# rmh.ppm

0th

Percentile

##### 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.

Keywords
spatial
##### Usage
rmh.ppm(model,start=NULL,control=NULL,..., verbose=TRUE, project=TRUE)
##### Arguments
model
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
start
A list of arguments determining the initial state of the Metropolis-Hastings algorithm. See rmh.default for description of these arguments. Defaults to list(x.start=model$Q$data)
control
A list of arguments controlling the running of the Metropolis-Hastings algorithm. See rmh.default for description of these arguments.
...
Further arguments passed to rmh.default.
verbose
Logical flag indicating whether to print progress reports.
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 project=TRUE the closest valid model will be simulated; if
##### Details

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 mpl.

The current implementation enables simulation from any fitted model involving the interactions DiggleGratton, Geyer, MultiStrauss, MultiStraussHard, Poisson, Strauss, StraussHard and Softcore, including nonstationary models, provided the trend does not involve spatial covariates. See 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 mpl 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. They are passed directly to rmh.default. See rmh.default for details of these parameters. Note that if the model has a trend then the expand component of control will be ignored. The value of expand must be equal to 1 in this setting.

After extracting the relevant information from the fitted model object model, rmh.ppm simply invokes the default rmh algorithm rmh.default, unless the model is Poisson. If the model is Poisson then rmh.default is not needed, and a stand-in function pseudo.rmh is invoked to do the simple simulation that is required.

See rmh.default for further information about the implementation, or about the Metropolis-Hastings algorithm.

##### Value

• A point pattern (an object of class "ppp"; see ppp.object).

##### Warnings

See Warnings in rmh.default.

rmh, rmh.default, ppp.object, mpl, Poisson, Strauss, StraussHard, Softcore, Geyer, DiggleGratton

• rmh.ppm
##### Examples
require(spatstat)

data(swedishpines)
X <- swedishpines
plot(X, main="Swedish Pines data")

# Poisson process
fit <- mpl(X, ~1, Poisson())
Xsim <- rmh(fit)
plot(Xsim, main="simulation from fitted Poisson model")

# Strauss process
fit <- mpl(X, ~1, Strauss(r=7), rbord=7)
Xsim <- rmh(fit, start=list(n.start=X$n), control=list(nrep=1e3)) plot(Xsim, main="simulation from fitted Strauss model") # Strauss - hard core process fit <- mpl(X, ~1, StraussHard(r=7,hc=2), rbord=7) Xsim <- rmh(fit, start=list(n.start=X$n), control=list(nrep=1e3))
plot(Xsim, main="simulation from fitted Strauss hard core model")

# Geyer saturation process
fit <- mpl(X, ~1, Geyer(r=7,sat=2), rbord=7)
Xsim <- rmh(fit, start=list(n.start=X$n), control=list(nrep=1e3)) plot(Xsim, main="simulation from fitted Geyer model") # soft core interaction process fit <- mpl(X, ~1, Softcore(kappa=0.1)) Xsim <- rmh(fit, start=list(n.start=X$n), control=list(nrep=1e3))
plot(Xsim, main="simulation from fitted Soft Core model")

data(cells)
plot(cells)
# Diggle-Gratton pairwise interaction model
fit <- mpl(cells, ~1, DiggleGratton(0.05, 0.1))
Xsim <- rmh(fit, start=list(n.start=cells$n), control=list(nrep=1e3)) plot(Xsim, main="simulation from fitted Diggle-Gratton model") # marked point pattern data(amacrine) Y <- amacrine plot(Y, main="Amacrine data") # marked Poisson models fit <- mpl(Y) Ysim <- rmh(fit) plot(Ysim, main="simulation from mpl(Y)") fit <- mpl(Y,~marks) Ysim <- rmh(fit) plot(Ysim, main="simulation from mpl(Y, ~marks)") fit <- mpl(Y,~polynom(x,y,2)) Ysim <- rmh(fit) plot(Ysim, main="simulation from mpl(Y, ~polynom(x,y,2))") fit <- mpl(Y,~marks+polynom(x,y,2)) Ysim <- rmh(fit) plot(Ysim, main="simulation from mpl(Y, ~marks+polynom(x,y,2))") fit <- mpl(Y,~marks*polynom(x,y,2)) Ysim <- rmh(fit) plot(Ysim, main="simulation from mpl(Y, ~marks*polynom(x,y,2))") # multitype Strauss models MS <- MultiStrauss(types = levels(Y$marks),
Ysim <- rmh(fit, start=list(n.start=X$n), control=list(nrep=1e3)) plot(Ysim, main="simulation from fitted Multitype Strauss") fit <- mpl(Y,~marks*polynom(x,y,2), MS) Ysim <- rmh(fit, start=list(n.start=X$n), control=list(nrep=1e3))
plot(Ysim, main="simulation from fitted inhomogeneous Multitype Strauss")