Default Expansion Rule for Simulation of Model
Defines the default expansion window or expansion rule for simulation of a fitted point process model.
default.expand(object, m=2, epsilon=1e-6, w=Window(object))
object |
A point process model (object of class |
m |
A single numeric value.
The window will be expanded by a distance
|
epsilon |
Threshold argument passed to |
w |
Optional. The un-expanded window in which the model is defined. The resulting simulated point patterns will lie in this window. |
This function computes a default value for the
expansion rule (the argument expand in rmhcontrol)
given a fitted point process model object.
This default is used by envelope,
qqplot.ppm, simulate.ppm and other functions.
Suppose we wish to generate simulated realisations
of a fitted point process model inside a window w.
It is advisable to first simulate
the pattern on a larger window, and then clip it to the original
window w. This avoids edge effects in the simulation.
It is called expansion of the simulation window.
Accordingly, for the Metropolis-Hastings simulation algorithm
rmh, the algorithm control parameters specified by
rmhcontrol include an argument expand that
determines the expansion of the simulation window.
The function default.expand determines the default expansion
rule for a fitted point process model object.
If the model is Poisson, then no expansion is necessary.
No expansion is performed by default,
and default.expand returns a rule representing no expansion.
The simulation window is the original window w = Window(object).
If the model depends on external covariates (i.e.\ covariates other than
the Cartesian covariates x and y and the marks)
then no expansion is feasible, in general, because the spatial domain
of the covariates is not guaranteed to be large enough.
default.expand returns a rule representing no expansion.
The simulation window is the original window w = Window(object).
If the model depends on the Cartesian covariates x and y,
it would be feasible to expand the simulation window, and this was the
default for spatstat version 1.24-1 and earlier.
However this sometimes produces artefacts (such as an empty point pattern)
or memory overflow, because the fitted trend, extrapolated outside the
original window of the data, may become very large.
In spatstat version 1.24-2 and later, the
default rule is not to expand if the model depends
on x or y.
Again default.expand returns a rule representing no expansion.
Otherwise, expansion will occur.
The original window w = Window(object) is expanded by
a distance m * rr, where
rr is the interaction range of the model, computed by
reach. If w is a rectangle then
each edge of w is displaced outward by distance m * rr.
If w is not a rectangle then w is dilated by
distance m * rr using dilation.
A window expansion rule (object of class "rmhexpand").
Adrian Baddeley Adrian.Baddeley@curtin.edu.au
and Rolf Turner r.turner@auckland.ac.nz
data(cells) fit <- ppm(cells, ~1, Strauss(0.07)) default.expand(fit) mod <- rmhmodel(cif="strauss", par=list(beta=100, gamma=0.5, r=0.07)) default.expand(fit)
Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.