R: Define Point Process Model for Metropolis-Hastings...

rmhmodel.list {spatstat} | R Documentation

## Define Point Process Model for Metropolis-Hastings Simulation.

### Description

Given a list of parameters, builds a description of a point process model for use in simulating the model by the Metropolis-Hastings algorithm.

### Usage

       ## S3 method for class 'list'
    rmhmodel(model, ...)

### Arguments

`model` | A list of parameters. See Details.
`...` | Optional list of additional named parameters.

### Details

The generic function `rmhmodel` takes a description of a point process model in some format, and converts it into an object of class `"rmhmodel"` so that simulations of the model can be generated using the Metropolis-Hastings algorithm `rmh`.

This function `rmhmodel.list` is the method for lists. The argument `model` should be a named list of parameters of the form

`list(cif, par, w, trend, types)`

where `cif` and `par` are required and the others are optional. For details about these components, see `rmhmodel.default`.

The subsequent arguments `...` (if any) may also have these names, and they will take precedence over elements of the list `model`.

### Value

An object of class `"rmhmodel"`, which is essentially a validated list of parameter values for the model.

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

### Author(s)

Adrian Baddeley Adrian.Baddeley@curtin.edu.au

and Rolf Turner r.turner@auckland.ac.nz

### References

Diggle, P. J. (2003) Statistical Analysis of Spatial Point Patterns (2nd ed.) Arnold, London.

Diggle, P.J. and Gratton, R.J. (1984) Monte Carlo methods of inference for implicit statistical models. Journal of the Royal Statistical Society, series B 46, 193 – 212.

Diggle, P.J., Gates, D.J., and Stibbard, A. (1987) A nonparametric estimator for pairwise-interaction point processes. Biometrika 74, 763 – 770. Scandinavian Journal of Statistics 21, 359–373.

Geyer, C.J. (1999) Likelihood Inference for Spatial Point Processes. Chapter 3 in O.E. Barndorff-Nielsen, W.S. Kendall and M.N.M. Van Lieshout (eds) Stochastic Geometry: Likelihood and Computation, Chapman and Hall / CRC, Monographs on Statistics and Applied Probability, number 80. Pages 79–140.

### See Also

`rmhmodel`, `rmhmodel.default`, `rmhmodel.ppm`, `rmh`, `rmhcontrol`, `rmhstart`, `ppm`, `Strauss`, `Softcore`, `StraussHard`, `MultiStrauss`, `MultiStraussHard`, `DiggleGratton`, `PairPiece`

### Examples

       # Strauss process:
       mod01 <- list(cif="strauss",par=list(beta=2,gamma=0.2,r=0.7),
                     w=c(0,10,0,10))
       mod01 <- rmhmodel(mod01)

       # Strauss with hardcore:
       mod04 <- list(cif="straush",par=list(beta=2,gamma=0.2,r=0.7,hc=0.3),
                    w=owin(c(0,10),c(0,5)))
       mod04 <- rmhmodel(mod04)

       # Soft core:
       w    <- square(10)
       mod07 <- list(cif="sftcr",
                         par=list(beta=0.8,sigma=0.1,kappa=0.5),
                         w=w)
       mod07 <- rmhmodel(mod07)

       # Multitype Strauss:
       beta <- c(0.027,0.008)
       gmma <- matrix(c(0.43,0.98,0.98,0.36),2,2)
       r    <- matrix(c(45,45,45,45),2,2)
       mod08 <- list(cif="straussm",
                         par=list(beta=beta,gamma=gmma,radii=r),
                         w=square(250))
       mod08 <- rmhmodel(mod08)

       # specify types
       mod09 <- rmhmodel(list(cif="straussm",
                         par=list(beta=beta,gamma=gmma,radii=r),
                         w=square(250),
                         types=c("A", "B")))

       # Multitype Strauss hardcore with trends for each type:
       beta  <- c(0.27,0.08)
       ri    <- matrix(c(45,45,45,45),2,2)
       rhc  <- matrix(c(9.1,5.0,5.0,2.5),2,2)
       tr3   <- function(x,y){x <- x/250; y <- y/250;
       			   exp((6*x + 5*y - 18*x^2 + 12*x*y - 9*y^2)/6)
                             }
                             # log quadratic trend
       tr4   <- function(x,y){x <- x/250; y <- y/250;
                             exp(-0.6*x+0.5*y)}
                            # log linear trend
       mod10 <- list(cif="straushm",par=list(beta=beta,gamma=gmma,
                     iradii=ri,hradii=rhc),w=c(0,250,0,250),
                     trend=list(tr3,tr4))
       mod10 <- rmhmodel(mod10)

       # Lookup (interaction function h_2 from page 76, Diggle (2003)):
       r <- seq(from=0,to=0.2,length=101)[-1] # Drop 0.
       h <- 20*(r-0.05)
       h[r<0.05] <- 0
       h[r>0.10] <- 1
       mod17 <- list(cif="lookup",par=list(beta=4000,h=h,r=r),w=c(0,1,0,1))
       mod17 <- rmhmodel(mod17)

[Package spatstat version 1.63-3 Index]