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)
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.
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.
Value
- An object of class
"rmhmodel"
, which is essentially a list of parameter values for the model. There is aprint
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.
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))