R: Determine Initial State for Metropolis-Hastings Simulation.

rmhstart {spatstat.core} | R Documentation

## Determine Initial State for Metropolis-Hastings Simulation.

### Description

Builds a description of the initial state for the Metropolis-Hastings algorithm.

### Usage

       rmhstart(start, ...)
       ## Default S3 method:
    rmhstart(start=NULL, ..., n.start=NULL, x.start=NULL)

### Arguments

`start` | An existing description of the initial state in some format. Incompatible with the arguments listed below.
`...` | There should be no other arguments.
`n.start` | Number of initial points (to be randomly generated). Incompatible with `x.start`.
`x.start` | Initial point pattern configuration. Incompatible with `n.start`.

### Details

Simulated realisations of many point process models can be generated using the Metropolis-Hastings algorithm implemented in `rmh`.

This function `rmhstart` creates a full description of the initial state of the Metropolis-Hastings algorithm, including possibly the initial state of the random number generator, for use in a subsequent call to `rmh`. It also checks that the initial state is valid.

The initial state should be specified either by the first argument `start` or by the other arguments `n.start`, `x.start` etc.

If `start` is a list, then it should have components named `n.start` or `x.start`, with the same interpretation as described below.

The arguments are:

n.start

  The number of “initial” points to be randomly (uniformly) generated in the simulation window `w`. Incompatible with `x.start`.

  For a multitype point process, `n.start` may be a vector (of length equal to the number of types) giving the number of points of each type to be generated.

  If expansion of the simulation window is selected (see the argument `expand` to `rmhcontrol`), then the actual number of starting points in the simulation will be `n.start` multiplied by the expansion factor (ratio of the areas of the expanded window and original window).

  For faster convergence of the Metropolis-Hastings algorithm, the value of `n.start` should be roughly equal to (an educated guess at) the expected number of points for the point process inside the window.

x.start

  Initial point pattern configuration. Incompatible with `n.start`.

  `x.start` may be a point pattern (an object of class `ppp`), or an object which can be coerced to this class by `as.ppp`, or a dataset containing vectors `x` and `y`.

  If `x.start` is specified, then expansion of the simulation window (the argument `expand` of `rmhcontrol`) is not permitted.

The parameters `n.start` and `x.start` are incompatible.

### Value

An object of class `"rmhstart"`, which is essentially a list of parameters describing the initial point pattern and (optionally) the initial state of the random number generator.

There is a `print` method for this class, which prints a sensible description of the initial state.

### Author(s)

Adrian Baddeley Adrian.Baddeley@curtin.edu.au and Rolf Turner r.turner@auckland.ac.nz

### See Also

`rmh`, `rmhcontrol`, `rmhmodel`

### Examples

       # 30 random points
       a <- rmhstart(n.start=30)
       a

       # a particular point pattern
       b <- rmhstart(x.start=cells)

[Package spatstat.core version 2.3-0 Index]