Out[2]=2

Some properties are available only after fitting the model to data:

In[4]:=4

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https://wolfram.com/xid/0ixk51ut6s6bhlp-9eou09

Out[4]=4

In[3]:=3

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https://wolfram.com/xid/0ixk51ut6s6bhlp-9pebd

Out[3]=3

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