Define Point Process Model for Metropolis-Hastings Simulation.
Given a list of parameters, builds a description of a point process model for use in simulating the model by the Metropolis-Hastings algorithm.
## S3 method for class 'list' rmhmodel(model, ...)
model |
A list of parameters. See Details. |
... |
Optional list of additional named parameters. |
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.
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.
Adrian Baddeley Adrian.Baddeley@curtin.edu.au
and Rolf Turner r.turner@auckland.ac.nz
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.
# 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)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.