# 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:
•  Automatic automatically determined boundary correction None no 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.

#### 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

#### BibTeX

@misc{reference.wolfram_2024_spatialboundarycorrection, author="Wolfram Research", title="{SpatialBoundaryCorrection}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/SpatialBoundaryCorrection.html}", note=[Accessed: 14-September-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_spatialboundarycorrection, organization={Wolfram Research}, title={SpatialBoundaryCorrection}, year={2020}, url={https://reference.wolfram.com/language/ref/SpatialBoundaryCorrection.html}, note=[Accessed: 14-September-2024 ]}