SpatialBoundaryCorrection

SpatialBoundaryCorrection

is an option to various spatial statistics functions that control how to correct for boundary effects of observation regions.

Details

  • SpatialBoundaryCorrection is also known as edge correction or border correction.
  • Boundary correction attempts to correct the bias introduced when spatial statistics is computed over a bounded region near the boundary.
  • A typical statistic will count the number points within distance r of a location. If that location is closer to the boundary than r, the resulting count will be too low and hence introduce a bias.
  • Possible general settings include:
  • Automaticautomatically determined boundary correction
    Noneno boundary correction
    "BorderMargin"creates an interior boundary margin
  • The "BorderMargin" for a given radius will drop points closer to the boundary than .
  •     
  • Possible special setting include:
  • "Ripley"uses weights depending on the point distance to boundary
    "Hanisch"drops points for which the distance to the nearest neighbor is greater than the distance to boundary
    "KaplanMeier"SurvivalDistribution method: the point distance to its nearest neighbor is censored by its distance to the region boundary
    "NelsonAalen"SurvivalDistribution method: the point distance to its nearest neighbor is censored by its distance to the region boundary
  • Different functions may document additional settings available for that particular function.

Examples

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Basic Examples  (2)

Use specific edge correction method:

Turn off border correction:

Applications  (2)

With no boundary correction, the estimator of RipleyK is biased and should not be used unless with a large point set:

The default method "BorderMargin" only considers the points that are distance from the boundary:

Boundary correction method "Ripley" weights each pair of points to make the estimator unbiased:

Empirical RipleyK with border correction may not be increasing (especially for smaller sets):

The uncorrected RipleyK is increasing:

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

Text

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

BibTeX

@misc{reference.wolfram_2020_spatialboundarycorrection, author="Wolfram Research", title="{SpatialBoundaryCorrection}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/SpatialBoundaryCorrection.html}", note=[Accessed: 05-March-2021 ]}

BibLaTeX

@online{reference.wolfram_2020_spatialboundarycorrection, organization={Wolfram Research}, title={SpatialBoundaryCorrection}, year={2020}, url={https://reference.wolfram.com/language/ref/SpatialBoundaryCorrection.html}, note=[Accessed: 05-March-2021 ]}

CMS

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

APA

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