rmhmodel.default

Build Point Process Model for Metropolis-Hastings Simulation.

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)

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]

The argument par supplies parameter values appropriate to the conditional intensity function being invoked. These 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]

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.

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.

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

Aliases

• rmhmodel.default

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))