Simulate from a Fitted Point Process Model
Given a point process model fitted to data, generate a random simulation of the model, using the Metropolis-Hastings algorithm.
## S3 method for class 'ppm'
rmh(model, start=NULL,
control=default.rmhcontrol(model, w=w),
...,
w = NULL,
project=TRUE,
nsim=1, drop=TRUE, saveinfo=TRUE,
verbose=TRUE, new.coef=NULL)model |
A fitted point process model (object of class
|
start |
Data determining the initial state
of the Metropolis-Hastings algorithm. See
|
control |
Data controlling the iterative behaviour of
the Metropolis-Hastings algorithm. See |
... |
Further arguments passed to |
w |
Optional. Window in which the simulations should be generated. Default is the window of the original data. |
project |
Logical flag indicating what to do if the fitted model is
invalid (in the sense that the values of the fitted coefficients do not
specify a valid point process).
If |
nsim |
Number of simulated point patterns that should be generated. |
drop |
Logical. If |
saveinfo |
Logical value indicating whether to save auxiliary information. |
verbose |
Logical flag indicating whether to print progress reports. |
new.coef |
New values for the canonical parameters of the model.
A numeric vector of the same length as |
This function generates simulated realisations from a point
process model that has been fitted to point pattern data. It is
a method for the generic function rmh for the
class "ppm" of fitted point process models. To simulate
other kinds of point process models, see rmh
or rmh.default.
The argument model describes the fitted model. It must be
an object of class "ppm" (see ppm.object),
and will typically be the result of a call to the point process
model fitting function ppm.
The current implementation enables simulation from any fitted model
involving the interactions
AreaInter,
DiggleGratton,
DiggleGatesStibbard,
Geyer,
Hardcore,
MultiStrauss,
MultiStraussHard,
PairPiece,
Poisson,
Strauss,
StraussHard
and Softcore,
including nonstationary models. See the examples.
It is also possible to simulate hybrids of several such models.
See Hybrid and the examples.
It is possible that the fitted coefficients of a point process model
may be “illegal”, i.e. that there may not exist a
mathematically well-defined point process with the given parameter
values. For example, a Strauss process with interaction
parameter gamma > 1 does not exist,
but the model-fitting procedure used in ppm will sometimes
produce values of gamma greater than 1.
In such cases, if project=FALSE then an error will occur,
while if project=TRUE then rmh.ppm will find
the nearest legal model and simulate
this model instead. (The nearest legal model is obtained by
projecting the vector of coefficients onto the set of
valid coefficient vectors. The result is usually the Poisson process
with the same fitted intensity.)
The arguments start and control are lists of
parameters determining the initial state and the iterative
behaviour, respectively, of the Metropolis-Hastings algorithm.
The argument control is first passed to
rmhcontrol. Then if any additional arguments ...
are given, update.rmhcontrol is called to update the
parameter values. See rmhcontrol for details of
the iterative behaviour parameters, and default.rmhcontrol
for their default values.
Note that if you specify expansion of the simulation window
using the parameter expand (so that the
model will be simulated on a window larger than the original data
window) then the model must be capable of extrapolation to this
larger window. This is usually not possible for models which
depend on external covariates, because the domain of a covariate image
is usually the same as the domain of the fitted model.
After extracting the relevant information from the fitted model
object model, rmh.ppm invokes the default
rmh algorithm rmh.default, unless the model
is Poisson. If the model is Poisson then the Metropolis-Hastings
algorithm is not needed, and the model is simulated directly, using
one of rpoispp, rmpoispp,
rpoint or rmpoint.
See rmh.default for further information about the
implementation, or about the Metropolis-Hastings algorithm.
A point pattern (an object of class "ppp"; see
ppp.object) or a list of point patterns.
See Warnings in rmh.default.
Adrian Baddeley Adrian.Baddeley@curtin.edu.au
and Rolf Turner r.turner@auckland.ac.nz
Interactions:
AreaInter,
DiggleGratton,
DiggleGatesStibbard,
Geyer,
Hardcore,
Hybrid,
MultiStrauss,
MultiStraussHard,
PairPiece,
Poisson,
Strauss,
StraussHard,
Softcore
live <- interactive()
op <- spatstat.options()
spatstat.options(rmh.nrep=1e5)
Nrep <- 1e5
X <- swedishpines
if(live) plot(X, main="Swedish Pines data")
# Poisson process
fit <- ppm(X, ~1, Poisson())
Xsim <- rmh(fit)
if(live) plot(Xsim, main="simulation from fitted Poisson model")
# Strauss process
fit <- ppm(X, ~1, Strauss(r=7))
Xsim <- rmh(fit)
if(live) plot(Xsim, main="simulation from fitted Strauss model")
if(live) {
# Strauss process simulated on a larger window
# then clipped to original window
Xsim <- rmh(fit, control=list(nrep=Nrep, expand=1.1, periodic=TRUE))
Xsim <- rmh(fit, nrep=Nrep, expand=2, periodic=TRUE)
}
if(live) {
X <- rSSI(0.05, 100)
# piecewise-constant pairwise interaction function
fit <- ppm(X, ~1, PairPiece(seq(0.02, 0.1, by=0.01)))
Xsim <- rmh(fit)
}
# marked point pattern
Y <- amacrine
if(live) {
# marked Poisson models
fit <- ppm(Y)
fit <- ppm(Y,~marks)
fit <- ppm(Y,~polynom(x,2))
fit <- ppm(Y,~marks+polynom(x,2))
fit <- ppm(Y,~marks*polynom(x,y,2))
Ysim <- rmh(fit)
}
# multitype Strauss models
MS <- MultiStrauss(radii=matrix(0.07, ncol=2, nrow=2),
types = levels(Y$marks))
if(live) {
fit <- ppm(Y ~marks, MS)
Ysim <- rmh(fit)
}
fit <- ppm(Y ~ marks*polynom(x,y,2), MS)
Ysim <- rmh(fit)
if(live) plot(Ysim, main="simulation from fitted inhomogeneous Multitype Strauss")
spatstat.options(op)
if(live) {
# Hybrid model
fit <- ppm(redwood, ~1, Hybrid(A=Strauss(0.02), B=Geyer(0.1, 2)))
Y <- rmh(fit)
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