rStrauss {spatstat.random} | R Documentation |
Perfect Simulation of the Strauss Process
Description
Generate a random pattern of points, a simulated realisation of the Strauss process, using a perfect simulation algorithm.
Usage
rStrauss(beta, gamma = 1, R = 0, W = owin(), expand=TRUE, nsim=1, drop=TRUE)
Arguments
beta |
intensity parameter (a positive number). |
gamma |
interaction parameter (a number between 0 and 1, inclusive). |
R |
interaction radius (a non-negative number). |
W |
window (object of class |
expand |
Logical. If |
nsim |
Number of simulated realisations to be generated. |
drop |
Logical. If |
Details
This function generates a realisation of the
Strauss point process in the window W
using a ‘perfect simulation’ algorithm.
The Strauss process (Strauss, 1975; Kelly and Ripley, 1976)
is a model for spatial inhibition, ranging from
a strong ‘hard core’ inhibition to a completely random pattern
according to the value of gamma
.
The Strauss process with interaction radius and
parameters
and
is the pairwise interaction point process
with probability density
where represent the
points of the pattern,
is the number of points in the
pattern,
is the number of distinct unordered pairs of
points that are closer than
units apart,
and
is the normalising constant.
Intuitively, each point of the pattern
contributes a factor
to the
probability density, and each pair of points
closer than
units apart contributes a factor
to the density.
The interaction parameter must be less than
or equal to
in order that the process be well-defined
(Kelly and Ripley, 1976).
This model describes an “ordered” or “inhibitive” pattern.
If
it reduces to a Poisson process
(complete spatial randomness) with intensity
.
If
it is called a “hard core process”
with hard core radius
, since no pair of points is permitted
to lie closer than
units apart.
The simulation algorithm used to generate the point pattern
is ‘dominated coupling from the past’
as implemented by Berthelsen and Moller (2002, 2003).
This is a ‘perfect simulation’ or ‘exact simulation’
algorithm, so called because the output of the algorithm is guaranteed
to have the correct probability distribution exactly (unlike the
Metropolis-Hastings algorithm used in rmh
, whose output
is only approximately correct).
There is a tiny chance that the algorithm will run out of space before it has terminated. If this occurs, an error message will be generated.
Value
If nsim = 1
, a point pattern (object of class "ppp"
).
If nsim > 1
, a list of point patterns.
Author(s)
Kasper Klitgaard Berthelsen, adapted for spatstat by Adrian Baddeley Adrian.Baddeley@curtin.edu.au
References
Berthelsen, K.K. and Moller, J. (2002) A primer on perfect simulation for spatial point processes. Bulletin of the Brazilian Mathematical Society 33, 351-367.
Berthelsen, K.K. and Moller, J. (2003) Likelihood and non-parametric Bayesian MCMC inference for spatial point processes based on perfect simulation and path sampling. Scandinavian Journal of Statistics 30, 549-564.
Kelly, F.P. and Ripley, B.D. (1976) On Strauss's model for clustering. Biometrika 63, 357–360.
Moller, J. and Waagepetersen, R. (2003). Statistical Inference and Simulation for Spatial Point Processes. Chapman and Hall/CRC.
Strauss, D.J. (1975) A model for clustering. Biometrika 62, 467–475.
See Also
rmh
,
Strauss
,
rHardcore
,
rStraussHard
,
rDiggleGratton
,
rDGS
,
rPenttinen
.
Examples
X <- rStrauss(0.05,0.2,1.5,square(50))