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Percentile

Resample a Point Pattern by Resampling Quadrats

Given a point pattern dataset, create a resampled point pattern by dividing the window into rectangular quadrats and randomly resampling the list of quadrats.

Keywords
spatial, datagen
Usage
replace = FALSE, nsamples = 1,
verbose = (nsamples > 1))
Arguments
X
A point pattern dataset (object of class "ppp").
nx,ny
Numbers of quadrats in the $x$ and $y$ directions.
...
Ignored.
replace
Logical value. Specifies whether quadrats should be sampled with or without replacement.
nsamples
Number of randomised point patterns to be generated.
verbose
Logical value indicating whether to print progress reports.
Details

This command implements a very simple bootstrap resampling procedure for spatial point patterns X.

The dataset X must be a point pattern (object of class "ppp") and its observation window must be a rectangle.

The window is first divided into N = nx * ny rectangular tiles (quadrats) of equal size and shape. To generate one resampled point pattern, a random sample of N quadrats is selected from the list of N quadrats, with replacement (if replace=TRUE) or without replacement (if replace=FALSE). The $i$th quadrat in the original dataset is then replaced by the $i$th sampled quadrat, after the latter is shifted so that it occupies the correct spatial position. The quadrats are then reconstituted into a point pattern inside the same window as X.

If replace=FALSE, this procedure effectively involves a random permutation of the quadrats. The resulting resampled point pattern has the same number of points as X. If replace=TRUE, the number of points in the resampled point pattern is random.

Value

• A point pattern (if nsamples = 1) or a list of point patterns (if nsamples > 1).