# rmh.ppm

##### 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.

##### Usage

```
## S3 method for class 'ppm':
rmh(model,start=NULL,
control=rmhcontrol(),
..., 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
- 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))`

- control
- Data controlling the running of
the Metropolis-Hastings algorithm. See
`rmhcontrol`

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 `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 `rmhstart`

and
`rmhcontrol`

respectively.
See `rmhstart`

and
`rmhcontrol`

for details of these parameters.

Note that if you specify `control$expand > 1`

(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 excludes models which depend on external covariates.
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 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.

##### Value

- A point pattern (an object of class
`"ppp"`

; see`ppp.object`

).

##### Warnings

See Warnings in `rmh.default`

.

##### See Also

`simulate.ppm`

,
`rmh`

,
`rmhmodel`

,
`rmhcontrol`

,
`rmhstart`

,
`rmh.default`

,
`ppp.object`

,
`ppm`

,
`PairPiece`

,
`Poisson`

,
`Strauss`

,
`StraussHard`

,
`Softcore`

,
`Geyer`

,
`AreaInter`

,
`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))
Xsim <- rmh(fit, control=list(nrep=1e3))
plot(Xsim, main="simulation from fitted Strauss model")
# Strauss process simulated on a larger window
# then clipped to original window
Xsim <- rmh(fit, control=list(nrep=1e3, expand=2, periodic=TRUE))
# Strauss - hard core process
fit <- ppm(X, ~1, StraussHard(r=7,hc=2))
Xsim <- rmh(fit, start=list(n.start=X$n), control=list(nrep=1e3))
plot(Xsim, main="simulation from fitted Strauss hard core model")
# Geyer saturation process
fit <- ppm(X, ~1, Geyer(r=7,sat=2))
Xsim <- rmh(fit, start=list(n.start=X$n), control=list(nrep=1e3))
plot(Xsim, main="simulation from fitted Geyer model")
# Area-interaction process
fit <- ppm(X, ~1, AreaInter(r=7))
Xsim <- rmh(fit, start=list(n.start=X$n), control=list(nrep=1e3))
plot(Xsim, main="simulation from fitted area-interaction model")
# soft core interaction process
Q <- quadscheme(X, nd=50)
fit <- ppm(Q, ~1, Softcore(kappa=0.1), correction="isotropic")
Xsim <- rmh(fit, start=list(n.start=X$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$n), control=list(nrep=1e3))
plot(Xsim, main="simulation from fitted Diggle-Gratton model")
X <- rSSI(0.05, 100)
plot(X, main="new data")
# piecewise-constant pairwise interaction function
fit <- ppm(X, ~1, PairPiece(seq(0.02, 0.1, by=0.01)))
Xsim <- rmh(fit, control=list(nrep=1e3))
plot(Xsim, main="simulation from fitted pairwise model")
# marked point pattern
data(amacrine)
Y <- amacrine
plot(Y, main="Amacrine data")
# marked Poisson models
fit <- ppm(Y)
Ysim <- rmh(fit)
plot(Ysim, main="simulation from ppm(Y)")
fit <- ppm(Y,~marks)
Ysim <- rmh(fit)
plot(Ysim, main="simulation from ppm(Y, ~marks)")
fit <- ppm(Y,~polynom(x,y,2))
Ysim <- rmh(fit)
plot(Ysim, main="simulation from ppm(Y, ~polynom(x,y,2))")
fit <- ppm(Y,~marks+polynom(x,y,2))
Ysim <- rmh(fit)
plot(Ysim, main="simulation from ppm(Y, ~marks+polynom(x,y,2))")
fit <- ppm(Y,~marks*polynom(x,y,2))
Ysim <- rmh(fit)
plot(Ysim, main="simulation from ppm(Y, ~marks*polynom(x,y,2))")
# multitype Strauss models
MS <- MultiStrauss(types = levels(Y$marks),
radii=matrix(0.07, ncol=2, nrow=2))
fit <- ppm(Y, ~marks, MS)
Ysim <- rmh(fit, control=list(nrep=1e3))
plot(Ysim, main="simulation from fitted Multitype Strauss")
fit <- ppm(Y,~marks*polynom(x,y,2), MS)
Ysim <- rmh(fit, control=list(nrep=1e3))
plot(Ysim, main="simulation from fitted inhomogeneous Multitype Strauss")
```

*Documentation reproduced from package spatstat, version 1.16-3, License: GPL (>= 2)*