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SpatialBinnedPointData
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SpatialBinnedPointData

[Experimental]

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SpatialBinnedPointData[{reg1val1,reg2val2,…}]

represents values vali associated with disjoint regions regi.

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SpatialBinnedPointData[{reg1,reg2,…}{val1,val2,…}]

gives the same result.

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gives the overall observation region reg.

Details and Options

  • SpatialBinnedPointData makes it possible to work with aggregated spatial point data, as is often reported reported in census information, infectious disease data and crime data.
  • SpatialBinnedPointData can be used like individual point data for many kinds of computations by simulating it as InhomogeneousPoissonPointProcess.
  • The regions regi and reg can be either geometric or geographic regions, but should all be of the same type.
  • The regions regi and reg should be parameter-free, fully dimensional and bounded, as tested by SpatialObservationRegionQ.
  • The regions regi are assumed to be disjoint and contained within the observation region reg.
  • The values vali can be scalars or vectors of any dimension, but must all be of equal dimensionality.
  • The integer values vali are understood to correspond to point count per region and such SpatialBinnedPointData can be treated as an InhomogeneousPoissonPointProcess with a piecewise-constant intensify function.
  • Basic properties include:
  • "Bins"a list of binning regions
    "BinCount"number of bins
    "BinMeasures"measures of the binning regions
    "Dimension"dimensionality of the binning regions
    "Values"values for each binning region
    "ConfigurationCount"number of binned observations over the same binning
    "ObservationRegion"global observation region
  • SpatialBinnedPointData can be used in functions such as PointProcessFitTest and SpatialRandomnessTest.

Examples

open allclose all

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

Use geographic entities to specify bins:

In[1]:=1
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https://wolfram.com/xid/0bmtnhd30nylu32foe6-dy7dnl
In[2]:=2
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https://wolfram.com/xid/0bmtnhd30nylu32foe6-cdms23
In[3]:=3
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https://wolfram.com/xid/0bmtnhd30nylu32foe6-gxonin
Out[3]=3
In[9]:=9
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https://wolfram.com/xid/0bmtnhd30nylu32foe6-pe9l07
Out[9]=9

Scope  (4)Survey of the scope of standard use cases

Create SpatialBinnedPointData from quadrant observations:

In[1]:=1
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https://wolfram.com/xid/0bmtnhd30nylu32foe6-7da9i2
In[2]:=2
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https://wolfram.com/xid/0bmtnhd30nylu32foe6-5hah6k
Out[2]=2

Create random values:

In[3]:=3
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https://wolfram.com/xid/0bmtnhd30nylu32foe6-578amm

Use bins and values to create SpatialBinnedPointData:

In[4]:=4
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https://wolfram.com/xid/0bmtnhd30nylu32foe6-cf26nn
Out[4]=4

Create a corresponding intensity function:

In[5]:=5
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https://wolfram.com/xid/0bmtnhd30nylu32foe6-41hdh7
Out[5]=5
In[6]:=6
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https://wolfram.com/xid/0bmtnhd30nylu32foe6-847aca
Out[6]=6

Test for complete spatial randomness:

In[7]:=7
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https://wolfram.com/xid/0bmtnhd30nylu32foe6-lc4jqn
Out[7]=7

Use a list of regions as bins:

In[1]:=1
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https://wolfram.com/xid/0bmtnhd30nylu32foe6-cc7dpf
In[2]:=2
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https://wolfram.com/xid/0bmtnhd30nylu32foe6-on407t
In[3]:=3
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https://wolfram.com/xid/0bmtnhd30nylu32foe6-clfa4o
Out[3]=3
In[4]:=4
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https://wolfram.com/xid/0bmtnhd30nylu32foe6-yx6zi
Out[4]=4
In[5]:=5
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https://wolfram.com/xid/0bmtnhd30nylu32foe6-btj116
Out[5]=5

Define a point process with intensity defined by the binned point data:

In[6]:=6
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https://wolfram.com/xid/0bmtnhd30nylu32foe6-e9pmv9
Out[6]=6

Simulate the point collection:

In[7]:=7
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https://wolfram.com/xid/0bmtnhd30nylu32foe6-b4gcj
In[8]:=8
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https://wolfram.com/xid/0bmtnhd30nylu32foe6-3pje0
Out[8]=8

Input the counts and bins manually:

In[1]:=1
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https://wolfram.com/xid/0bmtnhd30nylu32foe6-klbgk8
In[2]:=2
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https://wolfram.com/xid/0bmtnhd30nylu32foe6-b2bgz1
In[3]:=3
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https://wolfram.com/xid/0bmtnhd30nylu32foe6-irea9t
Out[3]=3

Test for complete spatial randomness:

In[1]:=1
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https://wolfram.com/xid/0bmtnhd30nylu32foe6-6fsmxe
In[2]:=2
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https://wolfram.com/xid/0bmtnhd30nylu32foe6-wfctz
Out[2]=2

Properties & Relations  (1)Properties of the function, and connections to other functions

List the properties:

In[1]:=1
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https://wolfram.com/xid/0bmtnhd30nylu32foe6-4w81nr
In[2]:=2
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https://wolfram.com/xid/0bmtnhd30nylu32foe6-mvxyvs
Out[2]=2
Wolfram Research (2020), SpatialBinnedPointData, Wolfram Language function, https://reference.wolfram.com/language/ref/SpatialBinnedPointData.html.
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Wolfram Research (2020), SpatialBinnedPointData, Wolfram Language function, https://reference.wolfram.com/language/ref/SpatialBinnedPointData.html.

Text

Wolfram Research (2020), SpatialBinnedPointData, Wolfram Language function, https://reference.wolfram.com/language/ref/SpatialBinnedPointData.html.

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Wolfram Research (2020), SpatialBinnedPointData, Wolfram Language function, https://reference.wolfram.com/language/ref/SpatialBinnedPointData.html.

CMS

Wolfram Language. 2020. "SpatialBinnedPointData." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/SpatialBinnedPointData.html.

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Wolfram Language. 2020. "SpatialBinnedPointData." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/SpatialBinnedPointData.html.

APA

Wolfram Language. (2020). SpatialBinnedPointData. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SpatialBinnedPointData.html

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Wolfram Language. (2020). SpatialBinnedPointData. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SpatialBinnedPointData.html

BibTeX

@misc{reference.wolfram_2025_spatialbinnedpointdata, author="Wolfram Research", title="{SpatialBinnedPointData}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/SpatialBinnedPointData.html}", note=[Accessed: 23-March-2025 ]}

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@misc{reference.wolfram_2025_spatialbinnedpointdata, author="Wolfram Research", title="{SpatialBinnedPointData}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/SpatialBinnedPointData.html}", note=[Accessed: 23-March-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_spatialbinnedpointdata, organization={Wolfram Research}, title={SpatialBinnedPointData}, year={2020}, url={https://reference.wolfram.com/language/ref/SpatialBinnedPointData.html}, note=[Accessed: 23-March-2025 ]}

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@online{reference.wolfram_2025_spatialbinnedpointdata, organization={Wolfram Research}, title={SpatialBinnedPointData}, year={2020}, url={https://reference.wolfram.com/language/ref/SpatialBinnedPointData.html}, note=[Accessed: 23-March-2025 ]}