spatstat (version 1.31-3)

rmhmodel.default: Build Point Process Model for Metropolis-Hastings Simulation.

Description

Builds a description of a point process model for use in simulating the model by the Metropolis-Hastings algorithm.

Usage

## S3 method for class 'default':
rmhmodel(..., 
         cif=NULL, par=NULL, w=NULL, trend=NULL, types=NULL)

Arguments

...

Ignored.

cif

Character string specifying the choice of model

par

Parameters of the model

w

Spatial window in which to simulate

trend

Specification of the trend in the model

types

A vector of factor levels defining the possible marks, for a multitype process.

Value

• An object of class "rmhmodel", which is essentially a list of parameter values for the model. There is a print method for this class, which prints a sensible description of the model chosen.

Warnings in Respect of ``lookup''

For the lookup cif, the entries of the r component of par must be strictly positive and sorted into ascending order.

Note that if you specify the lookup pairwise interaction function via stepfun() the arguments x and y which are passed to stepfun() are slightly different from r and h: length(y) is equal to 1+length(x); the final entry of y must be equal to 1 --- i.e. this value is explicitly supplied by the user rather than getting tacked on internally.

The step function returned by stepfun() must be right continuous (this is the default behaviour of stepfun()) otherwise an error is given.

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.default is the default method. It builds a description of the point process model from the simple arguments listed.

The argument cif is a character string specifying the choice of interpoint interaction for the point process. The current options are [object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object] It is also possible to specify a hybrid of these interactions. In this case, cif is a character vector containing names from the list above. For example, cif=c('strauss', 'geyer') would specify a hybrid of the Strauss and Geyer models. The argument par supplies parameter values appropriate to the conditional intensity function being invoked. For the interactions listed above, these parameters are: [object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object] For a hybrid model, the argument par should be a list, of the same length as cif, such that par[[i]] is a list of the parameters required for the interaction cif[i]. See the Examples. The optional argument trend determines the spatial trend in the model, if it has one. It should be a function or image (or a list of such, if the model is multitype) to provide the value of the trend at an arbitrary point. [object Object],[object Object] Note that the trend or trends must be non-negative; no checking is done for this. The optional argument w specifies the window in which the pattern is to be generated. If specified, it must be in a form which can be coerced to an object of class owin by as.owin.

The optional argument types specifies the possible types in a multitype point process. If the model being simulated is multitype, and types is not specified, then this vector defaults to 1:ntypes where ntypes is the number of types.

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.

Fiksel, T. (1984) Estimation of parameterized pair potentials of marked and non-marked Gibbsian point processes. Electronische Informationsverabeitung und Kybernetika 20, 270--278.

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

rmh, rmhcontrol, rmhstart, ppm, AreaInter, BadGey, DiggleGatesStibbard, DiggleGratton, Fiksel, Geyer, Hardcore, LennardJones, MultiHard, MultiStrauss, MultiStraussHard, PairPiece, Poisson, Softcore, Strauss, StraussHard, Triplets

Examples

# Strauss process:
   mod01 <- rmhmodel(cif="strauss",par=list(beta=2,gamma=0.2,r=0.7),
                 w=c(0,10,0,10))
   # The above could also be simulated using 'rStrauss'

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

   # Hard core:
   mod05 <- rmhmodel(cif="hardcore",par=list(beta=2,hc=0.3),
              w=square(5))

   # Soft core:
   w    <- square(10)
   mod07 <- rmhmodel(cif="sftcr",
                     par=list(beta=0.8,sigma=0.1,kappa=0.5),
                     w=w)
   
   # Area-interaction process:
   mod42 <- rmhmodel(cif="areaint",par=list(beta=2,eta=1.6,r=0.7),
                 w=c(0,10,0,10))

   # Baddeley-Geyer process:
   mod99 <- rmhmodel(cif="badgey",par=list(beta=0.3,
                     gamma=c(0.2,1.8,2.4),r=c(0.035,0.07,0.14),sat=5),
                     w=unit.square())

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

   # Multitype Hardcore:
   rhc  <- matrix(c(9.1,5.0,5.0,2.5),2,2)
   mod08hard <- rmhmodel(cif="multihard",
                     par=list(beta=beta,hradii=rhc),
                     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 <- rmhmodel(cif="straushm",par=list(beta=beta,gamma=gmma,
                 iradii=ri,hradii=rhc),w=c(0,250,0,250),
                 trend=list(tr3,tr4))

   # Triplets process:
   mod11 <- rmhmodel(cif="triplets",par=list(beta=2,gamma=0.2,r=0.7),
                 w=c(0,10,0,10))

   # 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 <- rmhmodel(cif="lookup",par=list(beta=4000,h=h,r=r),w=c(0,1,0,1))

  # hybrid model
  modhy <- rmhmodel(cif=c('strauss', 'geyer'),
                    par=list(list(beta=100,gamma=0.5,r=0.05),
                             list(beta=1, gamma=0.7,r=0.1, sat=2)),
                    w=square(1))