Simulate from a Fitted Point Process Model

Description

Given a point process model fitted to data, generate a random simulation of the model, using the Metropolis-Hastings algorithm.

Usage

rmh.ppm(model,start=NULL,control=NULL,..., verbose=TRUE, project=TRUE) 

Arguments

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 ppm.

The current implementation enables simulation from any fitted model involving the interactions DiggleGratton, Geyer, MultiStrauss, MultiStraussHard, PairPiece, Poisson, Strauss, StraussHard and Softcore, including nonstationary models. 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 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. 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.

Author(s)

Adrian Baddeley adrian@maths.uwa.edu.au http://www.maths.uwa.edu.au/~adrian/ and Rolf Turner rolf@math.unb.ca http://www.math.unb.ca/~rolf

See Also

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

Examples

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

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

   # Strauss process   
   fit <- ppm(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 <- ppm(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 <- ppm(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
   Q <- quadscheme(X, nd=50)
   fit <- ppm(Q, ~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 <- ppm(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")

   ## Not run: 
   X <- rSSI(0.05, 100)
   plot(X, main="new data")

   # piecewise-constant pairwise interaction function
   fit <- ppm(X, ~1, PairPiece(seq(0.02, 0.1, by=0.01)))
   Xsim <- rmh(fit, start=list(n.start=X$n), control=list(nrep=1e3))
   plot(Xsim, main="simulation from fitted pairwise model")
   ## End(Not run)

   # marked point pattern
   data(amacrine)
   Y <- amacrine
   plot(Y, main="Amacrine data")

   # marked Poisson models 
   fit <- ppm(Y)
   Ysim <- rmh(fit)
   plot(Ysim, main="simulation from ppm(Y)")

   fit <- ppm(Y,~marks)
   Ysim <- rmh(fit)
   plot(Ysim, main="simulation from ppm(Y, ~marks)")

   fit <- ppm(Y,~polynom(x,y,2))
   Ysim <- rmh(fit)
   plot(Ysim, main="simulation from ppm(Y, ~polynom(x,y,2))")

   fit <- ppm(Y,~marks+polynom(x,y,2))
   Ysim <- rmh(fit)
   plot(Ysim, main="simulation from ppm(Y, ~marks+polynom(x,y,2))")

   fit <- ppm(Y,~marks*polynom(x,y,2))
   Ysim <- rmh(fit)
   plot(Ysim, main="simulation from ppm(Y, ~marks*polynom(x,y,2))")

   # multitype Strauss models
   MS <- MultiStrauss(types = levels(Y$marks),
                      radii=matrix(0.07, ncol=2, nrow=2))
   fit <- ppm(Y, ~marks, MS)
   Ysim <- rmh(fit, start=list(n.start=X$n), control=list(nrep=1e3))
   plot(Ysim, main="simulation from fitted Multitype Strauss")

   fit <- ppm(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")