Last chance! 50% off unlimited learning
Sale ends in
Given a point process model fitted to data, generate a random simulation of the model, using the Metropolis-Hastings algorithm.
# S3 method for 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)
A fitted point process model (object of class
"ppm"
, see ppm.object
) which it is desired
to simulate. This fitted model is usually the result of a call
to ppm
. See Details below.
Data determining the initial state
of the Metropolis-Hastings algorithm. See
rmhstart
for description of these arguments.
Defaults to list(x.start=data.ppm(model))
Data controlling the iterative behaviour of
the Metropolis-Hastings algorithm. See rmhcontrol
for description of these arguments.
Further arguments passed to rmhcontrol
,
or to rmh.default
, or to covariate functions in the model.
Optional. Window in which the simulations should be generated. Default is the window of the original data.
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 project=TRUE
the closest valid model will be simulated;
if project=FALSE
an error will occur.
Number of simulated point patterns that should be generated.
Logical. If nsim=1
and drop=TRUE
(the default), the
result will be a point pattern, rather than a list
containing a single point pattern.
Logical value indicating whether to save auxiliary information.
Logical flag indicating whether to print progress reports.
New values for the canonical parameters of the model.
A numeric vector of the same length as coef(model)
.
A point pattern (an object of class "ppp"
; see
ppp.object
) or a list of point patterns.
See Warnings in rmh.default
.
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 ppm
will sometimes
produce values of 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 start
is passed directly to rmhstart
.
See rmhstart
for details of the parameters of the
initial state, and their default values.
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.
simulate.ppm
,
rmh
,
rmhmodel
,
rmhcontrol
,
default.rmhcontrol
,
update.rmhcontrol
,
rmhstart
,
rmh.default
,
ppp.object
,
ppm
,
Interactions:
AreaInter
,
DiggleGratton
,
DiggleGatesStibbard
,
Geyer
,
Hardcore
,
Hybrid
,
MultiStrauss
,
MultiStraussHard
,
PairPiece
,
Poisson
,
Strauss
,
StraussHard
,
Softcore
# NOT RUN {
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")
# }
# NOT RUN {
# 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)
# }
# NOT RUN {
# }
# NOT RUN {
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)
# }
# NOT RUN {
# marked point pattern
Y <- amacrine
# }
# NOT RUN {
# 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)
# }
# NOT RUN {
# multitype Strauss models
MS <- MultiStrauss(radii=matrix(0.07, ncol=2, nrow=2),
types = levels(Y$marks))
# }
# NOT RUN {
fit <- ppm(Y ~marks, MS)
Ysim <- rmh(fit)
# }
# NOT RUN {
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)
# }
# NOT RUN {
# Hybrid model
fit <- ppm(redwood, ~1, Hybrid(A=Strauss(0.02), B=Geyer(0.1, 2)))
Y <- rmh(fit)
# }
Run the code above in your browser using DataLab